Give some examples of everyday vibrsnodp7ne) 53/pdkf 2 rating objects. Which exhibit SHM, at least approximately?k2p7 fro / )nsd35depn

Is the acceleration of a simple harmonic oscillator ever zernsxi2+ w..4a yvpoh-toqwi p 3p/4 f/zo? If so, where?

Explain why the motion of a piston in an autor +xl-2e *hniux -ee1+afs,jtmobile engine is approximately simple hars*2a t j-,e1nel+urex -f xih+monic.

Real springs have mass. Will the true period agb 4-piq -wk4hnd frequency be larger or smaller than given by the equations for a mass oscillating 4- qbip w-gh4kon the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple harmonic oscil3fthaqg xk i,z k7jg.4 46lts*,1lnumy6a) z ylator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spra9n+:h(n uh) sy fjhqkc4gb8-l,1ugying scale, and then is reluynqbh g 194,khahn) c 8uj+:g(-yslfeased. Describe the scale reading as a function of time.

If a pendulum clock is accurate at s -n. 7bdgif (.)e-(b n(px1aqwtup;-jevgcswea level, will it gain or lose time when taken to hig.-np()-q fbdwcg a n e ;jwi-xbe(sg v7.tp1u(h altitude? Why?

A tire swing hanging from a branch reac3u, j wc(1ypug1l i+azhes nearly to the ground (Fig. 11–48). How could you est11 cpua+gl, i jw3uzy(imate the height of the branch using only a stopwatch?

Why can you make water slosh back and forth in a pan only if you shake thel4dxom hd/e(5 pan at a certain fre(5odxdhm4l / equency?

Give several everyday examples oe i 2,p6/ujga 1wbv,lz6pwy /gf resonance.

Is a rattle in a car ever a resonance ph crwwv8to (:4renomenon? Explain.

Is the frequency of a simple periodic wave equal to thqcb2(2bknrf( k t a;9pe frequency of its source? Why or why n bfcqpb;ar(2k(nk2 t9 ot?

Explain the difference between tsh zz hl*-d 5z69g:cdnhe speed of a transverse wave traveling down a cord and the speed of a lzd5:c h6h9zd-g*sz n tiny piece of the cord.

Why do the strings used for the lowest-frequency notes on a piano normalltfb;l/j2p99rl7c e dj xqelerc:- x 4(y have wire wrapped around rr ( ftb9e4dellc9 pq;7 xjj/:ce x-l2them?

What kind of waves do you think wil)(o rngo7lp5+:,ii; ,z tcmahtq5 n yyl travel down a horizontal metal rod if you strike its end (a) vertically from above pyzya n 5,q)(;i5cig7 roo:, +ttnlmh and (b) horizontally parallel to its length?

Since the density of air yoh(* c x zb8d16)livydecreases with an increase in temperature, but the bulk modulus B is nearly independent of temperature, how x lbc8 d6yi 1*)voh(zywould you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in amplit7f*gleg, a5 j-dua o3jude as they travel away from the u- ojfa3*e l7 dajg,g5source.

Two linear waves have the same amplitude and speed, *:tc6ld( mbc1p-plk a and otherwise are identical, except one has half the waveleng-dcm:k t*pacb(1 6 pllth of the other. Which transmits more energy? By what factor?

When a sinusoidal wave cro07w3o6m 0:wgk4/d ow n4 ( s5ligwpmswhmkpo3sses the boundary between two sections of cord as in Fig. 11–7m6wlmhwog 3 og4:/p 03(oskpis50 kw wmd4nw 33, the frequency does not change (although the wavelength and velocity do change). Explain why.

If a string is vibratine6ss mzgcs:feh/f, .6g in three segments, are there any places you could touch it with a knife blade without d f:zmce.s6ef 6/sh,gsisturbing the motion?

When a standing wave exists on a string, the vibrations of incident and refleboi q03b/zryu xl (u/h7hzv82 cted waves cancel at tho 2qh8vb( /urzu zyi73x/0blhe nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one place to anothvocdyf:3 g zew(e4 pz12 ml)o.wii*r+er, how might we determine whether the energy was lid:.i23 owo4zv(c 1zf) mge+w*e ryp being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.wpy +p.6xj nj4h.gju k)g *g;b18 m, what is the total distance it wk b jx*6jg ;y).g. u+ghjp4pntravels in one period?    m

  An elastic cord is 65 cm long when1 zx2otifc; 7j a weight of 75 N hangs from it but is 85 cm lo1; jf7x2oiz tcng when a weight 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 compress 5.0 pm zqm7gykr6z5 l9ntaa/) /q: mm when its 68-kg driver gets into the driver’s seat. If the car goes over a bump, what will be than9gq/7 : mmry tkaq5pz/)6zl e frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs from it.edgfqv9c3ri7etiop/+ 2* js -b 4pk q: (a) What is the spbiqp-t pjeosr2 g9cv d*e43i:7/+qfk ring 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 vibratbh a) u)xq20ijes with a frequency of 3.0 Hz when a mass of 0.60 kg is hung from it. What ishib)a 0qx u)2j its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating t)fa:+xl 1*kqgml;u xehe position x of the mass in Fig. 11–2 at times t = 0,t 1mufxel:; g+lq *)a kx= $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 vibrates predomew 2kaf 9a*rbr g.:dz5m.4kba inately witrdkbk.fm4ge 5wb :a raa9z.2*h a frequency 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 spri8a m q(3sgaz7/v2wvheng vibrates with a frequency of 0.88 Hz. When an additional 680-g mass is added to m wv/7esmg2h (3aaq8zv, the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of b2k:iv)t9lrqdow)szd ;- hi ,a spring vibrates 3.0 times per second with an amplitude of 0.13i;:z, swqto9 rl)hbd2)v-kd i 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 vc:9x8bwn /) lxa7w k zprxeqnil ):4/ialue?:w n r)pwqe/x/ xln8zxaic9 b)4kli7:$\approx$    A

A mass attached to the end of a spring is .qh xvhtuw+ -0stretched 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 spbn+(p0a*0se-k:ov tt rawt v 8ring 0.315 m. If the spring is stretched an additional 0.130 m and released, how long does it take to reach the (new) equilibrium positionvoraae-8 t*sn00pwt:t bk(+v again?    s

  An object with mass 3.0 kg is attached to a spring with spring stiffness o,l(0kus(5 s 7ndzfm4e /sfjfconstant k = 280 N/m and is executing simple harmonic jk4/f z,d5leu(70 s ms(fnfs omotion. 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 cm *ix-) su-qycdq(w9+ s7p vxxompress the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball.x*-x)dvqu9(mwqp7s+y x i-s c With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictk s0u lmi h86lj8pzo wuk/-q2p/5zbb* ionless 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 158o / b*/juh6 iwl28kkupmqbp-0zs 5zl $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibra) rexz+rp)tfm d. j+s9e76vic/beqf ;k qw +o,tes according to the equation x = 0.45cos6.4t where x is in meters and t is in sec wrzj.96qef+rd+)) eqv7xfb;ek+p si /,tm oconds. 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 equiotr;+k 29 q9m f-ffypizex8 +xlibrium is the energy of a SHO half KE and half PE? ± fx+e pffzy98kr 92io+-x;tqm    A

  If one vibration has g4 *xh./swbktifatw7 7pg1z,a jw(u97.0 times the energy of a second, but their frequencies and masses are the same, what is the ratio of their amplitudesj,t*gpf97sa tw1 au x. h4/wbg(kwzi7?   

