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习题练习:Vibrations and Waves



 作者: 王信东Wood发布日期: 2024-12-27 14:41   总分: 111分  得分: _____________

答题人: 匿名未登录  开始时间: 12月27日 14:41  切换到: 整卷模式

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1#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
Give some examples of everyday vibrating objects. Which exhibit SHM, at le6n8iiw9ec gtbjz/w 36 ast approximately? ni69e j6t8cw3bzg/w i
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2#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
Is the acceleration of a simple rfj otpz d,h -6kr(;h+harmonic oscillator ever zero? If so, where?
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3#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
Explain why the motion of a piston in an automobile engine is appro:9vlcie:. 6,d m.t u ynic r4a;p6aupoximately simple harmoico dmalery,ct.v. ni :p96p:6 au;4unic.
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4#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
Real springs have mass. Wilu7.n6is e j is:4 +nmivl;(lhal the true period and frequency be larger or smaller than given by the equations for a mass oscillating on the endi4l;ml+:a vj(h e.ni7is u6ns of an idealized massless spring? Explain.
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5#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
How could you double the maximum speed of a simple harmonic oscillasafggmq 4(.o 8l .-mqttor (SHO)?
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6#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
A 5.0-kg trout is attached to the hoo g0 vf2p8qy3nuk of a vertical spring scale, and then is released. De nypu8qg3v02f scribe the scale reading as a function of time.
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7#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
If a pendulum clock is accurate at sea level, +9g8-mqp. eqjrzav)u ydwy 79 will it gain or lose time when taken to v8qy) zu9jpmye rw. dgq- a79+high altitude? Why?
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8#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
A tire swing hanging from a branch reaches nearly a,hevf /rzr4 4loek6,to the ground (Fig. 11–48). How could you 4,h4f,vreo kze6l/ arestimate the height of the branch using only a stopwatch?
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9#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
Why can you make water slosh back and forth in a pan only if you shake the panmc l8tass-u4( atlass 4-c8(tm u a certain frequency?
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10#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
Give several everyday examples of resouu-*5ij p,j sgnance.
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11#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
Is a rattle in a car ever a resonance phenome*zz )qv6qo.a onon? Explain.
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12#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
Is the frequency of a simple periodic wave equal to the frequency of ivwf z*v .latg(e: q,*kts source? Why oraq(, l:vzek* .gtfwv * why not?
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13#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
Explain the difference between the speed of a transverse wave tnl nx1 52n 3c8wfsxr)a08zsscraveling down a cord and the s nss)c3nclxsxn1r z08a52 fw 8peed of a tiny piece of the cord.
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14#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
Why do the strings used for the lowest-frequency notes on a piano norpwe92 )b gy;ekmally have wire wrapped aroun)py 9bw;2g eked them?
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15#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
What kind of waves do you -gmxi8i c6*mmthink will travel down a horizontal metal rod if you strike its end (a) vertical i -*mmgm8ixc6ly from above and (b) horizontally parallel to its length?
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16#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
Since the density of air decreases with an increase in temperaturefg : 1v2w9wnxtsbgp6 +, but the bulk modulus B is nearly independent of temperature, how would you expect the speed ogwtg+b wpsx n619f:v 2f sound waves in air to vary with temperature?
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17#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
Give two reasons whyzvq t+9 su8guoou:w:1 circular water waves decrease in amplitude as they travel away u+g uvt: o9w:uo 1zsq8from the source.
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18#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
Two linear waves have the saufnv5d 30 9iw-wg tp1nme amplitude and speed, and otherwise are identical, except one has half0fu nw593-gtnpvdw1i the wavelength of the other. Which transmits more energy? By what factor?
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19#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
When a sinusoidal wave crosses the boundary8si(5fa jzl8q )hi r9ol*.k yp between two sections of cord as in Fig. 11–33, the frequency does not change (although the waveleng iy*z89l(aksr 5il).o8p jfhq th and velocity do change). Explain why.
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20#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
If a string is vibrating in three segments, are there any plftlodmtg) t2h 9p2;6c aces you could touch it with a knife blade without2mgo h2 tf)tcp d;6lt9 disturbing the motion?
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21#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
When a standing wave exists on a string, the vibrations of incil8d +9xo+a6:it z(cil/mnkppl): icident and reflected waves cancel at the nodes. Does this mean that energy was destroyez(m)til+ a c:ipc9li knd+pl8 : xi/o6d? Explain.
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22#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
If we knew that energy was being transmittedj4d etfvfim (hog e75xx6:(- u from one place to another, how might we determine whether the energy was being carrxxighv(:j(f f uo5met64-d 7e ied by particles (material bodies) or by waves?
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23#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  If a particle undergoes SHM with a2b kghjrnye:+ jt+5 /tmplitude 0.18 m, what is the total distance it travels in one perie h r52k+ /gnt+y:jtbjod?    m

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24#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  An elastic cord is 65 cm long when a weight of 75 N hangs from it but is 85 bm 4w.n-nb2las*if0icm long when a weight of 180 N hangs from it. What is the n sb4 ab-* ifln2wmi.0“spring” constant k of this elastic cord?    N/m

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25#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  The springs of a 1500-kg car compress 5.0 mm when its 68-kg driver gets ; yvb4*xwjpbm xzp;,bu jv7-(into the drive- ;uz(my7xjvx vpbb;wb*j4 ,pr’s seat. If the car goes over a bump, what will be the frequency of vibrations?$\approx$    Hz

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26#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A fisherman’s scale stretches 3.6 cm when a 2.7-kg f v ;d1c.alcxec:2 w8pktv;l 2oed4w4kish hangs from it. (a) What is the spring sti8d; 2 :tedvlwx;pv wo2ce.4cla k14kc ffness constant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

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27#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  An elastic cord vibrates with a freqo m6/yk)1mvm(fw oje .uency of 3.0 Hz when a mass of 0.60 kg is hung from it. What is mko)ym 1omje/fw. 6v (its frequency if only 0.38 kg hangs from it?    Hz

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28#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
Construct a Table indicating the position x of the mass inn) s+,o ux:vwssef. 6cg6: ekv Fig. 11–2 at times t = 0,:k+o c:vfsw,ev6e)n 6 sg.xust = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

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29#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A small fly of mass 0.25 g is caught in a spider’ssr qrec)gqmt y *gv q*x,:4d(hp 33(fa web. The web vibrates predominately with a frequeng qf*adr ce t qp4 )yr*hx3:svgm(q(3,cy of 4.0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

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30#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A mass m at the end ofjn;m 5y/z7 qjt a spring vibrates with a frequency of 0.88 Hz. When an additionalj zj5n;7tyq m/ 680-g mass is added to m, the frequency is 0.60 Hz. What is the value of m?    kg

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31#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A 0.60-kg mass at the end of a spring vibrates 3.0 times pts0,9dg:4wky ,g dywxj yg :.i+b(d bz7ew1iger second with an ampl gy,g we0id+b: wt wj(x1g,z794yb s .kddi:gyitude of 0.13 m. Determine
(a) the velocity when it passes the equilibrium point,$\approx$    m/s(round to one decimal place)
(b) the velocity when it is 0.10 m from equilibrium, $\approx$ ±    m/s(round to one decimal place)
(c) the total energy of the system,$\approx$    J(round to one decimal place)
(d) the equation describing the motion of the mass, assuming that x was a maximum at x = (0.13π)cos(  πt)

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32#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  At what displacement from equilibrium is the speed of a SHO half (lfop67uiv 3v the maximum valup6vo(fv 37 iule?$\approx$    A

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33#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
A mass attached to the end of a spring il4yhv.*0 : mmy g)vwios stretched a distance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?
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34#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A mass of 2.62 kg stretches a vertit4q f9a ys6+vg2+z-shiosnfdgwi64 9 cal spring 0.315 m. If the spring is stretched an additional 0.130 m and released, how long does it take to reach the +d ay64s v2znwgif + og9h9s 64iftsq-(new) equilibrium position again?    s

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35#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  An object with mass 3.0 kg is attac96qbb;vpgdhrz 2c rijk u0n8j+9h1h0hed to a spring with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is movipk;j68un 0qghr bhcd19 20z r9hb+ ivjng with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

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36#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  It takes a force of 80.0 N to compress the spring of a toy popgun 0.2004 iylsn4 a((e +or(l:lz3bkhf m to “load” a 0.180-kg ball. With what speed will4 +i3(yns(bz :lakoef lh(4 rl the ball leave the gun?    m/s

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37#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A mass sitting on a horizontal, frich*vil2 . az ic1tib4-rbpg(i3oh ) ox58.ohumtionless surface is attached to one end of a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, the mass experiences a maximum acceleratiov( o)mic3li io*bh4ht81h5 .2g-.ru ibzaxopn of 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

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38#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A 0.60-kg mass vibrates according to the equation x = 0.45cos6.4t whererqynv4,+1i7sgrux * p x is in ipy rg1,xr4 sv7qu+ n*meters and t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

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39#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  At what displacement from equilibri3) bn drbl;3tpum is the energy of a SHO half KE and half PE? ) 3bbr p;3lntd±    A

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40#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  If one vibration has 7.0 times the energy of a secondydtb 8/iyhyk ** zl.1d, but their frequencies and masses are the same, what is the ratio of theil /tdby8k1* z*i. yydhr amplitudes?   

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41#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A 2.00-kg pumpkin oscillates 7o ,bheokp*czn :)flc(/z-23gzb yygfrom a vertically hanging light spring once every 0.65 s. yp72 g(ko bgz*: /n,-hlyezc fo3b) zc
(a) Write down the equation giving the pumpkin’s position y (+ upward) as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. y = (   m)cos($\frac{2\pi t}{0.65s}$)
(b) How long will it take to get to the equilibrium position for the first time?    s
(c) What will be the pumpkin’s maximum speed?    m/s
(d) What will be its maximum acceleration, and where will that first be attained?   $m/s^2 $

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42#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
A block of mass m is supported by two identical parallel vertical springs, eachl)xdjdcgt;uoi,0k q* r9+/i u with spring stiffnes;d0cdqi,)txrj+g /*9uiuk ols constant k (Fig. 11–49). What will be the frequency of vibration?
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43#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A 300-g mass vibrates acr0-dkburhdq7: 1mqw +cording to the equation x = 0.38sin6.5t where x is in meters and t is in seconds. Deter d - mk0:+bhq7qr1urdwmine
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

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44#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Figure 11–50 shows two examples or8;lee9mlu.-x d( xu mf SHM, labeled A and B. For each, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)


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45#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  At a 755-g mass at rest on the end of a horizontal s*qhyk obhj(6 0pring (k = 124 N/m) is struck by a hammer, which 0kj(o6 qhh*by gives the mass an initial speed of 2.96m/s Determine
(a) the period and frequency of the motion,    s    Hz
(b) the amplitude,    m
(c) the maximum acceleration,    $m/s^2$
(d) the position as a function of time, x = (    m)sin(4.08$\pi$t)
(e) the total energy.    J

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46#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
A vertical spring with spring stiffness conf9,l9 25xh sgp.gry jjhqv8m-stant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 gh.xr9-q8pj2mfljy 9h,5sgvkg hangs from it. The mass passes through the equilibrium point (x=0) with positive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?
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47#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
A mass m is connected to two sp5 1b cea w/4cccv)g*gbrings, with spring stiffness constants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

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48#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A 25.0-g bullet strikes a 0.600-kg block attached to a fixed horizontal s/(j f mh.sffn84 *lswcpring whose spring stiffness consfm .fs /wlnf8c(4 h*jstant is $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

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49#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A bungee jumper with mass 65.0 8cj9v x +xnr1dkg jumps from a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. 9xc+x vd8n 1rjCalculate the spring stiffness constant and the unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

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50#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A pendulum makes 36 vibrations in exactly :x, 3w ofn7hnxqah ib:ed ;i9460 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

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51#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  How long must a simple pendulum be if it is to make exactly one swing per sec 40i+,kz ppn n-zm5z45omsm f 3l-mcjvond? (That is,+ m3m iz5m4pnz5-z,vfnco0jpklm 4-s one complete vibration takes exactly 2.0 s.)    m

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52#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A pendulum has a period of 0.809qa evvliwtb 7hn3:ni p,-k 0- s on Earth. What is its period on Mars, where the nla vkwt,in3 v0 b:--he7q9pi acceleration of gravity is about 0.37 that on Earth?    s

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53#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  What is the period of a s+r uy6ko7u l,ebju5ji3gy.;v (wx x(yimple pendulum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

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54#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  The length of a simple pendulum is 0.760 m, the pendulum bob has a mas9vgpjmxzhac8ts;fz2l*k - 51 y* : cqes of 365 grams,85 1ktjvc: yqszl;zcpx g*f-ahe2 9 m* and it is released at an angle of 12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

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55#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Your grandfather clock’s pendulum has a lenlr:c5-s *qgxg:6hi jp gth of 0.9930 m. If the clock loses half a minute per day, how should yoi:x5 cp -jsl*grqg6:h u adjust the length of the pendulum? shortened by    mm.

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56#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
Derive a formula for thf nh2zk0o46kie maximum speed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$
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57#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A clock pendulum oscillates at a frequency x siidu9aledju4+/ o ;j2 vu f9,ky-s6of 2.5 Hz. At it is released from rest starting at an angle 9+ui6ufod2jy;i kd4u-s,9 jlv e xas/of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

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58#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A fisherman notices that wave crests pass the bow of hq:r1 a:j.5xalhk fn3gis anchored boat every 3.0 s. He measures the distance betwgf k.r :lh1aa5 j3qxn:een two crests to be 6.5 m. How fast are the waves traveling?    m/s

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59#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A sound wave in air has a frequency of 262 8: pn :atfmtnwpw/9dm5c31hjHz and travels with a speed of 343 m/s How far w3m9t :p :1fh 5ct8jw/mn apndapart are the wave crests (compressions)?    m

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60#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  (a) AM radio signals have frequencies between 550 kHz ) +rmz* pei 3zq*toj+uand 1600 kHz (kilohertz) and travel with ate*3zozm +rj+u )*iq p speed of $ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

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61#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Calculate the speed of longitudinal wave3g-tpvj5rb)m4b rt1n/tzb : kk w g;d)s in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

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62#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Two solid rods have the same elam7iv,-gb 2zqm stic modulus, but one is twice as dense as the other. In whigvqb mmz-7, 2ich rod will the speed of longitudinal waves be greater, and by what factor?   

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63#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A cord of mass 0.65 kg is stretched between two supports 28 m apart. ocgaqwl g37mc3h u*4ke s 0t1;ma.+aa If the tension in the cord is 150 N, how long will it take a pulse to travel fro4mag7o ka3c10 csathgm+w;ql u a*e3.m one support to the other?    s

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64#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A ski gondola is connected to the top of3vzc1 rf)3un5ev5-vq veb9iybm3roz1 eo 4 r1 a hill by a steel cable of length 620 m and diameterio f-e1n3q c9b5b1v) 5e1vyovzv43e zmr3u rr 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and sends a wave pulse along the cable. It is observed that it took 16 s for the pulse to return.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

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65#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A sailor strikes the side of his ship just below the surface of the sxi lh.+8olls:g8tul* k)l ouh7: jp 0oea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. Ho8tlg s l.ho):ok*ho8uxl0:u i l7p+ljw deep is the ocean at this point?    m

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66#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  P and S waves from an earthquake travel at different speeds, and 2 ml za2 hic0 qbr/*oo8nph1u2this difference helpl8n/za2 r12q hci 02hpomuo *bs in locating the earthquake “epicenter” (where the disturbance took place).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

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67#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  An earthquake-produced surface wave can be approximated by a sinusoidal trans ao h7j4(iwdi5yhj+v0l2fc 1lverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, whi yf1l 7val5 jido0 c+2h(hwij4ch actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

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68#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  What is the ratio of (a) the intensitie qjrc(lv82s*mx( fna8s, and (b) the amplitudes, of an earthquake P wave passing through the Earth and detected at two points 10 km and 20 km from the soufrx2m*(v(8ljas qc8 n rce?(a)    (b)   

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69#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  The intensity of an earthquake st9tg9b)38 cke ge 1kcwave passing through the Earth is measured to be 8 bg3t99tesckgk1 c)e $ 2\times10^{6 }J/m^2$ at a distance of 48 km from the source.
(a) What was its intensity when it passed a point only 1.0 km from the source?(round to one decimal place)$\approx$    $ \times10^{9 }W/m^2$
(b) At what rate did energy pass through an area of $5m^2$ at 1.0 km?    $ \times10^{10 }W$

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70#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Two earthquake waves of the same frequency travel through the same portion or0b wr 2v:* ;win(m0pravqk;u(jooa5f the Earth, w*a0 u2rqiw m obrnk; p5ova(v ;:(j0rbut one is carrying twice the energy. What is the ratio of the amplitudes of the two waves?   

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71#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Two waves traveling along a stretche rn-,p /srzit:d string have the same frequency, but one transports three times the power of the othesrnt:zp-/,i rr. What is the ratio of the amplitudes of the two waves?   

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72#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A bug on the surface of a pond is observed to move up and down a totalnp9cdm f(r8(y cqfoc ;1dqej)(rr r )9kj-uq 6 vertical distance of 6.0 cm, from the lowest to the highest point, as a wave 1r( ;qpujcrdf8qjrye6c9kf 9c-d)rq )m( o (npasses. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

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73#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
The two pulses shown in Fig. 11–52 are moving toward each other. (a) Sketch thr .2a0l zqx kv f-tos0vj3x(b8e shape of the string at the moment they directly overlap. (b) Sketch the shape of the strxf28 vjkabzq(o -sx00 3 .vrtling a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight. What has happened to the energy at this moment?

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74#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  If a violin string vibrates at 440 Hz as its fundamentalxuej-s .lek7a2r36m,iezg 9j frequency, what are the frequencies of the first f jr -kal6e7z imju,2xe9 .es3gour harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

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75#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A violin string vibrates at 294 Hz when unfingered. At wqhr 6x)b8 6iwrgfq zv xe682-fhat frequency will it vibrate if itrxq 6hvg6r)x2f e-qzb6i8f8w is fingered one-third of the way down from the end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

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76#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A particular string resonates in four loops rb5b8 lugs132f lrid x,.uv7 sat a frequency of 280 Hz. Name at least tl b2 1ub3fdl7.r,gv8 sus5ix rhree other frequencies at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

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77#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  The velocity of waves on a )nzetqvwcc6y 0/a l8thgd., 6string is 92m/s If the frequency of standing waves is 475 Hz, how far apart are two adjacent nod0yae, w)vtdntlc68h6 zg. c/qes?   m

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78#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  If two successive overtones of a vibrating string are 280 na1. v aa;ngp/Hz and 350 Hz, what is the frequency of the fundp;aa . n/v1angamental?    Hz

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79#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A guitar string is 90 cm long and has a mass of 3.6 g. The distance from the bv6 d+9to rh(xiridge to the support post is L = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?+6vrh(xo 9 dti    Hz

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80#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A particular guitar string is supposed to vibrate at 20,o3n;qebk /wpzp-), lyhbgp 00 Hz, but it is measured tb,z/pg n3) hpqk,; - bp0lyeowo vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

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81#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A particular guitar string is supposed to vibrate a qf1ncmn9: a9mt 200 Hz, but it is measured to vibrate at 205 19m:fnc9 anmqHz. By what percent should the tension in the string be changed to correct the frequency? decreased by    %

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82#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  One end of a horizontal string is attached to a small-ampliyb5.g7 yk pq8zv 9di4+y9tsva tude mechanical 60-Hz vibrator. The string’s mabaty7z+9g54i yyvsvd89. pkqss per unit length is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg



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83#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  In Problem 59, the length of the string may be adjusted by moving the pulley. If3mkht umsc01g// y 96a*.hjvkf0 wck e the hanging mass m is fixed at 0.080 kgk*/h t1k.s ym9c gkjwu hv ef3/6a00mc, how many different standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

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84#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  When you slosh the water back and forth int0jd jg1ym:z2 a tub at just the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 H2gtmdz0y j1:j z. What is the speed of the water wave?    m/s

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85#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  An earthquake P wave traveling at k.0 km/s strikes a boundary within tl; o w/,u0 chzn4mcyu2he Earth between two kinds of material. If it approaches the boundary uc/0chwz on; ,24ylmu at an incident angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

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86#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Water waves approach an underwater “shelf” where v-mmw01 b akwgullssq.- ,6u2 the velocity changes from 2.8 m/s to 2.1 m/s Ifs .2mwk-b0-m 1wsalqvlu6g , u the incident wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

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87#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A sound wave is traveling in warm air whepgov sq-v-fm7850cfk n it hits a layer of cold, dense air. If the sound wave hits vqgp5c--o0 fs8 vmfk7the cold air interface at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

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88#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A longitudinal earthquak1khc49cz) ihlwu:+ sle wave strikes a boundary between two types of rock at a 38 9l siw1:klh+4)u zh cc$^{\circ} $ angle. As the wave crosses the boundary, the specific gravity of the rock changes from 3.6 to 2.8. Assuming that the elastic modulus is the same for both types of rock, determine the angle of refraction.    $^{\circ} $

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89#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A satellite dish is about 0.5 m in diameter. According to 2bzb 8wwz; king .fi60the user’s manual, the dish has to be pointed in the directiiw0;8f6bzgb zk2 wi n.on of the satellite, but an error of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

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90#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A tsunami of wavelength 250 km 1 vfx* pcx*bo9and velocity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time d*fp c v9ox1*xbo they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

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91#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  An energy-absorbing car bumper has a spring stiffness constantm c*az5t,m d+y of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conserv ,cazym+m*5dt ation of energy.]    m

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92#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A 65-kg person jumps from a window to a fire net 18 m 5b )kns7*qvcrbelow, which stretches the net 1.1 m. Assume that the net 5nsq*kr )7b vcbehaves like a simple spring, and
(a) calculate how much it would stretch if the same person were lying in it.    m
(b) How much would it stretch if the person jumped from 35 m?    m

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93#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A mass m is gently pla-y7gvx vnu8:gced on the end of a freely hanging spring. The mass then falls 33 cm before it stops and begins to rise. What iyu-: x7 ggvn8vs the frequency of the oscillation?    Hz

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94#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A 950-kg car strikes a huge sp-/mams b;4d kcring at a speed of 22 m/s (Fig. 11–54), compressing t/a4 s-kc d;mbmhe spring 5.0 m. (a) What is the spring stiffness constant of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s


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95#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  When you walk with a cup of coffee (diameter 8 cm) at just the ri /vabj :v1xcts / +cb9jvt-,ljght pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spijv/t:cb9v j , cj1st/lv-+ baxll over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

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96#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  The ripples in a certain groove 10.8st, - elc/9*xgf: unhrneya,y4-kte;j cxb6: cm from the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequency of the syxy csn-er ej 4 :*6l h,;, -ttc9ekx/bungaf:ound emitted?    Hz

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97#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t where x is .jmr.+a6wt* 3khzs nl in meters and t in seconds. Detewzt.j 6kra* +l.sh3n mrmine
(a) the amplitude,    m
(b) the frequency,(round to two decimal place)$\approx$    Hz
(c) the total energy,(round to one decimal place)$\approx$    J
(d) the kinetic energy and potential energy when x=0.260 m.(round to one decimal place) PE$\approx$    J KE =    J

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98#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A simple pendulum oscillates with frequency f. What is its fre,(ych+ s6qjscquency if it accelerates at 0.50g (a) upward, scychjq+6, ( s    f
(b) downward?    f

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99#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on the raft,rv zbd e83g2b78toly9 it s8re b7o 8dbvty29zl3g inks 4.0 cm deeper into the water. When he steps off, the raft vibrates for a while.
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

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100#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Two strings on a musical instrument are tuned to play at 392 Hz (G) an8v5qjl mz o0 5nec:n )ql3bj:xd 440 Hz (lcn5 0xjje q5v 8:bzl:qnm) o3A).
(a) What are the frequencies of the first two overtones for each string? G : $f_2$=    Hz $f_3$=    Hz A : $f_2$=    Hz $f_3$=    Hz
(b) If the two strings have the same length and are under the same tension, what is the ratio of their masses ($m_{\mathrm{G}}/m_{\mathrm{A}}$)   
(c) If the strings instead have the same mass per unit length and are under the same tension, what is the ratio of their lengths($L_{\mathrm{G}}/L_{\mathrm{A}}$)   
(d) If their masses and lengths are the same, what must be the ratio of the tensions in the two strings?   

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101#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
Consider a sine wave traveling down the stretched two-part0 j r ((:gbr6mp otza*rjj)sx/ cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (Thesm*r zgbj0r/p)( (roxjj :t6a frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

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102#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A tuning fork vibrates at a frequency of 264 Hz, and the tip of each e-qvg.kfz:g ncj ( 8igqok5)fe 5dm9 +prong moves 1.8 mm to either c8nk( + 5o.m9q5kqg )vegfz:d fjige-side of center. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

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103#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
A diving board oscillates with simple harmonic motion of frequency 1.5 cy f:;qo* k(xqftcles per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillati ;f otq*(xf:kqon?
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104#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
A string can have a “free” end if that end is attachedo). ii h,di8; xecos)r to a ring that can slide without frxc,8r i i o)e)s;doih.iction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with one end fixed and the other free.

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105#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A “seconds” pendulum:u1oyn3ul) qp has a period of exactly 2.000 s — each one-way swing takes 1.00yqu pun:o )1l30 s.
(a) What is the length of a seconds pendulum in Austin, Texas, where $g=9.793\mathrm{m/s}^{2}$    m
(b) If the pendulum is moved to Paris, where $g=9.809\mathrm{m/s}^{2}$ by how many millimeters must we lengthen the pendulum?    mm
(c) What would be the length of a seconds pendulum on the Moon, where $g=1.62\mathrm{m/s}^{2}$    m

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106#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
A mass hanging from a spring can oscillate in tpc 2md3ctaj,clh 0:cme6s0 4iot9,nbhe vertical direction or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period of the velt,cte9n s,c 3pboa:m 4jh2ccidm 006rtical oscillations or the period of the horizontal swings, and by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]
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107#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A block with mass $M=5.0\mathrm{kg}$ rests on a frictionless table and is attached by a horizontal spring $\begin{pmatrix}k=130\mathrm{N/m}\end{pmatrix}$ to a wall. A second block, of mass $m=1.25\mathrm{kg}$ rests on top of M. The coefficient of static friction between the two blocks is 0.30. What is the maximum possible amplitude of oscillation such that m will not slip off M?    m

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108#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A 10.0-m-long wire of mass 123 g is stretched under a tension of 255 N. gp ;.yk:/art*6c hbqt A pulse ip :t cbth kqar/y6*g.;s generated at one end, and 20.0 ms later a second pulse is generated at the opposite end. Where will the two pulses first meet?    m

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109#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
A block of mass M isqha( 1 sc zya-o7tk5s*k/vy(e suspended from a ceiling by a spring with spring stiffness constant k. A penny of msy1as-k( qo( v h *z57aetc/ykass m is placed on top of the block. What is the maximum amplitude of oscillations that will allow the penny to just stay on top of the block? (Assume $m \ll M$)
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110#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A crane has hoisted a 1200-kg car at the junkyard. The steel crane cablonhncv17ouy :.on 4 ikdj860je is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. What is the period of the bouncing? [Hint: Refer to Tac7:j k onvui0yd8oohjn14.6nble 9–1.]    s

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111#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A block of jello rests on,q+ffp1av kdfbrg. ,m ss 7*7s a plate as shown in Fig. 11–58 (which also gives the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this vibration, given that the shear modulus (Section 9–5) of jello is 5*pfkas ,fsf77s,rvg1bdq m+. 20 $N/m^2$ and its density is 1300 $kg/m^3$    Hz



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