Give some examples of everyday vibrating objects. Which exhi4firsdi(d 4 *g.vnauge l)-u0scsz+9bit SHM, at least approxiv c40i sues*dfug d.ar(4)- sgi+9lz nmately?

Is the acceleration of a simple harmonic oscillator ever zero? If so, w2rl 7g*kr89tekzr nl 4y(sgx4here?

Explain why the motion of a piston in an automobile engthf5g (2 idu81hm6and ine is approximately simple harmonighmafid h52td1(6 8 unc.

Real springs have mass. Will the true period and frequency be l6 6mzrk + yg)(1qfzutzarger or smaller than given by the equations for a mass oscillating on the end of k r)tq61ug(+6mzz zyfan idealized massless spring? Explain.

How could you double the8 b*4(tzh2zj6 dg1fpohn + ddr4 irf/a maximum speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scale, an 5 jst;;p(3drn y 0*c.vdddxkkd then is released. Describev;yj; d* 5drcdk.dk(0x 3pst n the scale reading as a function of time.

If a pendulum clock is accurate at sea level, will it ga2/ sb cpq7iv-n znu go/w;ec;w .hlou2g3m99xin or lose time when taken to high altngwwigh-ep/obvu o7; n 23mz sqxcl; 9/29 uc.itude? Why?

A tire swing hanging from a branch reachekuj02b1wf3 b nxu xsap3iy. 44s nearly to the ground (Fig. 11–48). How could you e. 4fxap313 u4bbi w2u0yj kxsnstimate the height of the branch using only a stopwatch?

Why can you make water sl;2t+h vfleiia 5, hxi79of+sgosh back and forth in a pan only if you shake the pan ai,sh; 2lha9+ o7giefvxf i 5t+t a certain frequency?

Give several everyday1 ifi14rb, bh9ikf e5l examples of resonance.

Is a rattle in a car ever a resonance 2tgal+w0i f ob--(wj pphenomenon? Explain.

Is the frequency of a simple periodic wave equal to thev *mifem1ut.56ddo )a frequency of its source? Why or w tve5afm *m.i1uo)d6dhy not?

Explain the difference between the speed of a transverse wave traveling d, 1 sweaggff6/hs c)a6own a cord and the speed of a tiny piece of ts c g6ga/ 6,)1whfseafhe cord.

Why do the strings used for the lowest-frequency notes on a pian ob +(p gyy95qhb rs05qfb5.kpo normally have wire wrapped arouqbr0bp y q.h+gyokfb 5(9s5p5 nd them?

What kind of waves do you think will travel down a y hm-nhxi azlc9qb(3+ ao -z*;horizontal metal rod if you strike its end (a) vertically from above and (b) horizontally p3y ;z(zhmqb- l9axi-ha+noc* arallel to its length?

Since the density of air decreases with an ifxt4 rxo t*0 )7x wye1zblf6u6ncrease in temperature, but the bulk modulus B is nearly indtwftobzr7x) u*6fex4 6yxl 01 ependent of temperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decreasejkn6f f8x80oq in amplitude as they travel awayo jk8x8nff6q0 from the source.

Two linear waves have the same amplitude and speed, and otherwise are idms)eys78 e3 8 trztasa +l;q(dentical, except one has half the wavelength of the other8sty+8 (mt 7 ds)sqzaeae3;lr. Which transmits more energy? By what factor?

When a sinusoidal wave cros0.p.kek ji +qqses the boundary between two sections of cord as in Fig. 11–33, the frequency does not chan+k.j0.pqkq eige (although the wavelength and velocity do change). Explain why.

If a string is vibrating-o(+ 1x cvjou opktb9skq-217 tjnby* in three segments, are there any places you could touch it wit* nk1 o s kot2+7jvp1y- cu-jt(9qbbxoh a knife blade without disturbing the motion?

When a standing wave exists on :9n1ib)gz mp(0x umuz a string, the vibrations of incident and reflected waves cancel at the nodes. xnuz9u:0m )(mpzbgi 1Does this mean that energy was destroyed? Explain.

If we knew that energ)bs-/d;rrgwqbl161j h lxf4 ay was being transmitted from one place to another, how might we deb 1f6s jl)agdx-wr /;4rhq lb1termine whether the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 myq a.p0*/ hgvw9- gxvg, what is the total distance it travels in one periop 0 hqg/vwxa9.*-gvgyd?    m

  An elastic cord is 65 cm long when a weight of 75 Nq *li87 oi6jaz hangs from it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring”oz* i ij7al68q constant k of this elastic cord?    N/m

  The springs of a 1500-kg car .6rol-f- tk/ig k qo;;i)gkzx compress 5.0 mm when its 68-kg driver gets into the driver’s seat. If thf.oo qx-k ilkg6;)gktr-/z ;ie car goes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs fromqw8kwa17w+ d( pn 0com it. (a) What is tn1awoww0 m+(7kq dp c8he 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 with a frequency of 3.0 itqdw0z* 9b :hHz when a mass of 0.60 kg is hung from it. What is bdh*0t: iqzw9 its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x + 6:bzvmowe w*of the mass in Fig. 11–2 at times t 6z:m*w eob+ wv= 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 g is caughtj yan,(4rjug 9 cl7o7w in a spider’s web. The web vibrates predominately withy(7w4jnu,jg lrao97c 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 spring vibrates with a frequem )mwl +vj)s5qncy of 0.88 Hz. When an addit )j5 v+smqlw)mional 680-g mass is added to m, the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end oww i:)zlx hc*c-t-p1j f a spring vibrates 3.0 times per second with an amplitude of 0.13 jci 1th:wwz-)lpx- c*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 SHOn x/1cvhxmj5jn ognr27j+84 b half the maximum valux/ gn8bo1jcr5n7+j4j n2 vxhme?$\approx$    A

A mass attached to the end of n 9d.os,g14mvcx2ai wa spring is stretched a distance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretches a vertical fw zjuua*e6i k(i,/6c c)f5bns:3njg spring 0.315 m. If the spring is stretched an additional 0.130 m and rel3zaikjwfnb6n/iu sc ,5(*6 :e g)ujcfeased, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is atta kv9t ptb.zk64ched to a spring with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. Whenvb.94tt k6k zp 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 compr/.; qso,ve ,smdb:rimnlncywv h( 8+o+k:y1zess the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will the ball leave the gk: 8+ylwq ob/y+o ch(z, nniv:dvrem.;, ssm1un?    m/s

  A mass sitting on a horizontal, frictef9o wm eazl*q*w 6)/lionless surface is attached to one end of a spring; the other end z)9*mqeef*l 6o/ awwl 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 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates according to the equation x = 0.45cos6.4t where /x9qku:vc ) /y, ursyhgad, 3wx,k5wa x is in meters and t is in s9uxgc:ayd,/5q w,,ykxr3s/ uh k w)vaeconds. 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 enerjuls ;vxty;s f3znl;4**.e t pgy of a SHO half KE and half PE? ±ls. *4;pxtyevjn*sl; z;fu3t    A

  If one vibration has 7.0 times the energy of a second, but their frequenci6djmd 9*0 ppiees and mass* dmij60dep 9pes are the same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light spring oiz3l f.d o nzi2*x0pb9nce every 0.65 xdbo *0fz2i9p n.lz3i 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 identicug/*9 s 6o(owrg6aher al parallel vertical springs, each with spse9gr 6u 6wohra */g(oring stiffness constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the eq9n y -c+ilrzfuw*p/pz nep19.uation x = 0.38sin6.5t where x is in meters and t is in fn9.+cniuweplp/pz9 - z r*1yseconds. 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. Fora eu qvfh-pwfva6(rzad:0zn((3mj( 4 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/-i/f 8:i joozzm) is struck by a hammer, which gives the mass an initial speed of 2.96m/s Determine -8/ofjiizz o :
(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 stiffnes(nh(kl z;7t+ en7mxqvs constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The m x7l(nvhz k (mq;7etn+ass 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 s;hb o 8lthqb+-7 3(robbee *tppring 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.qbipen8g 1n cf/b 7zij3o0 l)+600-kg block attached to a fixed horizontal spring whose s)bfnp+gqien o03z /1cbj 87ilpring 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 with)476s(k;plnr kjdapflwl/k, d sec )2ul1p1 i mass 65.0 kg 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. Cae ;u,kslfp cpr)1w/l i(a p nd4l)d6j2l k7sk1lculate 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 vibrationaodb s:qumo n3sy7 ;yz) yb8is,5 ik0:s in exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it ib iatdau zi;x. 6z87s.iy)5 vymm3vr,) iuo;xs to make exactly one swing per second? (That is, one complv m8xt)y zv6d;oiiy;ri.u s.)mbx5 3auaz, i7ete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth.1jn(g: epj6hi What is its period on Mars, where the acceleration on1epi j:(h gj6f gravity is about 0.37 that on Earth?    s

  What is the period of a simple sb36 kksko;0gpendulum 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 pendulum bob has a mass of 36a7. md5lz.xax5 grams, a57madz ..xla xnd it is released at an angle of 12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’hjy-0ozg*b ul2k56m)9v jo rps 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 pejkr)9omg5-u*h p6vlzj2yo b0ndulum? shortened by    mm.

Derive a formula for the maximum spee ifkvw/j 1:rm h,iu*(qd $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillate 4czi b512*+n pgrrruns at a frequency of 2.5 Hz. At it is released from rest starting at ab5 zc rn *ui+rr2png14n 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 every 3u.j,6u3ps7 t9svrhn x.0 s. He measures the distance between two crestsuv 3j.srxu s6,7ph9nt to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a f0noe hm-l0u9 srequency of 262 Hz and travels with a speed of 343 m/s Ho h-0msolu9en0 w far apart are the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHzn)6.nier v;wx :no sp u;:,tjq (kilohertz) and travel with aup:i6 o;; rs .x,)vet:njqnwn speed of $ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

  Calculate the speed of longitudinal b62dr1yftul tl3utvkp47p0q+4 1kizwaves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the 8 tz2 1wwbxbfa)n-s7kf:p 7r e6l 3pzcsame elastic modulus, but one is twice as dense as the other. In which rod will the speed of longitudinal waves be greater, 7wz8n 6ser)b l-1 fpax:3 c ztkb7fpw2and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apart. Ifbgrfk+5qjj2 e q- iv*:t-lwc8wyb.3q the tension in the cord is 150 N, how long will it take a pulse to wckej 5+-liqv 2bw- g:qfy.8 bqtj3r*travel from one support to the other?    s

  A ski gondola is connected to tor1vm0t-ua9ot gq/emq 1 -fu3he top 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 observed that it took 16 s for the pulse to return. 1 rq9tgteaq/ u01o u3fvo-m-m
(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 lbft rmj(*wbui9 zqq 3p3*4 1gsea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is the ocean at this point?g* i9 tj*p3b 3wmu q1lqbf4z(r    m

  P and S waves from an earthquake travel at different speeds, and this difs7r /,qo9mmuj2f mtbb*q6l 5i ference helps in locating the earthquake “epicenter” (where the disturbance took pl7bm9 /l26bsuoi*qfm5r mj, tq ace).
(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 wav k6xubn0, (ve( :kbsdge can be approximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is n(kd6 u:vs, bbxe(g 0kneeded 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 ap jpjkr84 z8,(b) the amplitudes, of an earthquake P wave passing through the Earth and detected at two pp8rk,azpj4j8 oints 10 km and 20 km from the source?(a)    (b)   

  The intensity of an eart 0vj/o*as;k87th lrf 6dp a7kshquake wave passing through the Earth is measured to be l 0pra7sjv;t7hf ako */6 kd8s$ 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 frequuw-lttc/ 0nwje b,myg1a+/rx:v :/ aeency travel through the same portion of the Earth, but one is carrying twice the energy. Whawe/ vut +:-mg1 bay/xl/0w ,cn :jertat is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same frequency, but on fhjq,i+80v4lf oe2 wsr)p *sae transports three times the power of the other. Wh pj+0 v)rq *2h4fseiosaw,l 8fat is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond )8cc*e k*s6aiwxo3 sa is observed to move up and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If ts8cwea)* xk *3s6aoiche ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 ,cnfh +np 2 qqo1.j*ozt 3vls8are 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 later. (c) In Fig. 11–36a, atvnosnf. z1p ,qt2c *3 8+ljohq 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 frequenccsq/*;f. hfiaxtz tg x4jt; +n11j;uuy, what are the frequencies of the fir.1t h+tg uinq 4*;;ajs; fztx/f 1xjcust four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At wh ifl7tg/ u a/gs1t6lw5at frequency will it vibrate if it is fingered one-third of the way down from the end? (T1faig7w g 5s/tu6/llthat is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loop u,fj/6 cjmol- /we5cbs at a frequency of 280 Hz. Name at least three otherl/j-cw/fo um ,6bec5j frequencies 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 frequboa2pi.g)w sr g. re8*lvx +;eency of standing waves is 475 Hz, how far apart ar;e)ixbpw8a.*r +r g.vg 2leos e two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 350 Hz, whawux hvkk741e6a d(so/t is the dkuxwk a/o7v6h1(es 4frequency of the fundamental?    Hz

  A guitar string is 90 cm lo5x up:1(cx ;id-opu..:pe utb naaoe:ng 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 tension of 520 N. What are the frequencies of the funda;a:bi.1d(:peoutxx -5 :o.unau ceppmental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, but b(l rmw5um)1rk1rkzht95 4j mv3 khu;it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed tob9(r3kt1) z 4h1hm jrku;m5w5mruk lv correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is suppo(: ky hin3qiqkuyx ,12sed to vibrate at 200 Hz, but it is measured to vibrate at 20,kn:h( y1i xk2iyq3qu5 Hz. By what percent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a xn bv6tvv,j4 f)m3z1 xsmall-amplitude mechanical 60-Hz vibrator. The strin v jz6x4vbn 1,v3x)fmtg’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 bedw o d)4e+e-.ht yzbe- adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how mhzeo4d)eey +-wd- b.t any different standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and * gzx .izk3v;g qf5 q m;l4q/9buxbky4forth 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 tobk 5uv 9lfqqz4ikg3.;m4*y xz gq /;xb 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 boundary withiq ta yq7.roymlk9k4/,n the Earth between two kinds of material y4,kqo . qtaklm9ry/7. 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 2.8 hk8 mxu l33o*;n3y8b :qcbuqym/s to 2.1 m/s If the incident wave crests mak3k8b;yxl: cobqnym uuqh *338e 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, densee/y63q2okprvrv lq pkx:79k 3 air. If the sound :ky3o7v9 er3qkrp 6/pql2xv k wave hits the cold air interface at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave strikes a boundary betwrc t g9zyte,zpztn j/ x319s1p yg59y5een two types of rock at ac pz/ten15gy,3t9 r591zzp y j9ysxt g 38 $^{\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 useroj6h9eeak x 319x6e rwwl+y*b’s manual, the dish has to ehy kal1bw99 * r+ew6ojxxe36be pointed in the direction of the satellite, but an error of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 25r z0nss5*q4 sq0 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 *4 5qqs 0sznrsknowledge 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 bum r4:urru pm(ke4)l,de yoc;uc;t0 p6yper has a spring stiffness constant of 550 kN/m Find the maximum compression of the bumper if the car, o) ep4r(ud6tcc0y kmu;yle:,r4 ;purwith 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 fipp .vsz8vc5 q7re net 18 m below, which stretches the net 1.1 m. Assume that the net behaves like a s8q5pv7 sv.cz pimple 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 place) feenyq6 -9sed on the end of a freely hanging spring. The mass then falls 33 cm before it stops and begins to rise. What is the nfeeye )9 s-6qfrequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring . ptrylqnd, (;vbz.qki+ha*3at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffness constanty tk;+i3zb.v rnq *.(qpl a,hd of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of coffee (diameter 8 cm) at just the right pace of abogzejh:o :f,l:ut 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the spez::,ehjfgl: oed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cmvb, qt. :nhl+jhtqc 0vk +6cb: from the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. Whc+bvcj.h +bhkqv::q ,6tln 0 tat will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t where x is 7 meis6a+bv9kj *r: btin meters and t in seconds.jtve b+r*isam9kb:6 7 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 frequencpr8z uhz7g xst/l.p9:y f. What is its frequency if it accelerates:gsz /z8up 7rt.pl9hx at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on-eq( ;mgu b;l/ er7rrd a lake. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the raft vibrates for a while. 7de;gr/;br( u-rlmeq
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a musical instrument are tuned to play at 397ccvd); a:uyy /aes c;2 Hz (G) and 440 Hz (ay7 cd /yv)cc:ua;;seA).
(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 xk lom d jx*v3hk*73*f v/w)thu:ps9htraveling 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. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater inlt3u7h k*:*sp9mw xhxfo/kv j)*dh 3v the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz,vz qobu 9g .ih5t3)cuj.d,d,1 g-it fh and the tip of each prong moves 1.8 mm to either side o1 gi)z.ufv uqghbchtj.,5-dt9id,o3 f center. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillar03fvx,i ykn-vz* v7k3 2ga gotes 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 placekznoiv,3v72a-yf rg* g x0 kv3d 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 -p eoh69decaao7f 3i 4attached to a ring that can slide without friction on a vertical pole (Fig. 11–5 di43c 9po h6oa-fee7a7). 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.i bw * 2po6q-ii2y1w2mud0cxo000 s — each one-way swing takes 1.000 s. 6p2o 1obidq-0wmi* i cy2xu2w
(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 directione/p :f2*.m cn,s, snonqqxo- v or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period of the ver , n*onf:qmscvqox.s n2-p e/,tical 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 gk3pv0tp/l fi hiy- o.3m w6la6 is stretched under a tension of 255 N. A pulse is generated at -3ip m0 k.p/fwh t66l3livyoa one end, and 20.0 ms later a second pulse is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a ske lje u7 9(x y37n+tn(z,ksivpring with spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillatn7se zxvke,i(k n9( 7l3+yujtions 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. g7fdhvuoy9 m2; mp+ s7The steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncfv 7u72d;sgompmy 9 h+ing 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 am/zst3 zg;*vs6 e zfc. plate as shown in Fig. 11–58 (which also gives the dimensions of the block). You push it sideways as shown, and then you let6 szs.3;gc m*z fetz/v 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