Give some examples of everyday vibrating objects. Which exhibit qn y/6j8zc77nnuko8 jSHM, at least app n7qzkj o/u8nj7 y6c8nroximately?

Is the acceleration of a simple m8ny6iu) h 6u1taz4 haq7sb8k harmonic oscillator ever zero? If so, where?

Explain why the motion of a piston in an automobile engine is appit-sd58 +sb*8 17kt;qwbfie ozy;hh eroximately simpoe+kby *8 w i17 bh-fdszi;5ts;hqt8e le harmonic.

Real springs have mass. Will the tr p2pbe s,4v.l *6*xvd p.nh7 nig3 p(jvcyamq0ue period and frequency be larger or smaller than given by the equations for a mass oscillating on thejvpen*36 pvm lh ,0p(ba7d2vscn*g.x py4qi. end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple harmo;d8uc: xmgthixv; 5d,nic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scale, and then is 1/aoxpt.di( xp)t2x cs + mrjtww7*n7released. Describe the scale reading as a functior /w+x ctw.odt7)1xm7s xi( j2npt ap*n of time.

If a pendulum clock is accwgd en2+jk 4x6urate at sea level, will it gain or lose time when taken t2 dxewgj+ 6k4no high altitude? Why?

A tire swing hanging from a branch reaches nearly to the ground (Fig.0pi/+,j kwseg 6byst: 11–48). How could you estimate the height of the branch using only bj6:/yks +s tip gew,0a stopwatch?

Why can you make water slosh back and forth in a pmz g9,wm1z-/ g3w*oe1j)l ev w m3tblpan only if you shake the pan at a certain fr3-1 ej9wzpbmwo)l,z/ vtwgmm l1eg*3equency?

Give several everyday examplesjx2/ *uw wl rs-g;6.r s2ovre27tr kog of resonance.

Is a rattle in a car ever a resonance phenom+e jdi)6,c1m,jjqb zkenon? Explain.

Is the frequency of a sim-: uu y..eobz; 8q,g f,iqprxwple periodic wave equal to the frequency of its source? Why or wh;xp-8uqge.ir wqo , .bfz,:y uy not?

Explain the difference between the speed of a trz: ph 7eo0o7em s4 2bzjbqas,*ansverse wave traveling down a cord *7hzsq zb,e 2someo4p:b j0a 7and the speed of a tiny piece of the cord.

Why do the strings used for the lowest-freqaz i d: azsfpyqn/kp 91:ax9u:d-*g(xuency notes on a piano normally have wpa d:9a9u/:n:q * fdpzk z(x sa-xygi1ire wrapped around them?

What kind of waves do you think will travel fm(:z ;mz6ltibpf(/ qk 7j-z tdown a horizontal metal rod if you strike its end (a) vertically from above and (b mj-btki( mp f /:z;z7lz6ft(q) horizontally parallel to its length?

Since the density of air decreases with an increase in tem* x( peqzl*1jajl,h8 operature, but the bulk modulus B is neaej*1oj8lp* qz,l a(hxrly 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 decrease in amp133xadm wh6: ; khvtfwlitude as they travel away from the1avfktww33;6 xh: dmh source.

Two linear waves have t+6 :tcqwqh6p the same amplitude and speed, and otherwise are identical, except one has half the wavelength of the other. Whq6pchtwt +q6: ich transmits more energy? By what factor?

When a sinusoidal wave0a17t4z9 2hbvdb 0, mo;lm tlgdh(lg h crosses the boundary between two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and 2;btahvbmd, 9odhgzt mhl7 0 40(l1lg velocity do change). Explain why.

If a string is vibrating in three segments,sh nko*mea8:efzdf2. 7ydb-1bi:p a5b 8b+fy are there any places you could touch it with a 7ezfbybisd 1-by.ea*b+a:nm pk o8d8f 52:fhknife blade without disturbing the motion?

When a standing wave exists on a string, the r7m* evs f7hc*vibrations of incident and reflected waves cancel at the nodes. Does this mea7rcs*7 mhevf *n that energy was destroyed? Explain.

If we knew that energy was be 0nj/qzcds r7sc3 w- y.*peopj 07vsn9ing transmitted from one place to another, how might we determine whether the energy was being carried by particle3*p-7dpcs joyn7rjw s 0se09cz nqv /.s (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the total distance (sz tu)p ncym: u-./,u(yvrpfit travels in one period?scpt-rpuf:y (yz , uvu.m) n/(    m

  An elastic cord is 65 cg 4eee .ugfnepwe. wys/4 )w-s+p.l /em long when a weight of 75 N hangs from it but is 85 cm long when a weigh +pe.yge w/e4le p /.nf4-ge)we.swust of 180 N hangs from it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car com3b.o t6hp,ftxafcis,4o3 c3k press 5.0 mm when its 68-kg driver gets into the driver’s seat. If the car goes over a bump,p.aosot xhtf63 fb3ci 43kc ,, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg r46vw*ge m2 ebfish hangs from it. (a) What is the spriw2*6g 4bv mereng 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 withvba11 .zmndx55dr+ wo se4x 3v a frequency of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency if only 0. rosxv3e.n5zvddbx5w a11 4+m38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fi6cequco9uz)mm: g z7 *g. 11–2 at times t cuz:g) 7czmoemuq*69 = 0,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 gso( l4 h61ra j((csytw is caught in a spider’s web. The web vibrates predominately with a freljhrc(yo (ts( 1sa6w 4quency 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 ofed/u0wq6lvack4 2u3 b a spring vibrates with a frequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 Hz. Wlk4 acv /qwb6u 032deuhat is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 t +f 5zrnmvzi26pj(f- nimes per second with an amplitude of 0v6m-2rzn5+jp ffn(iz .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 halfsa4*2yldg fukb :2y5 w the maximum valuew5sy bf2d2g:*la4 yku?$\approx$    A

A mass attached to the end of a spring is stretched a distg+ ne43a8ezag ance $x_0$ 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 dheda 3z/ d/0wnbzy:f0 ix:a- is stretched an additional 0.130 m and released, how ly/ 0 adbfzhdi ned:-/ 3:0xzwaong does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a k s21v ox7ogt1spring with spring stiffness constant k = 280 N/m and is executin vxksto2o 7g11g 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 nq ag25q7: 3u hbrm+lhyf:za7 popgun 0.200 m to “loa+hay7b 3uz:gn27h:maq5lrq fd” a 0.180-kg ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to one end of tjp*g w)8 mt.sa spring; the other end is fixed to a wall. 3.0 J of work is required to comprt)p *gmw.8 stjess 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 acco2 ,bx i7)usf1m / awleuzjq+e3rding to the equation x = 0.45cos6.4t where x is in meters and t is im f/eaw ej s2 b3l)+xiquz,u71n 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 0pdkyzm7 3.hz energy of a SHO half KE and half PE?zzkyd0ph m7 3. ±    A

  If one vibration has 7.0 times the energy of a second, but their fre. h3+5x5fa5a iix fkwhquencies and masses are the same, whath5w a k5 hf3xxfia.i+5 is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light sprikl:d)fwiw/ h 2c wj (z*-po3q1jris0e ng once every 0.65 szf*pj0rhkidi( q3- :wl c/w )2e1sojw.
(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 lt aj8z o 4clgu)eb+.-u zt4o;parallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What will be the flu -+ ul4t8 .;ab ogcjozte4z)requency of vibration?

  A 300-g mass vibrates according to the equation xbd:b*67 oy/s0eeji uu = 0.38sin6.5t where x is in meters and t is in seconds. Determs:7/6u beyjbo *du i0eine
(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.5fvc e :rp;4-vtj 1nll 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) is sek4 zc j(nnm 4hrl*(z4truck by a hammer, which gives the mass aj( n 44k (ecl*zzrhnm4n initial speed of 2.96m/s Determine
(a) the period and frequency of the motion,    s    Hz
(b) the amplitude,    m
(c) the maximum acceleration,    $m/s^2$
(d) the position as a function of time, x = (    m)sin(4.08$\pi$t)
(e) the total energy.    J

A vertical spring with spring stiffness constant 305 N/m vibrates with an ampsq:gw 4;wpd+d1 .hf yly:si6 jlitude of 28.0 cm when 0.260 k 4yw p:+g:wfh6 i1ddy.q;ljs sg 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 co.rx )p/ cw g25,efeucmh(hz-vnstants $k_1$ 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 attl d7av *2n8fkmj,euv 0ached to a fixed horizontal spring whose spring stil27euvdm*k n8a fj,v0ffness 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 sq3ut65bir4 b jumps from a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate tu q3b5irs b46the 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 s. What is iti5/5u, (utdze fsoh4 ys
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly one swingsudi9 b ,jr;y5 per second? (That is, one complete vibration takes exactly 2.0 s.) jis9 5rbdyu;,    m

  A pendulum has a periodrtbf+ 90kmt1hwdy b4e yiv fez411+ )d of 0.80 s on Earth. What is its period on Mars, where the acceleration of gravited 4e ) 1zy+1iwrbhf1v4tk0 m9 ybd+fty is about 0.37 that on Earth?    s

  What is the period of a p:1rbz(7rri vsimple pendulum 80 cm long
(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 penduldy 8sc-1ub,shg bt6g.ft-e9 bum bob has a mass of 365 grams, and it is rele.h-ytgtseb1d8,ub fc6s9 b g-ased 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 leng*it9,fqw l5 t3ysf0x 9agbd,sth of 0.9930 m. If the clock loses half a minute per day, how should you adjust the lysifs3 d9t,g*95 t,fa 0xbl qwength of the pendulum? shortened by    mm.

Derive a formula for the o8 s(: i 3s)sx ,gqyhx4p2rhbymaximum 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 fhzh gh6( apy,us t) dk /va:*qu03+bflrequency of 2.5 Hz. At it is released from rest starting at an alt/6ahkdh0, h+ua:p 3)f (* guvys zbqngle 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 o7jcap ec9a8/4cz r-mf f his anchored boat every 3.0 jz e9 8fc -/4acpcarm7s. He measures the distance between 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 withzqdyh:e)i0 :w.r)p)p( m ajqj a speed of 343 m/s How far apart are the wave crests (compresjrqai:) yz p:j) .q (edh0pmw)sions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (kiloheu927fi3: axa keox l0ertz) and travel with a speed of lxe9 3e 72kix0:af oua$ 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 longitude*qu pa 7rrh)(inal waves 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 awz 8zy( p:ylkhn;9z b8s the other. In which rod will z9y y8;z b( 8:wlphzknthe speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between tw hrsnu7,/j bi:o supports 28 m apart. If the tension in the cord is 150 N, howbh7jsnr/u i:, long 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 un mmg6 0m)uld +ff(.klength 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 cable. It is observed tm .(0gdl+m muf6fkn )uhat 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 u :v ,5fcog h-9vrs3aabelow the surface of the sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is the uvav:,53 o-gsfra c h9ocean at this point?    m

  P and S waves from an earthd.aogs fbkvzm b hmx7785 .0l:quake travel at different speeds, and this difference helps in locating the earthquakes0zdml 77xb :ag .mfkv boh58. “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 be approximated byp b/:o lw6lz:ea 5x5g82h r m4mexw)fw a sinusoidal transverse wave. Assuming a m2bzox5x8w )wel r/leh p5fa:g4w:m6 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 ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplitudes, of 7w mt6raf;px8 hh ;-q ia98eqdesd:f2an earthquake P wave passing through the Earth and detected at two points 10 km and 20 p hf9t-x 8qirwd826dee7maqh ;f: s;a km from the source?(a)    (b)   

  The intensity of an earthquake wav4rg; ac f: ny blt26:3b/wgztte passing through the Earth is measured to be 2ttg:l/c ;tnbby 6fazr:34w g$ 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 port,rjs z/ 1ntt(hion of the Earth, but one is carrying twice the ertj z1nsht,(/nergy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling a o,www-b cib,l;aqinau dr :9k,y.6, blong a stretched string have the same frequency, but one transports three times the power of the other. What is the rat,ra-w b.,wna:bq,l ;ci wu 9okd,6i byio of the amplitudes of the two waves?   

  A bug on the surface of a pond is obsv5j ,: eimtr rieb)5q b(9y5cierved 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 9i5reby5 c:,)eitqbm v( i jr5what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each other. (a) a/y)hn7 thlj-r,quo ,Sketch the shape of the string at tojh/nt- r)7ah,l,y uqhe 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. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundamentald*gqx;- mxe umx(ef88mxeg* 3 frequency, what are the frequencies of the first four harmonimd8;u( me qg*xeex*m g3xx8 -fcs?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingewqis+74 ur2mm 3 h9vqlred. 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 string vibrates as a standing w3 uw4ims 2ql v7rh9qm+ave.)    Hz

  A particular string resonates in four loops at a frequency of 280 Hz. Name -ffe9szl)1 ljv k5lx*at least three other frequencies at which j* zef f ll)l-5x9s1vkit 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 fhvo-z5,uy5 a0 u7a 4vjkjike ,requency of standing waves is 475 Hz, how far apart are two adjacent nzo0 yiv,j,ke5aj-h vuk74 u a5odes?   m

  If two successive overtones of a vibrating string are 280 Hz,e/ 98sjr bgbe and 350 Hz, what is the frequencyb er bg9js/,e8 of the fundamental?    Hz

  A guitar string is 9u3 wa* ,xqawnb (vihdd7qm1 )30 cm long and has a mass of 3.6 g. The distance from the bridge to the support post is L = 62cm and the string is under a te1 duiqhm337wwnb qvx ( ,aa)*dnsion of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vfwo 8 .-ie 4g)tro9,nhmm;b 5b ikjp4kz6/hk tibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to) e ,ti w.i;6ko tn8kg b5-b9mm4f/ rzkophhj4 correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate/im4z/ 9 j;wye4v qhascfbb :* at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should thmicve* f4qwajs4 y;9/:hz /bbe tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a smalfl- a fe*xa8x tht82*ol-amplitude mechanical 60-Hz vibratot28lax8 a *tof*fx-he r. 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 be adjusted k uc)ct w1x+d3ucr (emmn0z8uoc.b;8by moving the pulley. If the han(k8m8nte 0cw;x c) 1dm+bu3.uccur ozging mass m is fixed at 0.080 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 right frequency,: o7x0nt(x sto the water alternately rises :on7o0x ( xttsand falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 kma63abl y ,9cfs/s strikes a boundary within the Earth between two kinds of material. ,9y6la3 absfcIf 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 changes from 2.c-d ,tlzs/sf6 8 m/s-ssl ,ft z6cd/ to 2.1 m/s If the incident 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 wh6dx y3c:y/oi;ip8dxxen it hits a layer of cold, dense air. If the sound wave hits the cold ai8 ; o3p xxyc:di/ix6ydr 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:. qg9raw z4ce types of rock at a re wa .qg9:4zc38 $^{\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 man69ez.vk,h rmt w2s bn9ual, the dish has to be pointed in the direction of the satellite, but an erre,2.rv m6 nhs 9b9kwtzor 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 wavelengtnw:acwycv-70s 9y(j, b3gcumh 250 km and velocity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they n7awv- ycgs: m,(w30 byu9cjc 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 kN/m Fin/-s:vj;8pvn;xvzsld ri u( g9d the maximum compression of the bumper if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approximately 5: vr9s /p 8j;vvid; -gzlx(uns mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from*6 n3vjm0pi3 ,m6d tx7ln bsvz a window to a fire net 18 m below, which stretches the net 1.1 m. Assume that n0zvjtvm dbp6,n3l36m *s7 xi the net behaves 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. The meoir5s 1i1tlu6 /thv0ass then fa/i et slr1v ti5o061hulls 33 cm before it stops and begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a spee z3l2u nn1,bcbbg9/sc d of 22 m/s (Fig. 11–54), compressing the spr ,czb1b2gbl s/nuc n39ing 5.0 m. (a) What is the spring stiffness constant of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of coffee (diameter 8 cm) at just thr ds2mof,g202f -e wale 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). 2ffo a,e20lmrgwd- 2s 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-rpm phonograpt.huj2h2 /1bz bts a154;blnct-kawz h record have a wavelength of 1.70 mm. What will be the frequency of the soundbwa2ta5uzb4 tjn 2/-thl 11k h.b;zs c emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t whuwyto:: )x/zoere x is in meters and t o)uw/: t xoyz: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 wiyy9 83gx1,-pw seimx 2o-occxth frequency f. What is its frequency if it accelerates at 0.5cxxi8ycxowe yg12-,3-9p os m0g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lapcrf.q8d;1sn2aj, s oke. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the raft vibrasasp; nq8f jcr.d1o,2 tes 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 in 1 3hc(f/cxyqy62fdoustrument are tuned to play at 392 Hz (G) and 440 Hz (A). xf2/3h qccy(d oufy61
(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 trave:4 twp)fhh7go+hwg* xling 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)x owf gthg)h p74+*:wh 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 at a acdgd) +q1z 46 /7pdq/.zuqnxsxbsv* frequency of 264 Hz, and the tip of each prong moves 1.bg/cnxq.7zs )p 6sx/4dz vaq*+ uqdd 18 mm 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 simple harmo wr20wkg.vp7g nic 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 .r7gkwg 0w2 vpa pebble 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 ring that can slide c ) e zcp4tf)gin-iz8;g e2q6kwithout friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with one end ffc;ii-ge64c) ) nke8q2gp zztixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each one-rkava)zhox1l) :+,mp mwk+ : yway swing takes 1.000 s. +r)a:wmv m koh1:ka+l,p)z x y
(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 oscillate in b 9v/42 yr 4g::k:ocfej e/bt 8zjmtyhthe vertical direction or can swing as a pendulum of small amplitude, but not both at the same time. Which one is fogj/8/rbe4c zm :9:yvtkybjeh: t2 4longer, 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 a tension of 255 g9ovot,72qy/rs 6 swgvrozb,q+b: 9bN. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at the opposite end. Where will the two pulses fi7oz6v, y grgro9bvt2, so9b:/sqqw+brst meet?    m

A block of mass M is suspena,7eu 1;xfsca0g xiw7 ded from a ceiling by a spring with spring stiffness constant k. A penny og1;0s,uf xa cx7 eiaw7f 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 stx;jfuiic,,, o s,fbr0 eel crane cable is 22 m long and has a diameter of 6.4 mm. A ,s,,rxcf0iui;j ,fb o breeze 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 in Fig. 11–58 (which also gives the ,k 94on(i u2y 1enesmndimensions of the block). You push it sideways as shown, and then you let go. The jello springs 9nks,no4ene2mu 1iy(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