Give some examples of everyday vibrating objects. Which exhibit SHM, at erd di 438xpr 9oj-y4 x.cfe3zleast approximate 9j8iepdf33d. oerx z-44yx crly?

Is the acceleration of a simple harmonic oscillator ever zero? If so, where?nj /cfuu8+zm4pn zh/gjj+z7 7

Explain why the motion of a piston in an automobile engine is app+g gj*n/alcf, ue(hn 9roximately simple ha f* gcn/,g9(ju +nelahrmonic.

Real springs have mass. Will the true period and frequency be larger or smallersy :t5j as ,e,0jtsyf1 ety ,01tfjss ,5jys:a than given by the equations for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of i )9d*fekf +vyyidp2c.0lw1 -wkb9 c ma simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scale, and th -rgb.;gf6frb w;ql i3en is released. Describe the scale reading as a function o ggf-3w.;lfr6; birqbf time.

If a pendulum clock is accurate at sea level, zuilbv:13vgyca :*ats 9n67 p will it gain or lose time when taken to highnltacbu1 i3pvv*6syz79a ::g altitude? Why?

A tire swing hanging from a branch reaches nearly to the ground (Fig. 11–48). rr8/ hs8+gg632uxfe. qjjeka Horf+ha8/8j g. sjxekeq3g2ur 6w could you estimate the height of the branch using only a stopwatch?

Why can you make water slur3o3(l*+aduexft;s av/ bip/ cp ,a0osh back and forth in a pan only if you shake the pan at us/,(/ fdab+pov; 0t3crax*eua p li3a certain frequency?

Give several everyday examples ofw7.se aaz6nx-9 8plw fy4de1f resonance.

Is a rattle in a car ever a rcg5x3 pb1,fljr0z9 e cesonance phenomenon? Explain.

Is the frequency of a simple periodic wave equal to the freque1(6 gw 5k.duos7qr whuncy of its source? Why or kw6w(grs7do quu .h51why not?

Explain the differencaxtl9l*;j 8ctz/ b mz6e between the speed of a transverse wave traveling down a cord and the spej89 z6m l/*abcxzlt;ted of a tiny piece of the cord.

Why do the strings used for the low z) j5+ k,r 6fufgqbw/w 0k8q/tm)btpmest-frequency notes on a piano normally have wire wrap+zpj k 8f ),uwttbwmrfb)/ gmq/50kq6ped around them?

What kind of waves do you think will travel down a0 etcm vfj.q:z+.g 5ly horizontal metal rod if you strike its end (a) vertically from +ejmyglzc. 0.:t5vf qabove and (b) horizontally parallel to its length?

Since the density of aoi uoq1k;evvzn qrqh ol) +)-,-gn: ;rir decreases with an increase in temperature, but the bulk modulus B is nearly independent of temperature, how would you expect thz nvu:he )ng)o ;o qr1k-r v-qq;il+o,e speed of sound waves in air to vary with temperature?

Give two reasons why circular wate2 -uq7-fw9n 6 pfnvplir waves decrease in amplitude as they travel away from the source.l-qp6 i n9v2p 7nuwf-f

Two linear waves have the same amplitude and speed, and otherwise are identical tgenirt 0z+++, except one has half the wavelength of the other. Which transmits more energy? Byt +ernz+ t0+ig what factor?

When a sinusoidal wave crosses the boundary between75 djr s 48hfs:(ylfvl two sections of cord as in Fig. 11–33, the frequency dh7vflr: (4sjds85y floes not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, 2dvfen2 (bkz 1are there any places you could touch it with a knife blade without disturbing th ed 2nvbf(1kz2e motion?

When a standing wave exists on a string, the vibrations of incident and i6a+sty-df 6e reflected waves cancel at the n6d+6si-a f eytodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being0a fd81xg ixu2 transmitted from one place to another, how might we de2 u8fgx1ix0datermine whether the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, whao2qi/hm.gqljg;vf 4 d6 u v 5+2sd9zkzt is the total distance it travel2s2mhlguvqq +iz. dg5 ;d4o/fjzk 69vs in one period?    m

  An elastic cord is 65 cm long when a weight of ;db ze,dgsw 9f2ch/m- 75 N hangs from it but is 85 cm long when a weight of 180 N hangs from it. What is thebdm gc,-fw/ze2h s9d; “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg dril kc8l3sj6 1 ,p6jiumzver gets into the driver’s seat. If the car goes over a bump, what will be thep66u,1zlml3 8icjsk j frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs from it.tju) lxthjam ux.,c+24yd6 (w (a) What is the spring stiffness cou+ j.l2 u4d(cy,aht)wtx xm6j nstant $\approx$    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 Hz when a mass o9d r*e.+ a6jvj hfu.uvivt; ,of 0.60 kg is hung from itu. 6 vv.9orajt,udej+f;ivh *. What is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. 11–2 at times :jl7ss2smr f3for t:*k4q n/st = 0,t = n fq:sfls*trsr4/o:m k7s23j$\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 ;z0: zuwly-u iweb vibrates predominately with a freq0w u:y iluz;-zuency of 4.0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a spring vibrates with a frequency of 0.88 Hz. 4 *; ler*g nikdhvlq)) u7buc3When an additional 680-g mass is added to m, the frequency is 0.60 Hz. What is the value luq3kcr7;)*i dhl* vb4eu) gn of m?    kg

  A 0.60-kg mass at the end of a spring vibrateb zqddpb5 0 ;dyd.-(ebs 3.0 times per second with an amplitude of 0.13 m. Determbdqy;z dbb-d5ep0 (d.ine
(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 spe.4f*o -wemjr/, detc:v 6numw, xy3 qsed of a SHO half the maximum value?d6 smne / 4t*jmc,q 3x:uvy.ofw-rw, e$\approx$    A

A mass attached to the end of a wi-95 jbk,viqo/m8sw 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 stretchjf;remts e/*1 es a vertical spring 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 position again? /;jfme1etsr *   s

  An object with mass 3.0 kg wfxi -. u:gq6uis attached to a spring with spring 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 with a speed of 0xiw -g.uqf: u6.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compress the spring of a toy popve 9p/xqnt2a 1gun 0.200 m to “load” a 0.180-kg ball. With whan/2te av qp1x9t speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to i u9- 1jjeyp fya4c1ksgz11/h 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 weih11u1gz4jfsjay 1ck y9- /pith 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 equakv4b sd*/4l amtion x = 0.45cos6.4t where x is in meters and t is in seconds. Determinem*vd/k sla4b4
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equilibrium is the energy of a Swt obb2hq t;5k5;t 3wjf o13myHO half KE and half PE? ± b3b 13t okwy2;fqt;tm 55hjow   A

  If one vibration has 7.0 times the energy of a second,a q vuaifyj1g6p82l3xs0m-r * but their frequencies and qi26 mxuv0jsg83apy1lr f- a*masses are the same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light spring once every e 73 xz6s9t1 yxl6w/japd+ny w0.65 sy9 dj wz3+ 6n1ey xws7ltaxp6/.
(a) Write down the equation giving the pumpkin’s position y (+ upward) as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. y = (   m)cos($\frac{2\pi t}{0.65s}$)
(b) How long will it take to get to the equilibrium position for the first time?    s
(c) What will be the pumpkin’s maximum speed?    m/s
(d) What will be its maximum acceleration, and where will that first be attained?   $m/s^2 $

A block of mass m is supported by two identical pbsvm3g sci6w4g+* d/ parallel vertical springs, each with spring stiffness constant k (Fig. 1pv i cm/sdggw6*s +43b1–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38en 6rcd xdu 83*b2ib(esin6.5t where x is in meters and t is in8dcb2*r bud x(ei6n 3e seconds. Determine
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows two examples of SHM, labeled A and id*/j8a7yr1i g)kwqpB. For each, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on the end of a horizontal cttth*i;1i s2c .si)7,tf m ywspring (k = 124 N/m) is struck by a hammer, w7tcti,f s; 2csi). mhi1y*wtthich 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 u51xxy wh :39pvupd.k constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) witp5x19. phukdu xvy: w3h 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 connectea7gmme8f2t g4d to two springs, with spring stiffness constants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes a 0.600-kg block attached to a 4 +;wf.bjpsn k,xz.qe fixed horizontal spring whose sqbx;z4 j sf..n,k p+wepring 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 mass 65.0 kg jumps from a ncp/1,o+v zlnq - .ktohigh bridge. After reaching his lowest point, he povc-l qn.n+k/,z 1 otoscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrations in exactly5i1 zki ts3a7y 60 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 u h g5xv;wau0vio52*f swing per second? (That is, one comiw5vvah5f* g;u20 uoxplete vibration takes exactly 2.0 s.)    m

  A pendulum has a perioz,a--pu v q;ead of 0.80 s on Earth. What is its period on Mars, where the acceleration oaqv eu-a;z -,pf gravity is about 0.37 that on Earth?    s

  What is the period of a simple pe5jf epbw:e;k4ndulum 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 b3b wnsq6p w(t*ob has a mass of 365 grams, and it is released at an angl3b6q(sp wtw*n e 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 yt /s0lzzyt7/ b k39gb0.9930 m. If the clock loses half a minute per day, how should you adjust the lengthyt7byts gk/z 3l9z0/b of the pendulum? shortened by    mm.

Derive a formula for the maximum sp)kiyv 5pn88abn1b v: need $v_{max}$ 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 frequency of 2.5 Hz. At it is relv 2yxxa.i:ld1eased from rest starting at an aiax .:dvx 1y2lngle 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 thy1w+ zmw,qdpkm . l;8me bow of his anchored boat every 3.0 s. He mq p1mwl mm,8d; .+yzwkeasures the distance between two crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with a speed o7 fg0d xv40hnzz4)zaif 343 m/s How far ap0 zhf)daixv7z04zn4 g art are the wave crests (compressions)?    m

  (a) AM radio signals hae 2nzcicmmtwg 1d-eop( 5vb8em 6-7j2 ve frequencies between 550 kHz and 1600 kHz (kilohertz) and travel with a speed6jcw(7-b5e2 d mmn m2c-1epiozvgte8 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 longituvvh uy 4few.m;9xeoejg8; o-9kh o)7vdinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same e+th mhdkdtw, su5jcyfp( 0++(lastic modulus, but one is twice as dense as the other. In which rod will the hd0c(tj+fsuym+5d +h w(pk ,tspeed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 ufhilfk1w4:n) qlw m) z7d.z5kg is stretched between two supports 28 m apart. If the tension in k5uqm:fl )7)1.ln wwzz4fihdthe cord is 150 N, how long will it take a pulse to travel from one support to the other?    s

  A ski gondola is connl )j+b:qfn( 0ahwp,jk ected 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 its run, it bumps into the terminal and sends a wave pulse a+ ,(fjph:w) aknjb l0qlong 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 side of his ship just below tm , krz;1-e cusdr-1rghe surface of the sea. He hears the echo of the wave refleck ,d1rum1-er;s -zr gcted from the ocean floor 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- lq5f6qcsi )y difference helps in locating the earthquake “epsq5f yqc-6)i licenter” (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 b )i+mrf)+3m-twqx 6q5sqxg z iy a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes,+trzg xs6)3 m+x5 w)iqqfiq-m which actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the ampl1rs2f/ am51 wwha1wouitudes, of an earthquake P wave passing through the Earth and detected at two points 10m2f5u/aoaw rwh1s 1w1 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Ent5d7usl9rcxsl -7 vesc9xw:4/g wa: arth is measured to be w9lwx4t75 gce :9xn-cds/ sas :rlv7u$ 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 fr5qda 39(en yta)7 yomsequency travel through the same portion of the Earth, but one is carrying twice the energy.39) tn5e( samaydoq7 y What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretcn :q +oq( z2u i wwx-sr,xslc:o)*8 ebs0avod7hed string have the same frequency, but one transports three times the power of the wo,-(suszr 7x0qew+ova c2doxb )nl *:8q:isother. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move up and leax,g8-lpb68b sko 1down 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 does the bug’s maximgboxk6l81l8, sp b-eaum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each other. (a) Sketchw; hhe 6cnc93zjzy o9( the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments later. w3 c99o;zc6ynez hjh( (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 ail ;5dauqirx h*w0x0 2t 440 Hz as its fundamental frequency, what are the frequenciesx u;id05w*r 20lh xqai of the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what frequency will it v(rc0s 1a f* jlwm7+jwxibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of the string vibrates as a standi+frasw (jmj710xw lc*ng wave.)    Hz

  A particular string resonates in8aadoh ,4ja+ r*+ bzxv four loops at a frequency of 280 Hz. Name at least three other frequencies at whicbaaxjv*a o4hz d8,+r+h it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92a7+v*q5 6 uot) m9oju)ekvifrm/s If the frequency of standing waves is 475 Hz, how far apart are uu9re)kv*6 q7mj )iva+foto5 two adjacent nodes?   m

  If two successive overtones of a vibrating string are e,: i04z;n sfu)4g3qjvz0lu icc9map 280 Hz and 350 Hz, what is the frequency of the funmvia),iq u3 jl;9c4z:gcez0s fnpu 0 4damental?    Hz

  A guitar string is 90 cm lo1m dv,amxvg zj;ngo6na)7kj9py +y72 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 fundamental and first n+ ;)j7k1 2mmoavn6y apj9gd g 7,vxyztwo overtones?    Hz

  A particular guitar string is supposed top2e t3s5 f3wts vibrate 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 thew5sp se3ttf23 frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is vewzd; z;lvtr4)9m 13jwibw1 supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should t ) 1dzwezt41vrv m9l wwj;i;3bhe tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is ath fz72bnlvd)u h ebzd.l/ *g:9tached to a small-amplitude mechanical 60-Hz vibrator. The string’s massn2 z/*.b :l)dvze dhlb97fhg u 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 di,wv1w;vjf fte) g(cl silqv98;9g1the string may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by v9lq1i jevfgw 89)wc;di (;lg svv t,f1arying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at just the ri0*/jzmc7pqc l*fmj+5m5w qrfght frequency, the water alternately rises and falm0qp5m7/fjz *qlfcr+5wjm *c ls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave travel;ewnt 2 uxc++pvse3*u:)/3ck llk xpzing at k.0 km/s strikes a boundary within the Earth between two kinds of material. If it approaches the boundarypxt s )3cx ul *lv;zn+e:k2p+e3ukc w/ 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 undkzvrveh.(:d h9ni+iz+k7ig . erwater “shelf” where the velocity changes from 2.8 m/s to 2.1 m/s If the incident wave crriih:khn 7 vgz(+e.z d ki+9v.ests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air when it hits a layer of cold, dense air. k/ 8*k3b y2y rez,xkwxIf the sound wave hits the cold air interface at 8yzby*wrk/2 kxe 3 ,kxan 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 earthquakpyda38qjnr9)0ewso yvo u*y / bi(i38e wave strikes a boundary between two types of rock at a 38/o8p ydsvn iow(j e303biy 8)ayqu*9r $^{\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 ;pvtli7 cfpt61m6qeb :h1e*i manual, the dis thmv1ie7:q6i6p 1eplf ;tcb*h has to be 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 250 km and velocity 750 km/h trqn,4 1 iqg:d*r 1,ato sxmryh8avels across the Pacific Ocean. As it aqo811 hdq4 n, mt,:gsaryr*ix pproaches 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 attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness constant of 550 kN/m Findg t ietsyw-4r-0l96p c the maximu0eicsg 9-rwtyt4- pl6m compression of the bumper if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps fr4m9v*x5sv/7+y ddn ,xk:edcx csue/e om a window to a fire net 18 m below, which stretches the net 1.1 9yxs x : kvedv5s mue+dc c*4xdn/7,e/m. Assume that the net behaves like a simple spring, and
(a) calculate how much it would stretch if the same person were lying in it.    m
(b) How much would it stretch if the person jumped from 35 m?    m

  A mass m is gently placed on the end of a freely hangingepd.c 3kwoj7 / spring. The mass then falls 33 cm before it stops and begins /j.pe3w ok7cdto rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge sv1q+. wp, )xtbu bka0dpring at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is ) .qd0vtua1b+ bwpxk,the spring stiffness constant of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of coffee (diameter 8 cm) at just thl qs f,l+cs;v1s1kail3-q 1xue right pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to;xv11lc+i u aqls ,sf3qs lk1- spill over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certai*rpozjs6q ws ;2t- qd0n groove 10.8 cm from the center of a 33-rpm phonograph r ; q*wtp6zd0s-2srqj oecord have a wavelength of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrat hz86+o rnjyipn+8 zu,es according to the equation x=0.650cos7.40t where x is in meters and t in seconds. Dete y+zp ,oujzhn6+8i8rn rmine
(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. What istd +b qupf2yts5-o: 7v:goqj d 3id46a its frequency if it accelerates at 0.50g (q ugdji6q of3v5po-:dby4sd2t+a 7:t a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a.rwyts ,3se5 ;6p cc6 qyo.1aydmdim; 75-kg man stands on the raft, it sinks 4.0 cm deeper ip. s.y1,56rccsq3;d ymi dtyem awo;6nto 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 instrument are tuned to playv2ywk:po cbowv+mzay. )w7 ;* at 392 Hz (G) and 440 Hz (ywvw opk)y mbo2;7* vw.z+ :caA).
(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 doa+gzc q ejq.t*mson:gl3ry8b2-/n5 qwn the stretched two-part cord of Fig. 11–33. Determine a formula (a) for the raz3q2gt .c-ylaq/jq8r*nso +g 5 :ne mbtio 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 vuw;+,) mk mer9cgnn,Hz, and the tip of each prong moves 1.8 mm to either side of centu+mcw9g) m ; rnev,,kner. 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 siu3r :).t1b+ofts q xhu;pkp-x/ wi-wmmple 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 pewk)xr: u .pti1ophw/3m+u- t;-bfsqxbble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that end is attached to a ring that x*u dspp)92c1heza)q can slide without friction on a vertical pole (Fig. 11–57). Depx*pa dc)s)9h 2e1zuqtermine the wavelengths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a per 2zw)llqhxq2 p:48r rsiod of exactly 2.000 s — each one-way swing takes 1.000 s. qw r2h:zs4 lxlr8q 2)p
(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 -y+2rwemdb u /ebq.t1l4o:p dor can 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 period of the horizontal swings+w b e- rddemy 14b.2luqp/:to, 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 unde ou)p ra3b4vaj,er80e r a tension of 255 N. A pulse is generated at one end, ande ra eur)b ,v4po8j03a 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 stiffnn4e pcybh d:85s*r 4imess constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillations that will allo e 4h8yprmb5*isn:4dcw 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 si; kq1isz51si teel 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 perio 1sk 5zisii1q;d of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (which alsot aw,9baaln 43 gives the dimensions of the block). You push it sideways as shown, and then you let go. T 4aa,w9bantl 3he 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