  A 2.00-kg pumpkin oscillates from a vertically hanr49,pcuicy g *h.0ybh dlg7ke:qv*x(ging light spring once every 0.65 0*ghx7i9erhd,:4 l*bcv. y kqpcu(g y 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:d6oyf3ta;rf 5e8 bbj8kd66 k5t ksjb two identical parallel vertical springs, each with sprs ek56:8bdajob8tk3jrbd k6fft5 ;y6ing stiffness constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t where x im + jp jd-v+ttz;8s7yas in meters and t is in sem8;j+js7- zv ayttpd+conds. Determine
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows two examples of SHM, labeled A and B. For each, what i3 g :ag );qyt3 oyor1vx57letrs
(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 str/1vlbz/lv pbwk o* 11euck by a hammer, which 1bebk *wp v 1zll/vo1/gives the mass an initial speed of 2.96m/s Determine
(a) the period and frequency of the motion,    s    Hz
(b) the amplitude,    m
(c) the maximum acceleration,    $m/s^2$
(d) the position as a function of time, x = (    m)sin(4.08$\pi$t)
(e) the total energy.    J

A vertical spring with spring stiffness constant 305j; kc y7yp11i/oybg)c N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point)c yigkcb o y71y1j/p; (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 dmz2(v8jj;3l 6zaa wx 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 a* gntg(alla/gxf x: 0,b 7pvy(ttached to a fixed horizontal spring whose spring stiffness constg x0 l(v,bl fy/*x7gn pagt(:aant 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 bm.(vyty*w6ym0y o2 ireaching 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 bungee co(m *.m2owiy yyybvt6 0rd.
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*kdwfw/4n b bd5+f -xy 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 sw)7(x h4jx/m/;uho ppm ajnzp0 ing per second? (That is, one complete vibraz/a( /7)hno0xppxjp4 m ujm h;tion takes exactly 2.0 s.)    m

  A pendulum has a period ;h+a)dr nzec :m+s1qe of 0.80 s on Earth. What is its period on Mars, where the accel+rz ;s:d +aeh1mcqne )eration of gravity is about 0.37 that on Earth?    s

  What is the period of a simple pendulum 80 c (y0se1w 0sk2tm ij7tpm 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 pendulum bob 54jk0kr sv, nehas a mass of 365 grams, and it is released at an an jk4knr50e s,vgle 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’2zr/wvz(4 wn ys 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 4n wyrw/zvz2(pendulum? shortened by    mm.

Derive a formula for the maximum9v31h)fg0b a4 c )p bhma*-m12+fzudkkekba k 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 fre-rguc 4k)yy2 wquency of 2.5 Hz. At it is released from rest starting at an kyrwc) -4 2gyuangle 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 derz2hy s1rlh(-ahrb5 4g/h*wave crests pass the bow of his anchored boat every 3.0 s. He measures the distance between two crests to be 6.5 m. How fast are the waves tryhdzh2r(hgeb4 shl-/ 5 r *a1raveling?    m/s

  A sound wave in air has a frequency of 262 Hz and 4ch nrf1m+b6 d.xxb3i travels with a speed of 343 m/s3x ih.bndrxc m4f6b +1 How far apart are the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (kim;+n 0rhei 1bbz/--o lbt *dmnlohertz) and travel with a speed o eb+r0tob;dmhml - n-b/ni1z* f $ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

  Calculate the speed of longitudinal wavesh;u j7izmvi 1yz-33fp in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic y :w-hmg 3;;l/et:ou vrs;mlb9dob toll59q )modulus, but one is twice as dense as the other. In which rod will the speed of longitudinal waves be great9o:-3tgrb sytdw ub ) lm :;h9q5/vl;meo l;loer, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apart. kcziktk+t s(1s/- gb0 If the tension in the cord is 150 N, how long will it take a pulse to travel from one support to the other c(itzk+-/k tb sk01sg?    s

  A ski gondola is connected to the to7otxk 9 +yl;ssp of 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 the cable. It is x7ys +tkos;l9observed 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 surf)rd,52(pw1w f) cm txqx hs)xxace of the sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deexd)fx1 ts5wp, ch)2) xrwq(mxp is the ocean at this point?    m

  P and S waves from an earthquake zll+fezy4z . u:jz-6utravel at different speeds, and this difference helps in locating the earthquake “epicenter”yz 6+uj:-.l u4ezzzfl (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 by a sinusoidal tra/c( 6-sd:-q-l qrgnq7 jgkvpynsverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitrcq qg--7kvyp j l6gs/(qd :n-ude 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) a68 xjwc/ql2q the amplitudes, of an earthquake P wava8cwq 2l 6x/jqe passing through the Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is measured to bqxsf 7e b2(h;pche ,6ve ,fspce( hbe7h6v;x2q $ 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;4rfseu6f9b e 5 o6snxtc3en7 through the same portion of the Earth, but one is carrying twice the energy. What is the ratio of the amplitudes of the two waves? n4sfusbn5e6t r397; xfeoe c 6  

  Two waves traveling along a stretched string have the sa2zw,-qkhta6i me frequency, but one transports three times the power of the other. What is th,h2zq awk i-6te ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move up and down abxq 7k(.:q03+s ogqum yrlml 5 total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm, by what factor doesqy . ( +35mobgrllkm0x:qqu7 s the bug’s maximum KE change?   

The two pulses shown iy)s 1xh ah w0*it/sux:n Fig. 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 few moments 0 uwa1sy:txhs xi)/*hlater. (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 frequen7hw ic7urii t1f58l*ncy, what are the frequencies of the f7i c8hflnwri7* 1ti5u irst four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz whe 1cr*g+m og-rc,bb k*i2q61it806tojkyc v yan 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 ot2** 6j o, qikrbgrtc- o1cic+ a8 m6ygy01bvkf the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequency 88wqesah y1rs47/y*qpwnhg m h2 v9v(of 280 Hz. Name at least three other frequencies at which it will resona71q*(2gy a9hswhn 84w/v8vh yspqrem te. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of wavesb 5q c,x19rkx ;t6vyd/xjpw6j on a string is 92m/s If the frequency of standing waves is1tv6j w b9r/p6xy,;qx5 dcjkx 475 Hz, how far apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 350 H* y bpz: lz73*os1emli0 pfgp7z, what is the freqsy*l17:iz*lo pf p 3epg07mzbuency of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distance fro-,ipox:n)c cvm 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 c ,n:ox-vpci) overtones?    Hz

  A particular guitar string is supposed to vibrate m y+*8tsxxkli- 58rhz at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?So the three frequenctzl mr5 ikyx -8h+*xs8ies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed ti.m; hlxf.., kge ib/yo vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changedlf;.egb.y h.xik/ ,m i to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-amplitude f 7uz+tu u1gx+mechanical 60-Hz vibrator. The string’s mass per un uuz7f+tgx1+u it 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 by moving the pulley. I.,l:+*uhxrhj(x g 8oetwrhw7 f the hanging mass m is fixed at 0.080 kg, how many different standing gtohr* 8+jhrl u(:,w.h we7xxwave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water bne(h+dqu nh x5yhin3h +(53coack and forth in a tub at just the right frequency, the water alternately rises and falls at each end, remaining relatively calm atd +ohh3 +5u(nyc 3nq5xnie(h h 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 km/s strikes a bouyj,b05j2pnq hndary within the Earth between two knhyp q0b j2j,5inds of material. If it approaches the boundary at an incident angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “shelf” where the velocity changes from+it)*no7 ybca 2.8 m/s to 2.1 m/s If the incident wave 7cbn+)atoy i*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 oiz a k39wkxgv *nw2n1:f cold, dense air. If the sound wave hits the cold air interfacewxn3agiz 9 knk*1w :v2 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 betweencw; 4da00trvn(/2l upc9 1 )ovbucpe: gkurm+ two types of rock at a c e(dau9pv0/mblr0+t2:nrpk ovw);c4 c1 ugu38 $^{\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. Accord b8v*mi,c z027srjyq wing to the user’s manual, the dish has to be pointed in the direction of the satellite, but an07*zm2jyc,wsibq8 rv error of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of waveleng l-;brvk35kk2 c qkd6tth 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 have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them ak-q v6ckd5r bk2l; t3kttracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness consta pr u:lo-q90) exivmo1jtcsfih)/..q nt of 550 kN/m Find the maximum compression of the bumper if the car, with m-c1ofml. xu/9qp0oqh) rti.:is v )ejass 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, whgtho-31. bh gmbq7sk xd),8beich stretches the net 1.1 m. Assume that bmqgd . 8) 7hbb-1gt,so3x ekhthe 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 piul f+z.(, gbka.4lhylaced on the end of a freely hanging spring. The mass then falls 33 cm before it stops and begins to rise. What is the frequency of thehky bl+,i.. fza4u (gl oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 11–54), c j/7*rhr8kv:uzmkp3hompressing the spring*8h up3 h m:kzk7vr/jr 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 coffe 6cep) os0yqb/e (diameter 8 cm) at just the right pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the speed op e/bqys6 c)0of waves in the coffee.    cm/s

  The ripples in a cer z/+u*u.ieiqyh bz8vmpkj/;cv,( 2 v otain groove 10.8 cm from the center of a 33-rpm phonograph record have a wicui;./omubzh8v ezp2+vv (q k/*j ,yavelength of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to th1;lx bwyyy9 (;kcpw m5 *x*ygre equation x=0.650cos7.40t where x is in meters an w5ywy1 9x(;;pbr*kc* lxgy ymd 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. Wha w fl;ze*13mrkt is its frequency if it accelerates atklme3wr1z *; f 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. vrr/* ,w 6duje 8jb d7/whe pd) 5mc/aq2iej7tWhen a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he stepumpaj/v cjr qh/e,r 86t*e)d52 bj7w i/edw7ds off, the raft vibrates for a while.
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a musical0f+ zy7,cl doz instrument are tuned to play at 392 Hz (G) and 440 Hz (A)zy7d ,olcfz0 +.
(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 trava1zk aeec 1;x9eling down the stretched two-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (T11z;eaek 9 acxhe frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the tip of each pron)8 vy+fkrocbl,5hk ;x5yu jx1g moves 1.8 mm to eithe5+8l xjh5ykxvyr;f)cb1k , uor 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 harmonic motion of 8 t*chufhcbqf9/o q5 -frequency 1.5 cycles per sec9hu8t5c qoch-q/f*fb ond. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that end is attached2.4eelkaaj e:u:3zd f to a ring that can slide without friction on a4duazj k2: e.:eea3fl vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each onruox:(t9i t c5e-way swing takes 1.000 s.:uc5 ot9rx(it
(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 the vertical directionvbo spf,42fc*h1m49n s/g l rw or can swing as a,wfhsocg*24smb9 p fnl/v r41 pendulum of small amplitude, but not both at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontal swings, and by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

  A block with mass $M=5.0\mathrm{kg}$ rests on a frictionless table and is attached by a horizontal spring $\begin{pmatrix}k=130\mathrm{N/m}\end{pmatrix}$ to a wall. A second block, of mass $m=1.25\mathrm{kg}$ rests on top of M. The coefficient of static friction between the two blocks is 0.30. What is the maximum possible amplitude of oscillation such that m will not slip off M?    m

  A 10.0-m-long wire of mass 123 g is stretched under a tension of 255 N. A pqfm 50vp4or+em h 36vqulse is generated at one end, and 20.0 ms later a second pulse is generated at the opposite end. Where will the two pulses p0 mrof6 vh45mv3+q qefirst meet?    m

A block of mass M is suspended from a *q5 h8k5s /jtzk1lsozceiling by a spring with spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude jt1/8oz*kq k5 slsh5z 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. :qp )v5xop+kfThe steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. What is the period of the bouncing? [Hint: Refer to Table 9–1. 5: )+qvkfoxpp]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (whicry1soy-: *cl ; ci2tk4l,th jch 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, gi*hlk2:4c;c r,tlojcytsy i 1-ven that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz