Give some examples of everyday vi,sr2vb; :sw1 yv lj9hlbrating objects. Which exhibit SHM, at least aphl21v;:sl,w rjs vy9 bproximately?

Is the acceleration of a simple harmonic oscillator ever zero? If so, where?m t6;j jq-vve.

Explain why the motion of a piston in an aut x8.ddxj rhw cz/rrep7y0nq 949w()kkomobile engine is approximately simpl/ 97cr(xd k9qdw)8k rh.n4w r0yzejpxe harmonic.

Real springs have mas6z2b, ubj g(hd*xgg +is. Will the true period and frequency be larger or smaller than given by the equations for hzjg+xbdbgu2(gi* ,6 a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple harmonio,1ot +afj x s-srkn4;c oscillator (SHO)?

A 5.0-kg trout is attached to t61 (s fh+myfpkhe hook of a vertical spring scale, and then is released. Describe the scale reading as a function of ti ms1fh y+p(k6fme.

If a pendulum clock is accurate at sea level, will it gain or + zkbup 7jhykvh,/l ;)lose time when takehb /kklv,z )pyj7u;+hn to high altitude? Why?

A tire swing hanging from a branch reaches nearly to the ground (Fig. a-k 7cijc qg2op* spkn a1xztk)z24ky 1a a*0511–48). How could you estimate the height of the branch using only a stopwatchq-*1akcp5pz7ioany2k) *gzc s1j k02aak4xt ?

Why can you make water slosh back and forth in ah ;b8j*r. g :2geebsa9mdpw4l eps-l, pan only if you shake the pan at a certj;g-ar*e ,w sgs4e ml bph82lp :9bde.ain frequency?

Give several everyday exaqmn:m;slv 5x7 mples of resonance.

Is a rattle in a car;*g lms v:ylx* ever a resonance phenomenon? Explain.

Is the frequency of a simple periodic wave equal aj/3lqkv m/pjyf),)g to the frequency of its source? Why or why not?g/v) amq),l j/ykfp j3

Explain the differen 4.:om( e q ojj7vx3+tbkge1c2jz1kfbce between the speed of a transverse wave traveling down a cord and the speed of a tiny piece ofmzbg (.7ke1toef 3 kqjox 24v1 +bjj:c the cord.

Why do the strings used for the lowest-frequency notes on ae3 nb067uxb mt piano normally have wire wrapped tmbx76b n0ue3around them?

What kind of waves do you think will travel down a horizontal metal roduz):rvm zu :5b1; rrcmkm+ qi6 if you strike its end (a) vertically from above and (b) horizontally pm+imuv:k6 rqzumr5 ):1;c zb rarallel to its length?

Since the density of air decreases with an increase in tempe*j2qpj)iyq g/ ovnq:/mn 1 ) tx8noc1yrature, but the bulk modulus B is nearly independent of temperature: t8)cvn*go /o/jm1nq jxyp) niq1q2y, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in ampliwxu+-m0dpe u4: pun8itude as they travel away from d08nep:pm4 w+uuui -xthe source.

Two linear waves have the same amplitude and speed, and otherwise are idev.,410anatrthn 9wmo ntical, except one has half the wavenn.mt 4tav0h a1wo,r9length of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses thcawd hj-vp5ztpp4 ,o/zd()o4 e boundary between two sections of cord as in Fig. 11–,zvadppjdo -c p 44w()o5h/zt33, the frequency does not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there any places you could toucf9 -lgnedcr*l ia5c+ -h it with a knife blade wi r ncla-ecg9+i*l- fd5thout disturbing the motion?

When a standing wave exists on a strin 5fo )ee)oj8vqa tok9t*via5-hx9 :qmg, the vibrations of incident and reflected waves cancel at the nodes. Does this mea8iojek)9 * qoqaefvt)5o9mva-t : h5x n that energy was destroyed? Explain.

If we knew that energy was being transmitted from one place to 6vqy ; i g zt6zb81:.d3wnbktr7.iswhvy)dd,another, how might we determine whether the energy was being carried by particles (material bodies) . .1 zb6,):rvvkz;8dgwb 3diw7std6q itnyyhor by waves?

  If a particle undergoes SHM with amplitude 0.1vbjfgy: -64lj9r :z cx8 m, what is the total distance it travels4l:y zv j:-cfxj rgb96 in one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it but bothct,au/d/,5v 1obis 85 cm long when a weight of 180 N hangs from it. tvu b,h ,ot5bd1/ a/ocWhat is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 6 7dliqw;3y8f - tgdwv-8-kg driver gets into the driver’s seat. If the car goes over a bump, what will be the frequency of vibrations w7i38qwy-v t; lfgd-d?$\approx$    Hz

  A fisherman’s scale stretches 3.6u,85t6kbl quw cm when a 2.7-kg fish hangs from it. (a) What is tbwlq,5u68 uk the spring 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 withnfgra. +k k/9e6sx rb1 a frequency of 3.0 Hz when a mass of 0.60 kg is hu exr91/fn+6b ksr .agkng from it. What is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass jf5 kox/x)mm7in Fig. 11–2 at times t = 0,t = 75x/)mofk j xm$\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 v oi/ c/13mzubk t/5jlvibrates predominately with a freq/bo/vl 31ci5juk/mt zuency 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

  A mass m at the end of a spring vibrates with a frequency of 0st;0us wuq;2yr w0zt6.88 Hz. When an additional 680-g mass is added to m,6 0t;w2wu;tqs0y suzr the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibratesxo: ckf8p5 k9m 3.0 times per second with an amplitude of 0.13 m. Detekm9 5o fpcx:k8rmine
(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 equi8v rfgk j:7 qr-.k17s/wrbpi elibrium is the speed of a SHO half the maximum valu/-p v7gr 1k:. sjb7q8erwikfre?$\approx$    A

A mass attached to the end of a spring is stretched a distan)1 159mj) xruomvzye gce $x_0$ 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:qa r/ ai;woovcgej.77 0b lp2 vertical spring 0.315 m. If the spring is stretched an additional 0.130arql. :oaco0;7b/eg vw72i j p m and released, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached fmqtj3kcb.mph0ss5dg s,713 to a spring with spring stiffness constant k = 280 N/m ansm5sq3tch1 3,fpsbg .0 dk7 jmd is executing simple harmonic motion. When the object is 0.020 m from its 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 popgu/cy*., -ucu wyi -b bdiw/c5fs076s rze(nlbbn 0.200 m to “load” a 0.180-kg ball. With what speed will the ball leave the gun? c *e,siybs .zwuw5-cbrbb(/df/-ui ny l06c7   m/s

  A mass sitting on a horizontal, frictionless surface is attached to omei3ah/i(5zo h,c gc7nf/h e7h1cj 5bne end of a spring; the other end is fixed to a wall. 3.0 J of work is reqzfh(e7, ccmoah b735jii1hcg5/ e /n huired 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 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 acco3s(l:ybk) c gtrding to the equation x = 0.45cos6.4t where x is in meters and t is )klbt:c ys 3g(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 from equilibrium is the energy of a SHO half K3nhd3 sjp/8rz E and half PE? 3hszrjp/8dn 3 ±    A

  If one vibration has 7.0 times tooc khe g,sbn*e,z/9,he energy of a second, but their frequencies and /on,g kse,ze bo*,hc9 masses are the same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin os*kwqw6g z.z8y/+;p rix e njw7cillates from a vertically hanging light spring once every 0.65rq6kg8wn zw/ +zyji*e;7pwx . 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 two identical parallel vertical euq 8h 5-qg)d)gw.3:szt tefo springs, each with spring stiffness)q8 eed:u. qo h5tg-) ft3wszg constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates accor49*dhb*dpzsb nss : 2rding to the equation x = 0.38sin6.5t where x is in meters rs2*n* 9 bdds4:bhpzs and t is in seconds. 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 ef(irp ma,:8 3qothgmds1f 4, lxamples 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 on the end of a horizontal spring (k = 124 N/m) ixpgn o5o:s13s s struck by a hammer, which gives the mass an initial speed of 2.96m/s Desn x3:15posog termine
(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 rh m:im7h z-9- 5kfkopconstant 305 N/m vibrates with an amplitude of 2 f5ikhzrk:opm 9 hm--78.0 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, b..vv e m9-wnowith 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 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes a 0.600-kg block attached to a fixed horizontal sprj9dn)p m hyql +nyx+1 y.(rou:ing whose sprin(num y1+jonr xy+lphq.) 9 dy:g stiffness 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 withb; ,bkto mg*q/i;ps f:uci0)u mass 65.0 kg jumps from a high bridge. After reaching his lowest point, uk)scqb m;i/ tf:*u; 0pgi,ob 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 vibrations in exactly 60 ox*3h 43-cflong2w m*kap n6a 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 3 txclnw8* k1l /4wcwgswing per second? (Thaxwwntcg cl*w48l k3/1t is, one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on Mzcby3l +g:z yc94kb0 ui0v4vwars, where the acceleration of gravity is about 0.37 that on Earth?+u 9b 4g3v vkyic:y0lzbwzc40    s

  What is the period of a simple pendulum 80 cm l p xv8n13d k;4fev ess3qkhm23ong
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 m, the pendulum bob has a mass of 365 zh01 x8:3 fvuj-cc8lzau szle*9 st/w+c;zjv grams, and it is releasja se:wu13 8*9svtu-8z+vz 0jzcc x zhf/;cl led 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 clock’s pendulum has a length of 0.9930 m. If the clock gjoq4z )h p rpqmep 01*8mnn1-loses half a minute per day, how z4)j-hopq10en*m81qr pgnp mshould you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximum speed 7eua/a-0zip fos/u ,n$v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillatc o;jxmh0u3z ze1o b9mwz*) a3es at a frequency of 2.5 Hz. At it is released from rest stau xj33 bzzmowc*az o10e;mh) 9rting 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 wave crests pass the bow of his anchored boat es lf,i dxz8- lqy0;qk:very 3.0 s. He measures the distance between two crests zl;8q:, y dkq0xl- ifsto be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and tpi-k2iyw yb4i (wq,pcg3z*0 zravels with a speed of 343 m/s How far apart are the wave crestsy- q( ,3wizbipy*42i0 gkcw zp (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (kilohertz owk/g-f,d i6gl;uvj-) and travel with a-,6 lgidfw/g; k -jvuo 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;4gme6n v,t ri longitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modul27f)y-ds:k;ld tox 6bug mijgwt, l71us, but one is twice as dense as the other. In which rod will the speed of longitudinal waves be greater, almbf sk67-i1xydg u,wlo :2;dg)tj7tnd by what factor?   

  A cord of mass 0.65 kg is stretched bn7i+e sh o;gryv y60-xetween two supports 28 m apart. If the tension in +- egxyv70nsor yi6;hthe cord is 150 N, how long will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to the top ofg t*l 24 -m+ubxo *zkz-: woysfzswj;8 a hill by a steel cable of length 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 t-bzmlw*f*2szy+8;gkwjo o4 xz -s ut:he 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 his ship just below the surface of the sgzkd ce l4. io:j+qcj ru/a--,ea. He hears the echo of the wave reflected from the ocean floor directly below .o4dc,ujlqj ziegr c: /-ak+-3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at differen5 .oylbw1xj.j t speeds, and this difference helps in locating the earthqubj1.5loyx. wjake “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 can b pzdkyb5j)f4iz4r bx+(x79dkwo2qo7hx i , p/e approximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually includeh9, 5i2 kzq4dfyx+p 7( o7o xkixz)b/rj b4wdp 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

  What is the ratio of (a) the intensities, and (b) the a .x 7 tv56h/igi,;zlegtjn:w rmplitudes, of an earthquake P wave passing through the Earth and detected at two points 10 km an,h.w n:e xzrlvgtij7i t/56;gd 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is mipfm4fw9v o p+74kk k79h )eoveasured to be p4vf okfmw9eh47 9k+v)p7oi k $ 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 1(a ao3jk)u laportion of the Earth, but one is carrying twice the energy. What is the ratio of the amplitudes of ajk 3 a)au1o(lthe two waves?   

  Two waves traveling along a stretcg,n*odw ryv09o8b1ct hed string have the same frequency, but one transports three times the power of the other. What is the ratio of the amplib coo1ryn dvtg,809w *tudes of the two waves?   

  A bug on the surface of a pond is observed tc y-2as)0oe u,vqwi2ersq2:ho 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 4.52a2y,swiec )o qe:2uq-0 hs rv cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each other. (a) Skqkxzlm )p6fu 3i 5+x4aetch the shape of the string at the moment they direcx5um6 p3a) ixklqzf+4tly 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. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundamental frequency, what g3d q.n6),9dje (ip6ka oefugare the frequencies of the first four)dpq ugegj6d9.aif (, 6e3okn harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 H eym.g mv8qj fm(3vseb:y a)uel/ 4j(huel91 .z when unfingered. At what frequency will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of the strin)mvql8. meaey s3vlhj(gy : 1/bufj eu9.(4emg vibrates as a standing wave.)    Hz

  A particular string resonates in four loops 6- m:b)h ysdhi nal9- h;+-doyiud *unat a frequency of 280 Hz. Name at least three other frhdn hsi-hom lu;9u: +ia- y*n-)dy b6dequencies at which 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 freque0ar0j .lrs(6o: ij+alq tb6.rhi (pjincy of standing waves is 40jq.br6phi(r.io sl jajrl6a: 0i + (t75 Hz, how far apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 350 Hz, w,yhgyw : f;ls 4 matxz/7cj*nn+q e-s7hat is the frequency of the fund zw yj4qy;she/n l77sn:c-fx+g m*,taamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6u tch09b)i nz*8f8mc)a fro;e g. The distance from 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 fundamental and first two overtb0 aec8ch9o)t i)8rn fu*zmf;ones?    Hz

  A particular guitar string is supposedsst ;ak0x5 ik6 to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be change5xasi ; 0s6ktkd to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrater6,q c:oflu:fb6 xosobh xn66g k.54v at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension igu 6sohfx54 nbboxf6 k.6: :vlcq,6ron the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-amdkoe((k: n j chd*q;i5plitude mechanical 60-Hz vibrator. The string’s mass per unitdidek:( h ojq5*kn;(c 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 oq) .f6lgrxz +may be 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 betz l oqrg)f+.6xween 10 cm and 1.5 m?   

  When you slosh the water back and f68pt6 ,3ga8 a vx,pmgutdy( .1 aokqgborth in 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 u6agtp gmva3,dx k6a81qy,.bto g 8p(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 r gf;i1 jvzuka.r5wu-u-u-k0k.0 km/s strikes a boundary within the Earth between two kinds of materiaria -5uk.gu1zk f u;-0-rjwuvl. 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” wherk y2 tie32)q0uuco6i0vm )qqq,b5jume the velocity changes from 2.8 m/s to 2.1 m/s If the incid0qy) mo3m jv q 50q26iu,ubiteu c)qk2ent wave crests make 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 air. Ipwy4sr 0ko7 -nc6h(:ee8 m.npdezp9j f the sound 7:wz4ym kp-ond eph9ee68cjnp0r (.swave 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 earthquakezoktoy /;ef )3 wave strikes a boundary between two types of rock at a )e fky/3oto; z38 $^{\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’s manual, e6xxi .g978ls1hzvy dthe dish has to be pointed in the direction of the satellite, but an error of about 2 iyd lv 16z.x89e g7xsh $^{\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 velocitjc6 u3l.*ux;rf9 lexn l;mz*yy 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observu;yz**l 3ume f9llc .rj xnx;6e 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, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car buc 0w 4npz n4cefn 3h3(fjvg,8smper has a spring stiffness constant of 550 kN/m Find the maximum compression of the bj83v(0f4ncf 3 c4 wngzse,nh pumper 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 conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m below, which sttj4c lia4 h5l-retches the net 1.1 m. Assume that the net b4 -i a4cllt5jhehaves 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

  A mass m is gently placed on the end of a freely hanging spring. Therot*xrkkz7j-1 *4xd ; iprzy8 mass then falls 33 cm befork;ox x4d ik 8 *1y*z-jrrr7ptze it stops and begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes d;j(rpjm58 ama huge spring at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the springa8m5r pjjdm; ( 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

  When you walk with a c)xus l8cmsf38 up of coffee (diameter 8 cm) at just the right pace of about 1 step per second, the coffee slo83 8ssu lxm)fcshes more and more until eventually 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 33-gm g +,.swd;smrpm phonograph recorg;d sgm s,+w.md have a wavelength of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.5;e7,yg s he zsk7+veo650cos7.40t where x is in mese e7zk+ o,5v;ey7sgh ters 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 oscillates with frequency f. Wd +ee)3eic y 2dom+ie)hat is its frequency if it acceleradi 3c2myi)e+do e+e )etes at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man sta*8)b3ayo mv qa 4ody*fnds on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the raft v a yod*b*yo4)8q3a fmvibrates 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 musical instrument are tuned to pl*ftl mcmju ;/t:dn2k. s4mh 3jay at 392 Hz (G) and 440 Hz (A).f :./4j*htju3l2 m;tdmcskn m
(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 two-part cord of Fig. 1d7(lk/do/hv d4a sq/ o6 r)+vfe5 xkk+epc7eu1–33. 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. (The frequency is the same in both sections. Why?) (c) Is the wavelengt6+drk / k/7v xdua4fsch /kv5l do7e+)oq ep(eh greater in the heavier section of cord or the lighter?

  A tuning fork vibrates asv 4t / y4bpzm/fbau 55yc;h:st a frequency of 264 Hz, and the tip of each prong moves 1.8 mm to either side of center. Calculate c 5z4/pv ah;b4um/5fbyssyt:
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscilmsw1 k2eq-:rglates with simple harmonic motion of frequency 1.5 cycles 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–wqk m2r:1 gse-56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that enoj3sw bs a 2tkqk.bnne-p) 9t,d(wn18d is attached to a ring that can slide without friction on a vertical pole (Fig. 11–57w)bpba snt2 sntke -d3j(q,8.1o 9nw k). 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 exactly 2.000 s — each ongqz ho(5cj8+bkt lk*yvqw4-* e-way swing takes 1.000 s. v(lj o+8k*ybqc* -k tzh45wgq
(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 can os)r/pp8vqax j 9cillate in the vertical direction or can swing as a pendulum of small amplitude, but not both at the same time. Which /ajqxrpp)v89 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 (1p )o )i3c ahaaclg:rmass 123 g is stretched under 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 g alic(p )h:o1r3c)aaend. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spring with sp v ic/*t)xnc3lring stiffness constant k. A penny of 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 th c3/)xl *nicvte block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel crane cable is 22 m 5+(4p ( ,b ;bxuo62i ng2yb oyqyiuliu.rk*je long and has a diameter of 6.4 mm. A . ii(yyo*6xn;g+kub5ir2l,e o2upbu(bjq 4ybreeze starts the car bouncing at the end of 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 sr *q rr;iud9kz:hp+0 in Fig. 11–58 (which also gives the dimensions of the block). You push it sideways as shown, and s kr;i0zur*hrd: +9 pqthen 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 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz