Give some examples of everyday vibrating objects.s ojm,l 6p,h+e Which exhibit SHM, at least approximathj+sme, lp6o ,ely?

Is the acceleration of a simple harmonic oscillator ever zero? If so, l.v l ;6mc al5ez-kvir:k fw05p6yr8dwhere?

Explain why the motion of a piston in an automobile engine is approximatednpb.u 50nqwsh2 yi8+ ly simple harms02+5hw ipq8dbuy.n nonic.

Real springs have mass. Will the true period and frequency be ladxs :wuf)zq 8;rger or smaller than given by the equations for a mass oscillating on the end of an idealized massless spr f8:d)swxu;zqing? Explain.

How could you double the maximum speed of a simple harmonicclq g.888 ejfu oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scale, and thh,npgax 1*qdb76s/gdco wu;pq 26sv *en is released. Describe the scale reading as a function od *;pab xd6sv*upo16sgh 2qwcg 7q,/nf time.

If a pendulum clock is accurate at sea lti72w *ck:fpd n8d, ylevel, will it gain or lose time when taken to c8n w dp*l,7ty:kdfi2high altitude? Why?

A tire swing hanging from a branch reachfn ip.nmw;g2z ca ef 0*txo4oy/0a 6t)es nearly to the ground (Fig. 11–48). How could you estimate the*c0apx0f4nw )o.;z t62 /n iymfetoag height of the branch using only a stopwatch?

Why can you make water slosh back and forth in a1:3pbp+cmys+ 5-.sd w qiior5 d*wozi pan only if you shake the pan at a-5 s:5iibdcmw do +ri+ szpy1*q3o .pw certain frequency?

Give several everydav7be,rsk)zmiey)e-4 b+ lk0 fy examples of resonance.

Is a rattle in a car ever a resonanmj h0 2mk g4dtrs2g:j+ce phenomenon? Explain.

Is the frequency of a simple periodic wave equal to ll1eyumtiej *467y zg.mgt74 the frequency of its source? Why or 14 eygy64 g.m*im7l7etlj tzuwhy not?

Explain the difference between the speed of a transverse wave trave4n3)wr :sxg gjling down a cord and the speed of a tiny piece of thejnsx43wgr: )g cord.

Why do the strings used for the lowest-frequency notes on a piano normally h8jb freeebn6*y u:tpdtm mj / zw(: f3np82u//ave wi b/r8te6t b/u:2e8*f:np jm(jn/pz e fdym3uw re wrapped around them?

What kind of waves do you think will travel downmd-ji e+pnto f:.u/nshjz 37 ( a horizontal metal rod if you strike its end (a) verticallh/s (jj fd+nni:et73 oum. -zpy from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase in temperature, but thepghvwxjqfv8zz:x . 3n s:8 j-0 bulkj.:-s:x n0 wx38zv g qj8vhfpz modulus B is nearly independent of temperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decreasuxd;x zn86. p 6,fy8mgss s2jze in amplitude as they travel away from the soy ,s8dfgz;8p jux62nmzx.6ss urce.

Two linear waves have the same amplitude and speed, and otherwik-)ax5hf n,j akh+*63lmxteuse are identical, except one has half the wavelength of the other. Which transmits m*3h 6,x an 5-xmujaktl+f)khe ore energy? By what factor?

When a sinusoidal wave crosses the boundary be8b/m +ivmw e4stween two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocity do change). Explain why. 48eiwmm vs/b+

If a string is vibrating in three segments, auceau 1obg /9)re there any places you could touch it with a knife blade without 1uo)ge9/c bua disturbing the motion?

When a standing wave exists on a string, tz5o1k0 ap3paulv n0 uo+iack/a(7 g6jhe vibrations of incident and reflected waves cancel at thepiook a5 +zuak/c(j370ag lnp1 u6 v0a nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one place to another, how / i-ovr d0ho8gmight we dr8io0g hod-/vetermine whether the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes y2hdwqq)h 8,,fz+twj SHM with amplitude 0.18 m, what is the total distance it travels in, w,thzy j8qwq) 2fd+h one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs frogxpg+54pmfc kbr3(5 n m it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” constant k of thisgf 5rmkgpp bnx +34c5( elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm whe mc9tqoj*i wn- -3xa+n(ch y6en its 68-kg driver gets into the driver’s seat. If the car goes nno +(93j*hyec q i--t6wxmcaover a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish ha1hoh qo4o(;pongs from it. (a) What is the spri4h ;oooqo1p( hng stiffness 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)

  An elastic cord vibrates with a frequencds9rk,g 3e,t;s x3 thoy of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency if e,xhot3,k3t 9d;g rssonly 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig.63w,wkz2- h tbna at8v 11–2 at times t = 0,t = zwak-aw63ntv8t b2h ,$\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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)?

  A small fly of mass 0.25 g is caught is33 kp uja8h(5mv-.xib o,.f w7p xerqn a spider’s web. The web vibrates predominately with a frequency of 4.0 Hz. 7 v3,sa-(pxxjo u38w5 .qihmb.kfpr e
(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

  A mass m at the end of a spring vibrates with a frequriqyx 2ou+ oj,lk;m,;;bj-il ency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is 0.6yjrlox kij qlbim ,-2o+;;;, u0 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per second with an a4* 3ps9k uztso:le:l yj9vzx:mplitude of 0.13 m. Dzk pl vszy:e ux9jlt43 :*9:osetermine
(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)

  At what displacement from equilibrium is the speed of a SHO half the--au yy2o1gnkix tb pw1 3t8z3otzh3* maximum valu a wt1x*pong3 i2t- h yuzob83ty31-zke?$\approx$    A

A mass attached to the end of a spring pzgw:bz8f tk a f((34cis stretched a distance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretchd, ,9 5 wg 7xw;xrcogy;.zozhpw.6efc es a vertical spring 0.315 m. If the spring is stretched an additional 0.130 m and released, how long does it take to reach the (new5 wfr7dz gw, ;wez;ypo.cx, cg6xho9. ) equilibrium position again?    s

  An object with mass rudsu+8 h.qf,3.0 kg is attached 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 h+sf,uud8qr. position, it is moving 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.]

  It takes a force of 80.0 N to compress the spring of a toy popgun 0.20+e imiugk) f:80 m to “load” a 0.180-kg8+e:fg iim)k u ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to onj qtd/p2q 8ik*e end of a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.1j/dk 8 q*iqp2t2 m. If the mass is released from rest with the spring compressed, the mass experiences a maximum acceleration of 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates according to the equation x = 0.45cos6.4t wpqn2 mxrtw11g 0k p1; llnvj6-here x is in meters and t is in secondm ;1x2vwnn1plgr-1t6q j klp0s. 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)

  At what displacement from equilibrium is the energy of a SHO)c :dn5-fg /j6nnqgob mxqp2( half KE and half PE?mqx5d6cf/gb -onpjn)2 qgn: ( ±    A

  If one vibration has 7.0 times thy5 vyd- gfsd;s;t; hm2e energy of a second, but their frequencies and masses are the same, what is the ratio of thfyg 5dtdy;s;v 2-m;s heir amplitudes?   

  A 2.00-kg pumpkin oscillates from5l xkpx da zkwj * 99v*dcr7g(h/(qj-q a vertically hanging light spring once every 0.65 7g-(9 dq px*zjxk havljc kd95(*rq/w s.
(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 $

A block of mass m is supported by tz)kf / (bqwkfr,s;vy)wo identical parallel vertical springs, each with sprifkqk/w,vs z r;y(bf))ng stiffness constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x p esiezmx 3-8s*jj.c8pze)(d = 0.38sin6.5t where x is in meters and t is in secon(i eme )x sj*z 83-dz8spcejp.ds. Determine
(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.

  Figure 11–50 shows two examples of SHM, labeled A and B. For each, what is ojf(t5cnjf z* lrai.4(pku1(
(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)

  At a 755-g mass at reswham( k8nhala ;t. j0i rh86)at on the end of a horizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.96jit; (68wharalaan0h8 . k)m hm/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

A vertical spring with spring stiffness constant 305 N/m vibrates 0p,2lgeb 8hsp-r: lbv with an amplitude v h,82bp0 -sl plr:bgeof 28.0 cm when 0.260 kg 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?

A mass m is connected to two springs, with spring stiffness consqy 9*8oy ca.ettants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes a 0.600-kg block attached z59up-t xgw (f ,4stbdto a fixed horizontal spring whose spring stiffnet-xwtb9ufz( sd5,g4p ss constant 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

  A bungee jumper with mass bm7/n,diynv0q4gy*; ztoz t 2 65.0 kg jumps from a high bridge. After reaching his lowest point,*bi tyn2 4mv0t7gz/;,znyq do 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. Calculate 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

  A pendulum makes 36 v/ 3ds9zn0wq;h i bry-f.b f0hnibrations in exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly one swing pery7y7;c5 m5d el zagk9e second? (That is, one complete vibra5d7zlkm9 5gy eea7;cy tion takes exactly 2.0 s.)    m

  A pendulum has a perix; p+jml( *(hghyyp4u od of 0.80 s on Earth. What is its period on Mars, where the accelerat(gy p4+ j(p yhml*u;xhion of gravity is about 0.37 that on Earth?    s

  What is the period of a simple pendulu8+f4c9gkz2jvorgg3 x 7fl jk+m 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pe+p1l 4wgvl au,ndulum is 0.760 m, the pendulum bob has a mass of 365 grams, and it is released at a4,a lv1l+ug pwn 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

  Your grandfather clock’s pendulum has a length of 0.9930 m. If th8iwuiuixs9 +g4g.l2q e clock loses half a minute per day, how should 2 84qis9li. uwg+igxuyou adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maxw gytuh),xh cfr);ki// ke5+uimum speed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at a frequency of 2.5 Hz. At it is rele ,qx)rb,phc+23d9f inl.ud r eased from rest starting at an an+) ,9urhqf li2 3pcedr,bx n.dgle 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.]

  A fisherman notices that wave+ nm+mn5rm6ieqn ql9r,5c* uh crests pass the bow of his anchored boat every 3.0 s. He measures the distance between two c+ m65hnn l*u qm,9rn+mqce 5rirests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz andu4 s0x1 eewe:m *ktj njavxr .2ws*12n,gxhb; travels with a speed of 343 m/s How far apart are t asvkx*mx0uw4*2w:nnj ;e r t2bex h,g1e .1sjhe wave crests (compressions)?    m

  (a) AM radio signals have freqracw/,dn6 .qfoi w1:fg vu6-auencies between 550 kHz and 1600 kHz (kilohertz) and travel with a 6wuf6av -a dn1 :ogqw ir,/cf.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

  Calculate the speed of longitudinal wh-zvw o xl aamowh sf;--yv:39we12 u+aves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one is twice as dense as the 8sbtf.1wk ,*qzac ytr +cx 6dmlz;h2,other. In which rod will the speed ofy;61w8z h d cbtk*m,cfsr,qxat2.zl+ longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apart. If the ten)s;marb+ksfk :kh 4a 6sion in the cord is 150 N, how long will it take a pulse to bm4k6aak+hs s :f);k rtravel from one support to the other?    s

  A ski gondola is connected to the top of a hill by a steel cable of lej:r rqvicq b:l 79q/g/ngth 620 m and diameter 1.5 cm. As/9r/q i :q cqlv7j:bgr 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

  A sailor strikes the side of hik6 (y4 ,.qw.e vw42 lrix)axs1lgg.y7sgpre ss ship just below the surface of the sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s l 1sgl4e 2xql,)yiws.eg64rrsv7(. k ygpxwa.ater. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at different speeds, and this difference1t atvhp9*oo+f)3jv o helps in locating the earthquake “epicenter” (where the disturbance to ohfot1)3 p+vv at9jo*ok 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.

  An earthquake-produced surfacr5hw ex.i.t w qm0,b:re wave can be approximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed i0.ermhwq :w,t. xrb5so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the inteylmd:hdawm :3 m7m+ n-nsities, and (b) the amplitudes, of an earthquake P wave passin3 a+ mmn-ddhlm :mw7y:g through the Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an eabv q4md4y0oj xvo4o 9.rthquake wave passing through the Earth is measured to be 40vy.bjxv 4o94 o qmod$ 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$

  Two earthquake waves of the same frequency tra4n y5qneze0r6wa ay 84vel through the same portion of the Earth, but one is carrying twice 8znyrn e6aw4 a405yqe the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same freqb gubh0ia32qt(2xu3v uency, but one tran(vbb2 uix 03g2 qhtua3sports three times the power of the other. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observjamhtwfc- y9h.d 88m zj:r-c6 ed to move up and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change? t dyhcahc8w6 m9 j-j z:m8-rf.  

The two pulses shown in Fig. 11–52 are moving ty t(yw1 v esd6sby.*o-oward each other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight. Whedy b(*vt6.wyso1- syat has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its funda os;vjkht21a1 y;yke/mental frequency, what are the frequencies of the first fou; yeh2sak;1 yvtk/ oj1r harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 H(s5zw +ha1cpj8lomv+ w71y y* )sm akuz when unfingered. At what frequency will it vibrate if it is fingered one-third of the way down from the end? (That +w1la+wy*)oza71psu m (v5 8 hcsyjm kis, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a freque1hptm2b3cm 0 yncy of 280 Hz. Name at least three other frequencies at which it will res03pctb yhm21monate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the frequency of stanjtt7+ 4s.+6fh mlxxgzk*/evj ding waves is 475 Hz, how far apart are two adjacent nodetl7j zj4 tke+sx m /xh+v.f*6gs?   m

  If two successive overtones of a vibrating string are 280 Hz amnqk g mgho;3c( 642 o05a-qks aelm*hnd 350 Hz, what is the freque h6k3 e2an5; smgagmqoo4mk*-0lhcq(ncy of the fundamental?    Hz

  A guitar string is 90 cm long anop2ghvp*+me3qmpgw 4 0x r/.,m c0g tv m9cvi+d has a mass of 3.6 g. The distance from the bridge to the support post is L = 62cm and g+3vm4pm/t+0qc gpmvc x0e ,orv gmp29*hiw .the string is under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposlad q*f6ans);ed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed q ana*6f)ld; sto correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hz, but it is wm-orq6 dxu3b.1 -jt xa8i/rzja l9r)measured to vibrate at 205 Hz. By what percent should the tension in t9d r16 )3w -xqlzatrmx/uao-j irb.8jhe string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attaurb4 ji /0j(n)lksn*wbd)uq b9ypd;2ched to a small-amplitude mechanical 60-Hz vibrator. The string’s mass per unit lenpdy 0/ ulbnbswk 2j b;qi*) u(9d4r)jngth 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

  In Problem 59, the length of the string may be adjuimxkij*f 8lb 9,/4 pvdsted by moving the pulley. If the hanging mass m is fixed at k pmi/ ,f4xvlb* jd8i90.080 kg, how many different standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at just the 7j/ ;d(fbnn;cbcdu o*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 t7d( b ;n; nc*f/dojcubub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s stri4yuvnoz : v3h:kes a boundary within the Earth between two kindv y3hvoz:n:u4s of material. If it approaches the boundary 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

  Water waves approach an underwater “shelf” where the velocity changesr tid/ec;+u+g from 2.8 m/s to 2.1 m/s If the incidenc+r/;dg+ ueit t wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is travelp;m:e k9bhcl 8ing in warm air when it hits a layer of cold, dense air. If the s embch:k;8l 9pound wave hits the 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} $

  A longitudinal earthquake wave strikes a boundary be)-sft7 n hyu8ytween two types of rock at a 8s)y tyhun7 -f38 $^{\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} $

  A satellite dish is about 0.5 m in diameter. According to the usej anx9n5t0c+l h:d/fu r’s manual, the dish has to be pointed in the dire/u : njcfn0 dlath5+9xction 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

  A tsunami of wavelength 250 km and velocity 750 km/h travellutwr0* m*i1bt,p*zss across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much timez tb1*sw 0ur*m* l,tip do 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

  An energy-absorbing car bumper has a spring stiffness constant of 550*.v*6hkh; gpb; 8)k fsarvuug kN/m Find the maximum compression of the bumper if thuskg k*f) r8g;p;huh6vva * b.e car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window z +)g8c,lgep2d hfvw2h-: u6a7liya y to a fire net 18 m below, which stretches the net 1.1 m. Assume that the net behaves like a sif)zy+awgluph,2e7 c ligy8v ad:6-2hmple 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

  A mass m is gently placed on the en p g2t:cmvg9cmc0.f7 ed of a freely hanging spring. The mass then falls 33 cm before it stops and begins7m cp:evct 9g2f0c.mg to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge s-y arz3y9i k5cpring at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffness constancyz953iya -rkt 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

  When you walk with a cup of coffee (diably 5::ri)msometer 8 cm) at just the right pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the speed of waves in tr) ms5oyi:l:b he coffee.    cm/s

  The ripples in a certain groove 10.8 cm frohw4(u,3 xtah am the center of a 33-rpm phonograph record hav huah,wx3(t4a e a wavelength of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates accw;oxp q)yrf (swta ,h4 wrj(78ording to the equation x=0.650cos7.40t where x is in meters and t in srwa)wr( hjxwf8tqsy7(;4 ,o peconds. Determine
(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

  A simple pendulum oscillates withn2 p6b8e4ne ob frequency f. What is its frequency if it accelerates at 0.50g (4p 6eon2b en8ba) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lak pn 69d.l*1m lii4pfmo-q, lrze. When a 75-kg man stands on the raft, it sinks 4.0 cm dee-, 4p1ldi. l*if oqzmm pl6n9rper 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

  Two strings on a musi r (jw3td4m0jhcal instrument are tuned to play at 392 Hz (G) and 440 Hz (A). rdm(jj43 ht0 w
(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?   

Consider a sine wave travelicfqstf, +(yqt / dl-n(p qh55(i glun-exek -9ng down the stretched two-part 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 th p qut hyns5fetld+q( e--(n (lxcgkfi/ -,q95e wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, a upvz)w)op65 fnd the tip of each prong moves 1.8 mz )wv o5)pfu6pm to either side of center. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with s 3qu6n2h cz:qrimple harmonic motion of frequency 1.5 cycles per second. Whanq6cu2z rhq:3t 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 oscillation?

A string can have a “frovbz:. geg3 z;ee” end if that end is attached to a ring that can slide without frictiezg: z.;gbov 3on 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.

  A “seconds” pendulum has a period of exactl6f9d rkoq hm1cefc-- *y 2.000 s — each one-way swing takes k cfd-em -*fqh1ocr961.000 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

A mass hanging from a spring cap2q lxw rxhjk 9)/qe77n oscillate in the vertical direction or can swing as a pendulum of small amplitude, but not both at the same time 9xjq2hl p)w7q k7/erx. Which one is longer, the period of the vertical 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.]

  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

  A 10.0-m-long wire of mass 123 g is stretched under /yh dz ;1e(xt d8g4duda tension of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is g1/ gdh dtuy84d;x zde(enerated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a cei:lfz2,g rq wp04ziy;pling by a spring with spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscilla;qr2 y w ,ppgzl:zf04itions that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the june(eqp .e.3a*7xsr ukf,pw z5gkyard. The steel crane cable 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 Table 9–1.x 7r z.e*5e3kuw( pgqf,apse.]    s

  A block of jello rests on vbz e6vv 4q5mml gb 11ij(3q7wa 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 spbm3 l7q qmeg14 v v1(zjb5iw6vrings 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 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz