Give some examples of everyday vibrating objects. Whichr/y/ i:n(c2ip5wqrj 0 vztopw(x6 . qh exhibit SHM, at least apprro0zt/ynwi 5i:q .v( jxw c6 (r2hqp/poximately?

Is the acceleration of av8 ,43wj5l6( bc8tzrhbjw (8i4zqcrjd1 pyvj simple harmonic oscillator ever zero? If so, where?

Explain why the motion of a piston in an automobile engine is approxim(im7szppjjlnqv46 j/q 1s*,vr,zcr .ately simple ,q(.j/7*srr qzp sj 6 4v,vpn1l mjzicharmonic.

Real springs have mass. Will the true period and frequency be larger or smaller pp0 :oq:lx t*sthan given by the equations for a mass oscillating on the end of an idealized qp:sx: lpt0*omassless spring? Explain.

How could you double the maximum speed of a simple harmonic oscillah mwy/to)/xb4tor (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scale, and then /)i 6 0 y8n5wwrpsygeois released. Describe the scale reading as a funcwo/ ns56ry )wy8pi 0egtion of time.

If a pendulum clock is accurate at sea level, will itcl/ o/zhm7 r-g gain or lose time when taken to high altitude? Wg // 7zm-cohrlhy?

A tire swing hanging fx))*o mz;c+ j* mwhs jq,izt2from a branch reaches nearly to the ground (Fig. 11–48). How could you e+ *)x; ,z2wmhsiz* fcoj qj)tmstimate the height of the branch using only a stopwatch?

Why can you make water slosh back and forth in a flu//.fqf7 )gvk .nhp pan only if you shake the pan at a certa .hnpklv//)f uqff7.gin frequency?

Give several everyday exampxnoueu3:)zjc *zm( kr8o x59i dy: 1lwles of resonance.

Is a rattle in a car ever a resonance phenomenon? Expw78j,1 klyrc) 9o4 jjmyj gh;elain.

Is the frequency of a simple periodic wave equal to the xzfsb qg;29sup d,; 3hfrequency of its source? Whgs;,x d;f 3puzh9b2 qsy or why not?

Explain the difference between the speed of a tran( jgjzggo)4u/ sverse wave traveling down a cord and the speed of a tiny pieceoz/g) g (gjuj4 of the cord.

Why do the strings used for the lowehqko(9 xlhs8)(u2 o p it-k(vhst-frequency notes on a piano normally have wire wrapped around them?k qv l ht i9xuo)(po(8(2shk-h

What kind of waves do you think fhnw.jx*qbr(t/ 6wim .a1g j+will travel down a horizontal metal rod if you strike its end (a) vertically from above a16+ /.m njhj(tairbf.qx*g ww nd (b) horizontally parallel to its length?

Since the density of air decreases with an increa ts 4f 7ug25ezpzn fdo3*28jpgrv5r9yse in temperature, but the bulk modulus B is nearly independent of temperatuo*et82 spf5 j7uv2 9rfrpdg5z4gy nz 3re, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water wav,h4cpwia6l 1n i:2capa2kh 1kes decrease in amplitude as they travel away from thpikc aa,1: 4lw1an2p 2h6hcike source.

Two linear waves have the same amplitude and speed, and otherwise ;wxpjsuavn s6r 92 +a,are identical, except ;,6waj 2srxpv + an9usone has half the wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the (a+k *rm0u*my6q-mloj z(teu boundary between two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocitj u aumql (ket0(*6 mr+-ozm*yy do change). Explain why.

If a string is vibrating in three segmeno6d4 (j j7+*)zi(ejkqfv fofx ts, are there any places you could touch it with a knife blade without distj foj vi(*f7jdze(x) k+6 qfo4urbing the motion?

When a standing wave exists on a string, the vibrations of incident and refltgb hv d)t8hd1;w0o(t )rsp,uected waves cancev t 1hbtddtw8)s;r( poh),gu0 l at the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energycdd*qv/ d+g;yh vz o-j8ie k2, was being transmitted from one place to another, how might we determine whether the energy was being carrvdi - ck;y/,2eddqj*gohz 8+ vied by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the total distanc*2co i4moy,eee it travels in one perio,o4ieyo2 me* cd?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs .0: 0c4jmf zyb6, zyfpczr 6qgfrom it but is 85 cm long when a weight of frjmcf 4z:q 060gpb.z6yyz, c180 N hangs from it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when iti61axe d8:sg ls 68-kg driver gets into the driver’s seat. If the cixl6ds 1g:e8 aar goes over 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 hangs f8e l p59)ufn--ru ijekrom it. (a) What is the spring stif-pn9jli 5ke8)e -r uuffness 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 frequency of 3k z2,lo8)wveyz+-zi4 vsi1v o.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency if only 0.38 kg hangs from+eyi) kwiv 1, 8lv4-so2zzzov it?    Hz

Construct a Table indicating the position -2hst8ceie4jwka c a99* zi0tx of the mass in Fig. 11–2 at times t = 0,24i s 0k9ja8-tz e ai9cetchw*t = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 in a spider’s web. The web 83u n46l 8n9zqypnlrivibrates predominately with a frequency ofp84n qlri6n9y 38lnz u 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

  A mass m at the end of a spring vibrates with a frequency of 0.88 Hz. When an dpj9 )sd9ls*)l+ synnov+4 n eadditional 680-g mass is added to m, the frequencn) )depl s49*d nn9 +l+osyjvsy is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per se h/t;yyrb:q w/cond with an amplitude o :/btry q;why/f 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)

  At what displacement from equilibrium is the speed of a SHO half the maximum z .cpil-lk :1ivalue?pzi:ckl i. 1-l$\approx$    A

A mass attached to the end of a spring is stretc*3jej7xv 8vfowzw 3di802s 3y*aw ve fhed 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 stretches a vertical spring 0.315 m. If the spring is str6ggw-lcst7d + j2nbkb h5f1rxl, g2bwky5 2m9etched an additional 0.130 m and released, how long does it take to reach the (new) equillf9r7jh6t 2mbw bw 1 d5x,g2n -2kys +clb5kggibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with spry b4ey*r+x xqv,7m: +xxkod( wing stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from e(xyx*r4my+bq kw 7v,x: +oxdits equilibrium 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 popg7okmun*(e0y aun 0.200 m to “load” a 0.180-kg ball. With what speed will the ball leaone(mu0 yk*7 ave the gun?    m/s

  A mass sitting on a horizontal, fr ut2u+fih-2x9w3 +bk czhy5 olictionless 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 acceleration of 15hil 5+2ou w yutzc-9xh32kb f+ $m/s^2$ 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 = 0.45co p 9dttao/-k/f1xk c9gs6.4t where x is in meters and 1t c9/x k-ga9dfk/otpt 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)

  At what displacement :uh8 ye .otte6from equilibrium is the energy of a SHO half KE and half PE? tut y :e6e8oh.±    A

  If one vibration has 7.0 times the energy of a second, but 8ki7y5 ka:fjej4rz0 54mejm otheir frequencies and masses are the same, what if4k7 re0mj m:yoj 8k5e4azj5is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hangi *50pfv*hh 0fbmt;smvng light spring once every 0.65 t0m**5hfpb 0shm;fv vs.
(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 two identmm .okn8: ih5lical parallel vertical springs, each with spring stiffness constant k (Fig. 11–49). W5ol.h m8im:knhat will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.39 -kw5x ey8z(x3bn 7dqfhlso- 8sin6.5t where x is in meters and t is in seconds. Determine l9w-(- 8yqnzx se 37d xfob5kh
(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 examp+t ut jcb0g/mv+gr)w fc rgq1 m3a:tz+57kzl2les of 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)

  At a 755-g mass at rest on7 u1tepgt.gv+ ad*q5i the end of a horizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.96m/s g de a751*i+ ttg.qpvuDetermine
(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 Nb1s.0vnpgrd.( k hikh f7)4zxm c8- xz/m vibrates with an amplitude .g f4nzxik1kbzphrs . - c(8v0hd)x7 mof 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 constants w28o np+(hzjw0qx: v)le e)ji$k_1$ 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 to a fixed horizontal spri 7-o bmmtyl)0vng whose spring stif - 07blmm)vtoyfness 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 65.0 kg jumps from a high bridge. After reachi qo1wrp1yp/j y3o2 gqb)dw8y 5;ydbdtp9*3n zng 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. Calculate the spring stiffness constant and the unstretched length of the bu z;8dog1py)ww2yn3tbq 5ypq/ d* 93dpjyor1bngee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrations in exactly 5qieyx+yhgwr9 8d vwp*0nt:q ,3p2zb 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum becvj*n q-cfi 36 if it is to make exactly one swing per second? (That is, one complete vibration takes exactly 2.0 vfjc 6q3*-cin s.)    m

  A pendulum has a period of 0.80 s on Eat 8mqs 6macx)vu5lq 62rth. What is its period on Mars, where the acceleration of gravit aq8m6 qm6vx5su)l 2cty is about 0.37 that on Earth?    s

  What is the period of a simple pendulum 81w5a2,a rt opj:cmpm(a,e ; di0 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is wkabv z-et*+ za7;dm v6pmn68 0.760 m, the pendulum bob has a mass of 365 grams, and ;+ m6vpz -86atv dmk7eanzw*bit 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

  Your grandfather cloz6+3poj7bx: jq robo. ck’s pendulum has a length of 0.9930 m. If the clock loses half a minute per day, how should you adjust the length of the pendulum? shortened7xobrj+ .zo:3jop6qb by    mm.

Derive a formula for the maximum s/7f2 .anbamid* y;dsipeed $v_{max}$ 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 released from r ggg-vi gc+ iq0z5l./aktt1( dest start/-( i tg.+tgqdzcgv 01agkl5iing at an angle 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 w7egl:6 b3rm9n/on nwbave crests pass the bow of his anchored boat every 3.0 s. He measures the distance rgl/e b:n69bm 7n3ownbetween two crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with a s0jsu qct+:r-0bw d1mk aps:u/peed of 343 m/s How far apart are the wave crestsp/mcdss+k: qaj:u -wrb0u01 t (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 160x2jw8 bd:ta;dqc7 ;vp 0 kHz (kilohertz) and travel cx72avd;j ;btw dq:8pwith a 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 longitudinalz2*liwjnwwnf dw ;,6 7 waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one i/6wzxaaerh / ,s twice as dense as the other. In hwr/6, e x/zaawhich rod will the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretcj 4 xlrqg;2t8j in+8rohed between two supports 28 m apart. If the tension in the cord is 150 N, how long 48rnjji;rqo 2+tg8lx will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to the top of a hill by a steel cable of le93,wgwej4 nc5biq 6*i ws6z - ksnl6zjngth 620 m and diameter 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 cnl66gbzknz93c-sew ,wsji* i 5w4 6jqable. 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 his ship just below the surface of the sea. Hd pgs7g s9mvsxy:3kj:. s9dhjz.bh-,es0s 2we hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. Ho.dbkh-j:sg 9syv2 7:sghmew. j9,3xsp ds s0z w deep is the ocean at this point?    m

  P and S waves from an earthquake travel at different speeds, and k)5s)wgv)+gkjn:if *4fl3arvtf mqvn.5g d7 this difference helps)3vgg 4 t):f)mk+i fad*rv75qwkfjsln n gv .5 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.

  An earthquake-produced surface wave(rt;n r ost;;p+zoq- s 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 so that objects begin to leave contact with the gronz (-r q;roposts ;;+tund? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, awcoyi2(l7urq g(y;isp8f .dve(;2 vcnd (b) the amplitudes, of an earthquakeqvi8o;7(gc;cwr2y . ((v2p l esdiuyf P wave passing through the Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquaksl1h-y402o gdgm5)nrq hgl1ee wave passing through the Earth is measured to be q y)gr s1 gllh1go -nhedm4052$ 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 travel through the same portion ob f;6r c6h kq:yrtroho z1:)m6f the Earth, but one is carrying twice the energy. What is the ratio of the akr:orc qoyh)t 6fm 6z6r 1:bh;mplitudes of the two waves?   

  Two waves traveling along a stretched string have the2pq+b r:e xyq7d3yy-w 3d)if p same frequency, but one transports three times the power odqi:yq 3d2+fy r3 -b) w7xeppyf the other. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is +*kfs+2l.lmupb 9 zsm observed 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 decre9 u*+z2k slfs. lmpb+mase to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 2d,ysz,p8z /tt5lhm jc*thgs6f6lpa 4t ur4 , 11–52 are moving toward each other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a fe/ l*2j4zfr hu6lptgt5dt6 ha ,sm,4ty,8psc z w 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?

  If a violin string vibrates at 440 Hz as its fun0 -5ras ;l9rl 6.mcevwo4za zcdamental frequency, what are the frequenci0lrew zl9;mz.6rv4sc oa -ca5es of the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. -h++ lfw e 6armoqf5b5At what frequency will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirdfrea fw5bqm+o +-hl65s of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequency of 2i*6lxgpc;.tq;yq iz3 80 Hz. Name at least three other frequencies at wh;qizt3 6;cp.yiql* xgich it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the frequency of standing waves i y34n:fqmv( *lt+up kgv -s0uds 475 Hz, how f g :s*dyvu(fp-v4+n m03lqu tkar apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 350 Hz, whaqz j lfmu-3(j3t is the frequency of the fundamental? ul fjm-3j3(qz   Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distance fromqjv*-b(t6hut the bridge to the support post is L = 62cm and the string is under a tension of 520 N. What are the frequencies of the fujbt-uhv t6(* qndamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 H-+y4d)onsalw lo01(jbdie ) pxzc;b 9z, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be bdw9 jsoyi( +xzb1a)olpl)dnc4;-e0changed to 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 -3kxlh*:xft n measured to vibrate at 205 Hz. By what percent should the tension :3* hxk lnft-xin the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-amplitude mechanical 60-Hz37nr,o l ga*xy vibrator.rxona 7*yl3, g The string’s mass 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

  In Problem 59, the length of the string may bt7tr0,;1fo) b n xibqve adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying L between 10 c tvx r 70ib;nfb,ot)q1m and 1.5 m?   

  When you slosh the water back and forth in a t1cvlmgq x56y6ub 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 standing6y mgclx5q61v wave in a 65-cm-wide tub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundary within the Egevb)nnx, *. tv 5w,jqarth between two kinds of material. If it appb q nvw5*) te,njgv.,xroaches 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” wv;o5v/ hgvy m- zguf5+here the velocity changes from 2.8 m/s to 2.1 m/s If the incident wave crests my vzfmogh5 u/ 5+-v;gvake a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air when it hits a layer of cold, dense ai5+*i8ql0js d unmu*yfr. If the sound wave hits th qdfu*ys nij+m08*ul 5e 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 between two types of rock at av)y0ztie.u/t br( z,++;b xgd9rhyrb 3td+,/ytir0.x ;gu9brr z) zhb+yebv(8 $^{\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 user’4ok.yxln1o5ie rl 31rs manual, the dish has to be pointed in the direction of the satellite, but an error of a5rr lk 3xo4.l1nie1o ybout 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 travels across the Pacifn dlp 9 ;6f7sh71zedswg/ 4nfkx. q fp*qd87jkic Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, peoplfnnzx sl8 sq; 9d4.pqhkdg77d/6ek7p w*fj1fe 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 kN/m Fiejy2ftf 2r +6knd the maximum compression of the bumper if the car, with mass 1500 kg, coe2 yftf j62k+rllides 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 to a fireb ax0(l1pfhe1, hqsq; net 18 m below, which stretches the net 1.1 m. Assume that the net behaves likes;xa ,qfhh q(1bel 01p 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

  A mass m is gently plaumbv n3yy( a+k(7qo7).ome xwced on the end of a freely hanging spring. The mass then falls 33 cm before it kmbeaoyn)(woy3 q(m7.7 xvu + stops and begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge s9o1kybs+n42p ljq. u;kulk ) zpring at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffness co2 qk4ul; konz1)+u.j bsk9yplnstant 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 (diameter 8 cm) at just the riyt5l c-od;ng;-fy +tp ght pace of about 1 step per second, the coffee sloshes more and more until eventual-+oncy d-l;;pfy t5gtly it starts to spill over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the center of a 33t*e , 6e9obx nntz-9rp-rpm phonograph record have a wavelength of 1o*tp9e-nx t6, 9z nbre.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t whe1*o )ik)w8tp bft7 wqfre x is in qtwt)8 *w7 1pkiob ff)meters and t in seconds. 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 oscillad8tet-kd7iib- kfd 9l 8:v+x vtes with frequency f. What is its frequency if it accelerates at 0.50g (b kd l8-di k vttfdei7:+89vx-a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When /9d pky ym+u:la 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the raft vibrates for a whypul :md+9ky /ile.
(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 musical instrument are tuned to play at 392 Hz (G) and 4:yix55o 0t2t0mi xtou40 Hz (A). tm5iotyx 2it 0o:xu 50
(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 traveling down the stretched toau/wa*l-.l j* n1op5aktv i:wo-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section ve k*no1it/pu*v.: aoaj 5lwal-rsus that in the lighter section, and (b) for the ratio of the 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 ytrw k74vxo/;at a frequency of 264 Hz, and the tip of each prong moves 1.8 mm to either side of center. Calculav4kwxo7r ;/ty te
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simple harmonic motion of frequen/a. a (p2rxqarml).e2fgj+u v.le k6yz* su;j cy 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order that a p+lq ve)pk .j ;2xzy.raju/2.*e6usf alg (marebble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that end is attached to a ring3 dv6ami 4nkv3x +t yhp.: zi5a1.klql that can slide without friction on a vertical pola.+lm331ikz6dy5. p4iv lkqtx:anv h e (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 pe,.ckxqt 83 my weav;-iriod of exactly 2.000 s — each one-way swing takes 1.000;8cq.w 3-m,avkx tey i 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 mridl bnjver0;*6s8 -va/m *r( gwo ybw,z50hcan oscillate in the 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 vertical r g r,b-wazn m85shld( *v0ivemj0rwyb6o/* ;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 und f4tz)mbq(j f3mh c,;zer a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at the opposite end. Where wijc,m) fbt4z3(hq zf;m ll the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spri*hm+cjn9* jucng with spring stiffness constant k. A penny ojcn9*+h u* cmjf mass 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 $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel crane cablmvpc m9 y5cr5 u.4*f vovn54ove is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of.4uomc4 cy n v55of5 m*pv9vrv the cable. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 t8jqf5 aavt16dbqw- :(4lnhw:e4j wlwlp;x- (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 tw4 l:8txjwlet nb - 4wpj;-5faw1v(a lq6:qh dhat the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz