Give some examples of everyday vibrating objects. Which exhibit SHM, at leas,.,wu,ehhn xo t ap.h,,uw e h,xnoproximately?

Is the acceleration of a sihd2k2nd. 4esyfxam-4/ pmwm 9 mple harmonic oscillator ever zero? If so, where?

Explain why the motionjsj yw m2 egow72(d-.k/gx9yp of a piston in an automobile engine is approximately simple 7y( j w9yxds./k o2 pw-2ggejmharmonic.

Real springs have mass. Will the true period and frequency be larger or smaller k twxb 3ohr: n)w6v:+hthan given by the equations fw:o:hwr nb36 h)t k+xvor a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the mav1o)fr7/ww3 f sh6xzy ximum speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attaa1c0(ip( xoi qched to the hook of a vertical spring scale, and then is released. Deso(ip1 i(0c qaxcribe the scale reading as a function of time.

If a pendulum clock is accurate at sea level, will it gain 1)pbm,ksu+9hr35p q h zmwav )or lose time when taken top,m+sk9 b3am5)vzruw)qhh1p high altitude? Why?

A tire swing hanging from a branch reaches nearly to the grouinauin p5/hc2q8y5 u/ nd (Fig. 11–48). How could you estimate the hipi cna /nu8qy2u55/height of the branch using only a stopwatch?

Why can you make water sloshj,(t gcj7:pbp back and forth in a pan only if you shake the pan at a certain fj7,j (gc b:ptprequency?

Give several everyday examples of resolayj o/ij /v+1nance.

Is a rattle in a car ever a reso .hcay 8pj3tf9xxs0: knance phenomenon? Explain.

Is the frequency of a sim;hz gf i,njiv2klwy )uof p 4b)-*8j6zple periodic wave equal to the frequency of its source? w2i y)v6)i*g jlh;,j -fnf8 kozbz4pu Why or why not?

Explain the difference between the speed of a transverse wave traveling dow 2n26qaihn.au n a cord and the speed of a tiny piece of th62n.au h nai2qe cord.

Why do the strings used for the lowest-freg5uv4y3+poiv osf:8jd pp d 07quency notes on a piano normally have wire wrapped arouno7v+dgpo53p py :df 840isjvud them?

What kind of waves do you thiboryftu/l5nb ). 7s*nnk will travel down a horizontal metal rod if you strike its end (a) vertically from above and (b) horizontal7y u/ .rn)lbobf 5*stnly parallel to its length?

Since the density of air decrea oe 9+2a61do dhqkqfh 8evs1rs* /l;aases with an increase in temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the6eq1; sfor+k9dv8dqh*aa /1a lo2 hs e speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in amplitude as they tr1y:9 tvoho b6gg(-s(pcm k( dvavel away fromt9 :s-kdc(govyp (o6 m1b vhg( the source.

Two linear waves have the same amplitude and speed, and otherwise )p)xmqf6nix . 0nd5q-4obhc* /ld ynaare identical, except one has halficx6nxnbadn0 yol4*d -m) q )f./hq p5 the wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sections of cord as in Fy -z.x s,)7eknckeu,nig. 11–33, the frequency does not change (although the wavelength and y,cnx 7, e-ek)zunk s.velocity do change). Explain why.

If a string is vibrating in(p no fq;evm01 three segments, are there any places you could touch it with a knife blade without me pv0(;qon1f disturbing the motion?

When a standing wave exists on a str85i,i cqltt2apevlnig2m- i( 8bey7)ing, the vibrations of incident and reflected waves cancel at the nodes. Does this mean that energy ea 8byi)5qlmpi tgn7li,v(-tci 2e 28 was destroyed? Explain.

If we knew that energy was being transmitted from one place to another x q(xes0d 6 l/b6oa-t)pkzx,mttl7m +, how might we determine whether the energy was being carrxtt +-7)ldl ,6x/e0t m6(kobzspma xqied by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 qtej;te nx .8;m, what is the total distance it ;8; tx.t eqejntravels in one period?    m

  An elastic cord is 65 cm long when j;12h9bzwvgna 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 cv2b;z9jwn1gh ord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg driver gets into 7weq -fvzt2v:the driver’s seat. If the car goes over a bump, what will be the frz tfv:v7wq2-eequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs bqijg)hho (-qs8s* v (from it. (a) What is qhs v-)h ((*sobj8qg ithe 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)qzvs .8mst/3h6 ag ww Hz when a mass of 0.60 kg is hung from it. What is its f)3smqw.w hsav8t /6zg requency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. 1f8oygo.+w tj -zfah+c4r2b09dla e5 b 1–2 at times t = 0,t f24-9g t+h.dzaab+oof5byl c r 80ewj= $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 caugu2br/5k ,jmck ht in a spider’s web. The web vibrates predominately with a frequencujk2 bc,r/5mky 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. When an adw) 4ikxzk(q my ho(75qditional 680-g mass is added to m, 7m(q(x4k 5hyziq k)o wthe frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0bi3 rd y ,zuso8fb7* n+w;vks3 times per second with an amplit8 odb sz+3,rw3;f b7*uskinvyude of 0.13 m. Determine
(a) the velocity when it passes the equilibrium point,$\approx$    m/s(round to one decimal place)
(b) the velocity when it is 0.10 m from equilibrium, $\approx$ ±    m/s(round to one decimal place)
(c) the total energy of the system,$\approx$    J(round to one decimal place)
(d) the equation describing the motion of the mass, assuming that x was a maximum at x = (0.13π)cos(  πt)

  At what displacement from equilibrium is thewme2ukc9vjm. rxpa y2/6 gp 3; speed of a SHO half the maximum val62p;p/ vejg2uw3r9may c . xmkue?$\approx$    A

A mass attached to the end of a spring is stretch c.m5cvgxq(z9 y6huo6 ed 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 sprinmi5 ;2 om:wl*gsq l5ays x-tz3g 0.315 m. If the spring is stretched an additional 0.130 m and relxa5g tm;ow*5lml3 s- iz2yq:seased, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is atta qjm)u)qzvidu -b03oo5 :x+bvched to a spring with spring stiffness constant k = 280 N/m and is executing simple h:u 0o d xm vb3)qb-+qov)5uzjiarmonic motion. When the object is 0.020 m from its equilibrium position, it is moving with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compress e6 2jhab+za 6;a.ptghthe spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will the ball leave the 6; ha aeh+pjta.z2gb 6gun?    m/s

  A mass sitting on a horizontal, frictionless surface is att 731np/( m zcsdzi.jouached to one end of a spring; thezz7( /npsoij.dc3 u1m other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, the mass experiences a maximum acceleration of 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 = 0.45cos62c ( zodu8 eq 88z9onvy62tpap.4t where x is in meters and t is in secondspoo6c9 ta8zv 228npudz(8eqy . 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 eq2um9uqcu 93p4 a py0fauilibrium is the energy of a SHO half KE and half PE? ±30y9 mf9ucpu uapa4q 2    A

  If one vibration has 7.0 times0(lu ca5xwt jm d5cllo l1,09jhbz-n4 the energy of a second, but their frequencies and mdjlb9j4mc1x50-z n o,wal l (culht05asses are the same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light spring once .dgm/ ow3ds-bevery 0.65 s. w .-/mdsb o3dg
(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 bdzx(8 uv u-ts-y two identical parallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What will be the frequency tduz- 8(sv -uxof vibration?

  A 300-g mass vibrates acco6amdq.n/:vf wjjx3* m ttl2n4rding to the equation x = 0.38sin6.5t where x is in metjj mt:m6xd.*2 4qanwl vt3f/n ers and t is in 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, 0 nzs2 77rev- lqiujh3labeled A and B. For each, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on the end of a horizontal spring (k = 124 N/m) is strqmzehu c-/;p :uck by a hammer, which gives th /:qpu;-ehz cme mass an initial speed of 2.96m/s Determine
(a) the period and frequency of the motion,    s    Hz
(b) the amplitude,    m
(c) the maximum acceleration,    $m/s^2$
(d) the position as a function of time, x = (    m)sin(4.08$\pi$t)
(e) the total energy.    J

A vertical spring with spring stiffness constant 305 N/m vibrates with an amplhuk ibecsq dk;8 ))s6(itude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium )d)sbihes c8q( ;uk k6point (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 springu/9huk c1/g )cjbp) gt 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 a4 .ok/f flpy(,k8slpw fixed horizontal spring whose spring stiffness conokl. pflwkfs4/p( ,8 ystant is $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with mass 65.0 kg jumps from a high bridge. After reachin5s(e)/p-yv3 fa3pf yvw; retwg his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s.f 33-s5wfytepv;)awe r/ vyp( 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 vibrationx;lb))a coscuhx3* :jft:(w us in exactly 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 swing per oe k,2she/2 tpsecond? (That is, one complete vibr peko t2/h2s,eation takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its per /x01 amuh4xmd7x50bmjm ye/liod on Mars, where the acceleration of grauyaj x /bm0 m1hmm4l07exx5/dvity is about 0.37 that on Earth?    s

  What is the period of a simple pnl0v)j 761dgq9 fqabo endulum 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 os :yy3us /jfi8f 365 grams, and it is released at fisu8 syy3 /j:an angle of 12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’s pendulum has a length of 0.9930 m. If s /k0mh2 vytayq vb).3the clock loses half a minute per day, how should you adjust k0y 2 )tayb3q m./vhvsthe length of the pendulum? shortened by    mm.

Derive a formula for the tl(7:l2tbh o)6xk4cgfpu: hi 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 frequency of 2.kgh+w ,d(d9)oe;oxvuz-:b ze: n4tfn 5 Hz. At it is released from rest startine; :nz d4nex o fgzt,bkov 9wu:()d-+hg 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 btx/bl j--m)s-hg i g- +shchm;oat every 3.0 s. He measures the distance between two crests to bcsgjlhht-s g/i -+m-)m-b;xh e 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 speedep4qq8, :24p0ogwnqz hl7 zn d of 343 m/s How far apart are the wave cr hngo7 8lqpnezpdq4,q0:zw2 4 ests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (kiloh u2ea 1qp*k3mb+d+c vaertz) and travel with a speed o1vd+qk b *p a2m3uec+af $ 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 waves in/5z; gvovxu1 v
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one is twice as dense as mcck9n j *du2)the other. In which rod will the speed of longitudinal waves be greater, and umj2 k* ncc9d)by what factor?   

  A cord of mass 0.65 kg is stretche rjx h4;s ;7t.s4kssved between two supports 28 m apart. If the tension in the cord is 150 N, how long will it take a pulse to travel from one suppvx7s;e s.rhstsk44 j ;ort to the other?    s

  A ski gondola is connected to: q)p ;e ,q4w4pxuuaih 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 pulsqawp;,i4u4ux) e hpq:e 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 side of h pmkbf z+vii3q)324d sis ship just below the surface of the sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later.f4+bmp vi 3 ks2qd)z3i How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at different speeds, ankxj,z;n1 6s(22pxm8is zhunm d this difference6 x2zsjnpis(x12h zmnu m,8; k helps in locating the earthquake “epicenter” (where the disturbance took place).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced surfac9dxhp(f;e7, p3p:eln-ara a re 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 amplitude is needed so that objects begin to leave contact with3ar ;lx:heaepf,rp7d(a np -9 the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, al bozs,hzx 98ag14k4dnd (b) the amplitudes, of an earthqua x4z1oh g9a,l d8k4zsbke P wave passing through the Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passin7(ck3y.p-0nw qi d vbog through the Earth is measured to be dnb7(3io.k 0y- wpqvc$ 2\times10^{6 }J/m^2$ at a distance of 48 km from the source.
(a) What was its intensity when it passed a point only 1.0 km from the source?(round to one decimal place)$\approx$    $ \times10^{9 }W/m^2$
(b) At what rate did energy pass through an area of $5m^2$ at 1.0 km?    $ \times10^{10 }W$

  Two earthquake waves of the same frequency travel through the samprd0uj5q,p6 )dyc os*e portion of the Earth, but one isp,6*5j d odcqp0 u)yrs 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 one sw2.6et. rzctt1( u optransports three times the power of the other. What is the ratio of the amplitudes of the two w(c w t2oz. tse.6r1tupaves?   

  A bug on the surface of a ;j . 2yx1 babxrv/w.edz7t (dtpond 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 thezv;db 7wt 1bt .2ea/dxyx. r(j ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each other. (a) Sketchlic*8w,ug3con b: j(s 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, at the moment the pulses pass each other, the string is straight. What has(on8 *cb igsl:,cwuj3 happened to the energy at this moment?

  If a violin string vibrates at 440 x:(:3eq i1 zb:y 4gjkrhh6e st qoz9ux:u+jg )Hz as its fundamental frequency, what are the frequencies of the first four har+ hrb: 9e6tyu gu k sox:)q4h:izj3q:jex(z1gmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz whe nmh739 ;zfd xrm-1zx-zy mk5fn unfingered. At what frequency will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of the string vib9xm;r 3x-7fdf-k5nz zym z1 mhrates as a standing wave.)    Hz

  A particular string resonates in four loops at a freq5ie4h bknk:( muency of 280 Hz. Name at least three5k(ebik4 mh :n other 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 * pvk3m.o5tob 92m/s If the frequency of standing waves is 475 Hz, hok*m3pt.5vb oow far apart are two adjacent nodes?   m

  If two successive overtones of a vibrating striwki7 (pk2) *)vmwujjx8 fq3rl ng are 280 Hz and 350 Hz, what is the frequency of wkk*l2j ifmqu 3w)jxv(p)r 87the fundamental?    Hz

  A guitar string is 90 cm long and has a )xrblib iv gebod5 ), n8g.,9tmass of 3.6 g. The distance from the bridge to the support post is L = 62cm and the string is under a tension xldr ,iv,o ebbg b)8.9 ni)g5tof 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate aq(q iwpao+x0 2t 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tenq(0ow2+ iaq pxsion 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 is owuvjht0391wfx* m 36sy cmr7measured to vibrate at 205 Hz. By what percent should the teosvy9hm w *jcwrm03f tu31 67xnsion in the string be changed to correct the frequency? decreased by    %

  One end of a horizont(orcr d wg9r y*04n.t,k+c gfmal string is attached to a small-amplitude mechanical 60-Hz vibrator. The string’s masswgc ry+4kt,9c*gr0.mrdnof( 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 be6 hpbcnx4 ez8i lp.7,m adjusted by moving the pulley. If the 7ep nlz ,phb6cx.m48i hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forthhl emgq:9h9;a 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 waaqh9:;9mlh ge ve 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 h xujwmpafs8 437u+w4at k.0 km/s strikes a boundary within the Earth between two kinds of material. If it approaw7xwu38f j+hp4sa 4umches 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 undertyl855ch dmz+(c t. 9kj-smxpwater “shelf” where the velocity changes from 2.8 m/s to 2.1 m/s If the inci8dc+m5t-m c hxpy9k .stz(5ljdent wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is trave ec.4f, i(j7oy+af (5bdxzj bmm b;i0.au y8rvling in warm air when it hits a layer of cold, dense air. I a7 af + .x5.8jizb fco(0rvji4mdby;e,yu (mbf the sound 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 between two types of ro.fp pcgouo5ks +6g: z,ck at a pof pc gs:z5+uog6k., 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 th6f1f0wu .vndump c3 ;z6l2dfje user’s manual, the dish hu1d 6wud 3.np0mcf6;2 zlvffjas 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 mob30i;5m0feaz gunese w av6.: j2+r velocity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted t gmi fr 50u+a: we20e3s v;zojam6b.neo the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stifydt 1rh jh,d/ u67b1qlfness 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 (approxim h6ytqhr1,dubd7lj /1ately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18fo-wz,bu9 4)h;ulk kk m below, which stretches the net 1.1 m4 u;k f)uo9kk lhz,-bw. 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 hanging spriw.(vby2 v exgfw+3.wh ng. The mass then falls 33 cm before iwe( .y2fwbxvh.wv +g3 t stops 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 m/s (Fig. q4tc, uug ye a:2p3d7mo i*nx411–54), compressing the spring 5.0 m. (a) What is the spring stiffness constant3m*,ic xoat7 e:qyng4u d24 pu 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 affifu q-5c9jy )n4 nb*j 1y*.fimo ;fj cup of coffee (diameter 8 cm) at just the right pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate f9 cmyoij*if1*q)f5f n y-ju;.bfnj 4 the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm *c9hzw1bl+hapu5u7o vs b d+c 0b+hy,from the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequencybw c hz1+u *5h++ubhvy90l p,sa7 dobc of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t where+ar xl/ fjyv.l.m/ whvb6 z-6q x is in mj/ -l.walq6h 6 brf/ +mvxvyz.eters 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 frequency f. What is its frequen p0 bl37q s2rdo aubqe584)pxfcy if it accelerb23)r8p 4bax l7s0 d5fpoqque ates at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on*+a7gdtag td m7, wzu6 the raft, it sinks 4.0 cm deeper into tw dtz,dug7*am+ tga67he 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 play at 392 Hz (G) and 440 Hz 8 e bv.sbj/e7h(A)h7bj8. e/ sebv.
(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 travelingukeid 3 5m(o)x down the stretched two-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds ofdi 3o)mx(5 uke 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 vibrate1 v4k nr+lu4g/1a9x fy(l yeppnc6e; vx9*oy ms at a frequency of 264 Hz, and the tip of each prong moves 1.8 mm to either side of cente+nv9rmu(6v 4a*;ey4pkg9 clx1 yo y pex1fln/ r. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simple harmonic motion of ukplw-9+7ak9p5 rc:*q psufd 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 (Fig. 11–56) will not lose7 +u9 alqupcswrpf*9dk5: p-k contact with the board during the oscillation?

A string can have a “free” end if that end is attached to a ring that ceg9epb 3caig 0f /,pi+an slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with one end fixed and th eic3 ei9bf/ ,0gap+pge other free.

  A “seconds” pendulum has a period of exactly 2.000 s d uk *4x,xo:wh— each one-way swing takes 1.00: *x,o4x uwhdk0 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 a2-i2ls: d,48h mqoii -jmb.vyzs ( rcc spring can oscillate in the vertical direction or can swing as a pendulum of small amplitude, but not both at (cyvjm-2,rs i sm4hd8 :qi.ozli2c-b the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontal swings, and by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

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

  A 10.0-m-long wire of mass 123 g is stretched under a t1fj 8yt5p 6u3c.fcjiu 2/k dhfension of 255 N. A pulse is generated at one end, and 20.0 ms later a 5uip6fdfhkt c/3j j 82u1.yc fsecond 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 stiffck;/4dhp rts 1ness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of 4p1dk h;/s rctoscillations 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 steel crane cable i2bbr- 4ya.2m y,sa.vsn zql)t s 22 m long and has a disyq ,m.rv-a).2b4la2n yb stz ameter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plat v,3:8x5cfnsp 5u bmdve as shown in Fig. 11–58 (which also gives the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mav:mxv8 cf , np3udb5s5ss 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