Give some examples of eversy83339a3kp ne-k bfy0vvxhe yday vibrating objects. Which exhibit SHM, at least apprskf k33he0vyn3xay8 e v9-3pb oximately?

Is the acceleration of a simple harmonic oscillator ever zero? If so,6(wr.xzgih x 10ayg) g where?

Explain why the motion of a piston in an automobile engine is approximately d,1z+:jeq vzosimple harmonq,e oz +d1v:jzic.

Real springs have mass. Will the tr8ut:3gbo 1 kka2szd;oue period and frequency be larger or smaller than given so3ubgd: 8k zota1k ;2by the equations for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed ofg;7u .av w9qsf a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring s/3 rf)fw)7 +slcesst rcale, and then is released. Describe the scale reading as a ff ))rf3c7eltr+s w/ssunction of time.

If a pendulum clock is accu,/pa3 k h6 za pl6k7r1t0c(etccnfdu/rate at sea level, will it gain or lose time when takenectt/ ul rzd7hc6a(,nk/ p1p06fck3 a to high altitude? Why?

A tire swing hanging from a branch reaches-2 hu x6b.o.g zxbkxx0 nearly to the ground (Fig. 11–48). How could you estimate the h.xu o x6b-xzhgx2kb.0 eight of the branch using only a stopwatch?

Why can you make water slosh back an.0xeue bqnofw9.y 9w6;ux4 o cd forth in a pan only if you shake the pan at a e9;oxc 6yenfb 09 owu4uwx q..certain frequency?

Give several everyday examples of y :yd14 bz xm:ck5fz2g/bz2eyresonance.

Is a rattle in a car ever a resonance phen85r k0,ifyw-kdizvp1 , cfx1 :oxzqf+omenon? Explain.

Is the frequency of a simple periodic wave equal tol (x9y9c7ubq g the frequency of its source? Why or why not9(uxglqyb7c9 ?

Explain the difference between the speed of a transverse w;0ype pu*4 elrt i,ll2ave traveling down a cord and the speed of a tiny piece of;l0u *4ie ppyl,r2tle the cord.

Why do the strings used for the lowest-frequency9nso f2svrz xzd- y4() notes on a piano normally have wire wrapped around t2oxz sf 4n)(zyv-sr9dhem?

What kind of waves d6g.wtoeh 4sk*rc; 3vd: 9k2hn )q57jb sf frajo you think will travel down a horizontal metal rod if you strike its end (a) vertically from above and (b) h:75fn9tqfs r4c; o e2vjwhdkr hk a* s36.bg)jorizontally parallel to its length?

Since the density of air decreases with an in ;w7/fw xqq *lhs3h2nmcrease in temperature, but the bulk modulus B is nearly independent of s/*hmn7qxww 3 lqf ;2htemperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in amplitude as thrszn-e)n0m ctelk/:/:jp zy + ey travel away from thn+z s k-tezl0/ cne:j ):ryp/me source.

Two linear waves have the same a7 b/aus sjf5 u2w sagnc),h;1 a;gah:implitude and speed, and otherwise are identical, except one has half the wavelength of the other. Which transmits more energy? By what)5ag;1a ; ,n/swhjicssh7baag 2 uuf : factor?

When a sinusoidal wave crosses the boundary between two sections of cor8i.x; lb81r xbm( efvsd as in Fig. 11–33, the frequency x(brsmv1.b;f8e8 lixdoes not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there any places ys .+pd*gzk c4pou could touch it with a knizsg. *4p+dkcp fe blade without disturbing the motion?

When a standing wave exists on a string, the v m,z)1utf hn7eibrations of incident and reflected waves cancel at the nodes. Does this mean that e1m) h7ntu efz,nergy was destroyed? Explain.

If we knew that energy was being transmitted from o57adstdl l7l )c 3pg(xne place to another, how might we determine whether the energy was being carried by particles (material b7s)53 lpl dcxgla( 7tdodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what u7n4jdy krt*1b+csd0gw8 w4yis the total distance it travels in one 4s7 4yrb8*nu +0wwy tdjg1kcdperiod?    m

  An elastic cord is 65 cm londueg;x,*y l*o09qy4mdgprn 27 zw ct8g when a weight of 75 N hangs from it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” constant k of this elastic cordr z8 u 70yg92 gnex4pdtm,* *c;wdyqlo?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg drhqw *dfv y;+j7iver gets into the driver’s seat. If v7hwq; *+jdyf the 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 h us3xeqv6t3q f. 80jyw6y;pylangs from it. (a) What is eq t8pfys33vwyy6xulq .j0;6 the spring stiffness constant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates withk ox5yh quv/m( qw+l-ua1jc95 a frequency of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency if uh5lqku9v (/-5wcoy m q+xa1j only 0.38 kg hangs from it?    Hz

Construct a Table indicating the positgt/: *fqupgf :ion x of the mass in Fig. 11–2 at times t = 0:ftgup/gq* f: ,t = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

  A small fly of mass 0.25 g is caught in a a ;oz-nnjl5j q 0a6v:kspider’s web. The web vibrates predominately wiaql v:n6 05-nazjk oj;th 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 vib tm7 9b *3a*56bkxgbn fml4t0q e7pbrerates with a frequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 Hz. What is the value of37e6nkelx ptbmt g5f0m7b b*4 *9arbq m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per second with angjv)y )m 4 d5riyx *ynhgye v7q3;3x-z amplitude of 0vyn7g;e4 * jg)yq3 3yd-r )xx5zhmyiv.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 fro.kka rt h niai2,86n0bm equilibrium is the speed of a SHO half the maximum value? ,ka kt6ira2i8 nnh.0b$\approx$    A

A mass attached to the end1r e x9o.-1zpb /c6wvkhelcp. of a 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 spring 0.315 m. If the spring is stretog3l, x/2v6uik qrux ,ched an additional 0.130 m and rl,3ui/2 xuqv o grx,k6eleased, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with cf 0ya x38bn9/swhq-espring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is moving witxwyc/sf8-9a nq0e3 hb h 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 nmg*..cvm(s/jm f ks2 the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will the ball leas/c2j*k(.g mm.fmsv nve the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to oneht +pd ( 0ya2;9fiy:fqedvr* e 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 sprirhav9 ; (p*tfe0y2ie+qyf:dd ng 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 = 0.45cos6.4qtg ; vlw:t.)et where x is in mete).t e :lq;gtvwrs and t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equilibriuk8mxlr0,q9* i:8zhywmcdq +gm is the energy of a SHO half KE and half PE?l8 q m8rxd ig09m+yh:zc wk,*q ±    A

  If one vibration has 7.0 timeso:: n7vno ae:sc:;r ecrv5a4uow2 r p8 the energy of a second, but their frequencies and masses are the same, what is the ratio of their amplitudes? 8vaco: ; :n7eacouve:rsp nw54or:r 2   

  A 2.00-kg pumpkin oscillates from a vertically hanging light spring oncv6hb.8otxt4cy)uqs a; p f t+4e every 0.65 s. t 6t.qpa;4f4+hx8 scybvo tu)
(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 su8 izb ( icyh1lt(b3r5opported by two identical parallel vertical springs, each witht co5bi((il1 y8 zb3rh spring stiffness constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin0cba :f1( ymrs6.5t where x is in meters and t is in seconds. D rmba1sc f(0y:etermine
(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 eac71 2ec0pfiqahh, 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 = 1245rwv4t- l rm(etg nw-, N/m) is struck by a hammer, which gives the mass anrt54ww, lnr-(v tm ge- 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 azf3avsow (1od 5fnnj4 ,1ydb /h21posn amplitude of 28.0 cm when 0.260 kg hangs from it. The mass pasjpz1nob 2dw o(h3f asf,4yd1/n15v os ses 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 vsoed4 v .p,2z yo4m:qconstants $k_1$ 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 a0l /l hg1 3j(x9y3k1m ttwvfma 0.600-kg block attached to a fixed horizontal spring whose spring stifjm1( atkmfy3hglw9/0vx l31 tfness 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 kgrww) v3jcw7+.f( nc zg 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 bewjwgfc wc.37n(z+)r vlow the level of the bridge. Calculate the spring stiffness constant and the unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrations in exactly 60 n9 q8v9dnw4s1 vno4k - 3 bdmd5occa2es. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly one swing per sv f3 jurfx:g84econd? (That is, one complete vibration takes exactly 2.0 s.:rj 8vf3u 4gxf)    m

  A pendulum has a period vjxe za2935 zxnx3tl1of 0.80 s on Earth. What is its period on Mars, where the acceleration of gravity is about 0.37 that x2n3xjl1ze 9zv3xat5on Earth?    s

  What is the period of a simpl1qgxlcc3) vynfh9t*f 5j* ph4e pendulum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum isxxq1,s57wiq p 0.760 m, the pendulum bob has a mass of 365 grams, and it is released at an anglex s17 qxiq,5wp of 12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’s pendulum has a length of 0.9930 yb-g ,t,d q4n aixn18tm. If the clock loses half a minute ngybn xti1dt4 -8,q,aper day, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for th(,vsrv y (1jkle maximum 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 l1 qt20oc +jqtu3e pm(frequency of 2.5 Hz. At it is released from rest startingjtel(q 23t+0m qp1 cuo at an angle of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests pass the bow of his anchored bopvv;jt/p 91rw ows t(+at every 3.0 s. He measures the distance between two crests to be 6.5 m. How fast are the waves trave jp(/1;v 9trv owpwt+sling?    m/s

  A sound wave in air has a freque(ogjyj/.d b d()e os:dncy of 262 Hz and travels with a speed of 343 m/s How far apart are the d(jeyds(g).j/b d o:o wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz 49 0lxmh6 ,fjkd 7xhdkumv9.y(kilohertz) and trav m0 ,uxxhl7 h6v dmk4f9d9.yjkel with a speed of $ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

  Calculate the speed of lonsr h.wpjva.h a8s25 gwhaq l-y29h)k;gitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the -s3,q; jc ehxr:ego,ysame elastic modulus, but one is twice as dense as the other. In which rod will the speed of longitudinal waves be grgjcqr3,oe xs,e- yh:; eater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 myf(w+f5s ;czn,dh u1pete*a2 apart. If the tension in the cord is 150 N, how long will it take a pulse to travel from one support to the othfnd zfp1,yeeth* wca;u(s25 + er?    s

  A ski gondola is connecti gd*v+ vz tnc7j4cw8 ,thjaf+)y4k8zed to the 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 it8*d) 4at znwvvk4y+tjccif8,z gh7+j s 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.
(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 sidebh6o7qwjo.w,l .ab 3 0vt:vwn of his ship just below the surface of the sea. He hears the echo of the wave reflected from the ocean flow3jq bwvt .hlbw0no7:v,a 6 o.or directly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at different speeds, and this differaj xs *n4vcdmkmo: 57.ence helps in locating the earthquake “epicenter” (where the disturbaa.dmo7 45 jk*vcs:mnxnce 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 ss6ok(-mi jv, z d3q1waurface wave 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 amplodq-jzk 3i(, maws6v1 itude 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 inl-(6 o(tmji gntensities, and (b) the amplitudes, of an earthquake P wave passing through the Earth aj n6iot(( glm-nd detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passin 8fojxi0i .sn7g through the Earth is measured to be jnfiis70.8xo $ 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 tdzoonb1qs-o7 tk:m:r:vx,. :, jaz tphe same frequency travel through the same portion of the Earth, but one.t kaqo omjd:,7sz:v z, :xntbo :1r-p is carrying twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same frequency, but oj;13ozpibk4 a; wglt,5kqkg5ne trk g j5qz;b 3ga4twp15o,;kiklansports three times the power of the other. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observiyo9.fvmd m*vh m(h z0:0r ax1ed 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 what factor doe o fmh*.zm00a 9mryidx(vh1v:s the bug’s maximum KE change?   

The two pulses shown idg q / t(0:7mdcjm(jpfn Fig. 11–52 are moving toward each other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the sh0f7(/:m( djdgq mt jpcape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundamental frequency, what are tcstvo4 uhnz h5k0z6s7+0a l j4he frequencies of the first four harmonich4c s 40nvz+ua st7l0oz56jhk s?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz whenco -nsypatpsg;4 -6s( unfingered. At what frequency will it vibrate if it is fo a;n6 4gpc ss-t-ps(yingered one-third of the way down from the end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequency of xzrfrvrr/; rvl4(z/; 280 Hz. Name at least three other frequencilz;z;f rr4/x rvr(/vres at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a strb2v9qol02bd cing is 92m/s If the frequency of standing waves is 475 Hz, how b2q2o9 v bldc0far apart are two adjacent nodes?   m

  If two successive overtonyq7yy1rck ,e/es of a vibrating string are 280 Hz and 350 Hz, what is the frequyky 1c,yr/7qe ency of the fundamental?    Hz

  A guitar string is 90 cm long anlv6al:r-h ;f0kcl*kjw8 i1phd 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 jh6hf:* lw k8pa1-v k ;irll0cfrequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vk7*xe m d-9qqj hb/n,sibrate at 200 Hz, but it is measured to vibrate at 205 Hz ,kh*-jxqq7e9 / mdsbn. By what percent should the tension in the string be changed to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hz, but it ikh/vg :t3 n9svtau hb( b(,o3zs measured to vibrate at 205 Hz. By what percent shoul(ha(bvs,t3tngko3u/h b9 zv: d the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string ifdv*n )4f w9ats attached to a small-amplitude mechanical 60-Hz vibrator. The string’s mass *9dvn4taf wf) 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 by moving the pulley. 0f 9bf5)pz3bvf (mrznIf the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying L between 1nmp0ffbz v b53r(f9)z0 cm and 1.5 m?   

  When you slosh the water back and folvjb,(z;g + ybwrzx,6rth in a tub at just the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the sp(6xr,bwlv +z, zb;ygj eed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundaryq69j fg;, pe9 v/e;abfy vhev3 within the Earth between two kgqva e93h,e/;yp 9f6;jevbvfinds 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 underwaterw4vy tzmr 7h-9e3fq v*7drx/b “shelf” where the velocity changes from 2.8 m/s to 2.1 m/s If the incident wave crests make a 34 f7/ 9xyvq zhwv4b*dr7t-em 3r$^{\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, densjfn/gg/r 4dixf4- 58shh ee1le air. If the sound wave-j/sge4 4r/ xhd5ng8hei 1f lf 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 wak*cpp8fsw6 0l ve strikes a boundary between two types of rock at alp8w kpsc6 0f* 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 user’s manual, n f- x-/mzp(m+pznd n2the dish has to be pointed in tnm-(xpndfn-+z 2/pzmhe 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 250 km and vez706czo + 9oumlc uwo6locity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease zoum woo676 z l9cu+0cof sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing 03ec+ bv3 ;znf6iwzr dcar bumper has a spring stiffness constant of 550 kN/m Find 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 (appre6c;n dwf3r+i z0zvb3oximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m below, which stretches t 5 2j enrtq4vul6.1s;z wouhr4+rb5amhe net 1.1 m. Assume that the net behaves like a simple spring, and b62l s4w t5jmzuq1n5r.u; rh ro+4vae
(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 mass ;c1n,yzeb qlr7ujq.w *; u-mg then falls 33 cm before it stopsq- bcgj .1 ;eu ;q7yzmnurw*l, and begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 mzqxy:kynz-xg 7f+/i4 /s (Fig. 11–54), compressing the spring 5.0 m. (g x7i +zyq/x4:-nzk fya) 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*oo1b gp*mv 2al uya)() at just the right pace of about 1 step per second,u p1)**l(mv o o2aygab the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certaiogh5x8:.qpm pn o6+utn groove 10.8 cm from the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequency of the sound emitted? :5mptpon gx qu8+6o h.   Hz

  A 2.00-kg mass vibrates according to thie juvq ujiba u+7ld4 /v4q-j;5n.qt)e equation x=0.650cos7.40t where x is in mete +u.l4tqibenuq-j v dqijuv5)/;74ajrs and t in seconds. Determine
(a) the amplitude,    m
(b) the frequency,(round to two decimal place)$\approx$    Hz
(c) the total energy,(round to one decimal place)$\approx$    J
(d) the kinetic energy and potential energy when x=0.260 m.(round to one decimal place) PE$\approx$    J KE =    J

  A simple pendulum oscillates with*84 )q1i za6oi n+p choc uy+6x:yooqi frequency f. What is its frequency if it accelerati+*c oh1q684zcn uy) i q+ ixo6poyoa:es at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man fsa::ga;djxsx, .jl5kan. s7 stands on the raft, it sinks 4.0 cm deeper inx s,7xa5.k l a. gs:nja:;dfsjto the water. When he steps 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 musical instr233 *zg m8:ecf0kmgf.g acukzument are tuned to play at 392 Hz (G) and 440 Hz (A). kg k3*c m20:z cg u.f8me3fzga
(a) What are the frequencies of the first two overtones for each string? G : $f_2$=    Hz $f_3$=    Hz A : $f_2$=    Hz $f_3$=    Hz
(b) If the two strings have the same length and are under the same tension, what is the ratio of their masses ($m_{\mathrm{G}}/m_{\mathrm{A}}$)   
(c) If the strings instead have the same mass per unit length and are under the same tension, what is the ratio of their lengths($L_{\mathrm{G}}/L_{\mathrm{A}}$)   
(d) If their masses and lengths are the same, what must be the ratio of the tensions in the two strings?   

Consider a sine wave traveling down the stretched two lk je *)wri5ihu);(tic9e4ln-part cord of Fig. 11–33. Determine a formula (a) for the rati)iwj(elct 94ki* )re;ul i5 nho 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 in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the t xniezqemz-8f du+n2oy. 10)pf ahu 7i/ *h/rkip of each prong moves 1.8 mm to either side o-.ofa d *7uher x0y/n1 n i/h+8k z2emipfq)uzf 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 harmok, g3usorgp b2w)r,x/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 a pebble placed there (Fig2/sxb,)okwg, p rrgu3. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” en7 pa5o;ot:r* lc/*wr1wh,fc rzkz 6m xd if that end is attached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine thewc ;hr*l/xw m6p,f57roza: c*o1rzkt 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 one-way swxm-,z ege ip.,ing takes 1.0z ,p-i, gem.xe00 s.
(a) What is the length of a seconds pendulum in Austin, Texas, where $g=9.793\mathrm{m/s}^{2}$    m
(b) If the pendulum is moved to Paris, where $g=9.809\mathrm{m/s}^{2}$ by how many millimeters must we lengthen the pendulum?    mm
(c) What would be the length of a seconds pendulum on the Moon, where $g=1.62\mathrm{m/s}^{2}$    m

A mass hanging from a spring can oscillate in the vertical direction or i(- a0erpcqrp.qg -, rcan swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period of the vertical oscillations or the ,r.0q(- e agrqr -ippcperiod 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 uuar) b*6 ba.jvx4cw.)7cvbl is stretched under a tension of 255 N. A pulse is genera)uba6brc*bw7x)jv4.l.v au c ted at 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 spring with spring stiffne 7)orz8kgojem;49 j dyss constant k. A penny of mass m is placed on top od 4)rky;7 emzgj8o9jof 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 s (:(7r bzmob,xx26ajrdk xl:rteel 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 isxxzo(r:,:lr2jmb 7r k6 a x(bd the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on lhxa kld3mwq9n2pi 7r5446tya plate as shown in Fig. 11–58 (which also gives the dimensions of the block). You push it sidewaysr t7mx h64la 3q li9wy25k4dpn as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this vibration, given that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz