Give some examples of everyday vibrating objects. Which exmqa)97z 3 wgcihibit SHM, at least approximately?w zaiqc3)7gm9

Is the acceleration of a simple harmonic osci; bl/h 72 briibcasq 3nd83f4ollator ever zero? If so, where?

Explain why the motion of a piston in an automobile engine is approximately simia;q*mh*.z5z e grit0:i-oa yple harmonice-otz* iz;r0i5amq :y.ia*h g .

Real springs have mass. Will the true period h.p+f6psb 3rr and frequency be larger or smaller than given by the equations for a mass oscillating on the endb.3p +f6 rprhs of an idealized massless spring? Explain.

How could you double the maximum speed of a simple harmonic osjefs3s .g: :cwvu p7c:cillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical: l2 qgsje 3i23sp)rvc spring scale, and then is released. Describe the scale reading as a function of pvs ic :2g3leqjs3r2)time.

If a pendulum clock is accurate at sea level, will it gain or lose time when tak2 wpynf,zu3d,zgc*w3 en to high altitudew,3p dz fz3c*uy2 wg,n? Why?

A tire swing hanging from a branch reaches nearly to the ground )ivsmm,)qxi 5(Fig. 11–48). How could you estimate the heigh q5imxm)s,iv )t of the branch using only a stopwatch?

Why can you make watervbc7fda,5da8 9sar k 9 slosh back and forth in a pan only if you shake the pan at a 5,arkaa 9b8fd9dvsc7 certain frequency?

Give several everyday examplec:ozdyf c ji.)j a2fi-(7:jnas of resonance.

Is a rattle in a car ever a resonance zdl) 3h.-rg mephenomenon? Explain.

Is the frequency of a simple periodic wave equal to the frk 1ownrz,.ut1equency of its source? Whyt1oz wk,n .ru1 or why not?

Explain the difference between the speed of a transverse wave traveling d7+ n t .72yiutkc6mwpaown a cord and the speed of a tinwt2ti77ayu. kpm+c6 ny piece of the cord.

Why do the strings used for the lowest-frequency notehc4 f3y9 2nxwy +ovb8 le/6sajs on a piano normally have wire wrapped ah9xeyls6 j8b2oc/ 3yv + an4fwround them?

What kind of waves do you think will travel down a horizontal metal rod if1sfw18cv6 zp 9s ndm5s you strike its end (a) vertically from above and (b) horizontally parallel to its lm wv1fc 1s5nss68zd p9ength?

Since the density of air decreases with an increase in temperatu hk/k:/k k,8 jmeum6nmre, but the bulk modulus B is nearly independent of te 6jh 8 mmk,um:k/eknk/mperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why br6* gk5 adk.zcircular water waves decrease in amplitude as they travel awk .k6*g ar5bdzay from the source.

Two linear waves have the same amplitude and speed, and otherwise are aeafc4th/u9bd92 f; yidentical, except one has half the wavelength of the other. Which transmits more energy? Byca;a2d4 9yeb f/9htf u what factor?

When a sinusoidal wave crosses the boundary between two sections of cord ase2)jxp jck)lps0u h(/ mlh+s1e3ux 0s in Fig. 11–33, the frequency does not change (although the wavelength and velocity do + /(slpe) e2 s0)jlkch3um0su1h xjpxchange). Explain why.

If a string is vibrating in three segments, are there any placec*dk8itt/ ghif4 m0s1s you could touch itd0 igkm 1ht4* cs/8fit with a knife blade without disturbing the motion?

When a standing wave exists on a string, the vibrati4p1k vof0 1u-nz dl4uykkq4o3ons of incident and reflected waves cancel at the nodes. Does this mean that energy44d u3vfponyz1k 1-0kou4k lq was destroyed? Explain.

If we knew that energy was being transmitted from one placeimgo je/3m( e, to another, how might we determine whether the energy we/3jom ime,(gas being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, euh 8sy3hf94r what is the total distance it travels in o 38sh hyrf9u4ene period?    m

  An elastic cord is 65 cm long when a weight v f5i7fuu1g(l7u9d zs of 75 N hangs from it but is 85 cm long 7g71f( 9uzld fvis5uuwhen a weight of 180 N hangs from it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 me*l ro +*n9jupm when its 68-kg driver gets into the driver’s seat. If the car goes over a bump, what will be the frequency of vibration+* l9unp jo*ers?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs from c6dkcypf t cy5)ooml4,k: * -; 2sfcnvit. (a) What is the spring stiffness coop c,5cds-c my vyf4);fn*tk:kc 2l 6onstant $\approx$    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 freqkk4p5pz )z1iy;i+k a:yth c/ u8u 8lztuency of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequenc8ykk1yz5 /p)utik:+hz;pul48i z t a cy if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. 11–2 at time-bh34pa5r qb;ydkp5n s t = 0,tkb 43npd -;r55pbahqy = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

  A small fly of mass 0.25 g is caught in a spider’s web. The web vibrates predb-m eodgq+k mhwez+6m g,16t*ominately with a frequency of 4.0 Hzgom*em -kegzw m+b + 661qh,dt.
(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 v v(te3jkzp*o6.- fx lhibrates with a frequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 Hz. What iftvkx epo*6j3lz .h (-s the value of m?    kg

  A 0.60-kg mass at the end of a spasvnr, r0ln .o6,2mk dring vibrates 3.0 times per second with an amplitude on.6,2d lm0skrrnav, 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 the speed of a SHO half:yd++kwwm0 f6s7rf2*zzng t 1i- vx yx the maximum valuedw szxzy-wnk60f 7 *iv+1xmft+2 g:ry ?$\approx$    A

A mass attached to the end l;i-aor lizrea8v 3+5of 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 i fek0uiw 0 -.+y4jca3ni8gqqthe spring is stretched an additional 0.130 m and released, how long does it take to reach the (new) equin0+ w4 -0.yeijf8u ag3 kicqiqlibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with spring stiffness/ *n v+jhzrqb8 constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, zn+qvh* jrb/8 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 compressv*al 7 yvnql *(hip06a the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will the ball leave yqv* plhin67(a* l av0the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to:4r vy9f brc9v 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 0.12fvy 4:brr99cv 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 04z.nt *(j cfww .qemqaccording to the equation x = 0.45cos6.4t where x is in meters and t is in seconds. D q.0 4we mftcwznj*(q.etermine
(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 ofysdhy+b uasa5fv(( uv :44 fp g;6;dnj a SHO half KE and half PE? ±u54;fgay4b(sd+ y;advfu( j:h s 6pvn    A

  If one vibration has 7.0 times the energy 1xkn6) c3ozcx *ztef9of a second, but their frequencies and masses are the sam)*etc6o k3 z1c9xfxn ze, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light sprin bm2jtzri n81;g once every 0.65 sbjni8 1rtz2 m;.
(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 5 ej ()7.mi5ep 2fp)c4yzbe5dxp5sn u.ewzq z by two identical parallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What wij p5)7nsz 2 zpwie..emf yxd)5( 45b q5pezuecll be the frequency of vibration?

  A 300-g mass vibrates according to tc xin3w77a9 5(xatxe y/mhi70 nzzab6 he equation x = 0.38sin6.5t where x is in meters and t is in seconds.37 x(6hz/bnn5 w0 xxy7c z9aea7ii mat Determine
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows two examples of SHM, labeled A and B. For each, wg 7uf3iqf 6k(hhat 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 horizontalwgv+uigx-as;ica.j:7 ,u h 8 l spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.96:c+jsa-uh .glg,iva 87; xw ium/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 stiffn;xpl /ux(z +kce n/vr5ess constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes throu/x/pu+ ;(evk nxr5lcz gh 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 con p1/hma8oouzh 6 4*kaikz/ w9tstants $k_1$ 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-k ) o+8klbwnxzl0hv+k6 g block attached to a fixed horizontal spring whose k wlo +08+v6znxk)bhl spring 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 h1mou+ plmi(, kigh bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Cukm (1lp, im+oalculate 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 n,yzl5 f6u3g t8p) : v5b0cz/fagndc o60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple9dm5l7shpl( f*yl:b x pendulum be if it is to make exactly one swing per second? (That is, one complete vibration takes exactly 2.0 yf75(ld plml*x9:shb s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its periount m i8r-1/qy 5fatqsn4z-i -d on Mars, where the accelzanqu y1r/sfn--58 tii-tm 4 qeration of gravity is about 0.37 that on Earth?    s

  What is the period of a simple pendulum 8cnz 8z8 dg1;pg0 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 h2 b ri), dnqtx1ir;t1fas a mass of 365 grams, and it is releabdt;x 2)1,rn1iq ftirsed at an angle of 12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’s pen0fze-:zhe+ ak ( :ddvbdulum has a length of 0.9930 m. If the clock loses half a minute per day,:zakz d f:(-h0vd+ebe how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximum speedgw : f3cs/93qvl7s(kj zviiubtyax + o:5td*1 $v_{max}$ 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 fr5lb5ln sgy5 h1equency of 2.5 Hz. At it is released from rest starting at an an1lh ly gs5nb55gle 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 boaoe7br:x7nsgq p/e68y.xoef 9t every 3.0 s. He measures the distanx gr q7 o7:s.e6en8o/xe9fbypce 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 andxgeq(ra 8)06*ejg, camibs5n travels with a speed of 343 m/s How far apart are the waveg mbr605(8ijgx,*easa )nceq crests (compressions)?    m

  (a) AM radio signals have frequencies behfspv;0buntvg+( (yau(v a; 6ru8v u00qgl6qtween 550 kHz and 1600 kHz (kilohertz) and travel with a speed ofq qgy gf0(v(st 8h l u(60 +uurapv60;vbv;nau $ 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 longitudi /yx7v,klvqr 9nal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but o ptz* -e4hzi9e84ssdyrzo6 vow xb1 06ne is twice as dense as the other. In which rod will the speed of longitudinal wa6 v b*zz-ooz0dyhseert689i xp4 w4s1ves be greater, and by what factor?   

  A cord of mass 0.65 kd31zk oz1k7 gbg is stretched 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 support to the other?3dz1z71gk bok    s

  A ski gondola is connected to the top of a hill by a st u)pkcc1(ak9 9a6 lpmdrh1e2 eeel 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 sendc9euh19l) r empa2d akcp k6(1s 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 side of his ship just below the surface of .50adnsbl - n+gqx;5e8aww mlthe sea. He hears the echo of the wave .;s l5x5qanlmw-aeg w8b n0 d+reflected 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 eartil 2:d3h+p wujhquake travel at different speeds, and this difference helps in locating the earthquake “epicenter” (where the distur:w2ijp uh3ld+ bance took place).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced surface wave can be approximated by a sinusoidetuy m j+g)4+nal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is nee+)te4 +gmuy njded so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the inteee8uy3qlq o3v2o/li/ nsities, and (b) the amplitudes, of an earthquakq q 3/luy8el2iovo3e/e 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 passing through t/ i 11uox)q )mihr0ixhhe Earth is measured to be xoxi )h)iiu01mrhq / 1$ 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 fre+xx-b+fi6f ff0eka 2 equency travel through the same portion of the Earth, but one is carrying twice the xe0xibf+-2 ffke +af6energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stixpb+-mq9e+9 c s71i /nscr/cm ;gcviretched string have the same frequency, but one transports three times the power of the other. What is the ratio of the amplitudes of the tceics/m9 mcrq+is-x9p; n+bc 1i 7/g vwo waves?   

  A bug on the surface of a pond is observed to move up and down a total verticam79l+ nycj, ,u4x rgttl 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 maximum KE ch jmu,r9x7,y l4+ntctgange?   

The two pulses shown in Fig. 11–52 are moving toward each other. (a) kl8 p+5 g)gi jo* ylywby78f0aic9n e2Sketch 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 s o0g+i* ny 8)y9ielfgcwk 78lab2j5yptraight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundamental frequenc5f r-hg7syof4i tm91k y, what are the frequencies of the first four hay r-k1fh4i5o9mgsf7 trmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfing p-l0cw er.tg7ered. At what frequency will it vibrate if it is fingered one-third of th.pr- 0ec7gwlte 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 2 u)yqnxc0ewsa(;,i( 9htcd/ c 80 Hz. Name at least three ;e at)d 0wcnc,( xcqi9ush y(/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 92m/s If th)w* bsn3060c ouztqj oe frequency of standing waves is 475 Hz, how far apart are two adjacetojuq s03c0n)zw*6b ont nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 350 Hz, ak(f 7n0lpbh9aq g 82ewhat is the flag b8h9n7fq p0(k ea2requency of the fundamental?    Hz

  A guitar string is 90 cm long and has acz 5brkqi5pb6,+zm9bw vg ;; j mass of 3.6 g. The distance from the bridge to the support post is L = 62cm and the string is under a q ;9wbc mpjibrkz5v,;+5gzb6 tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, but it is meas:kvhn4u5u9az 9ev aybr )w+d0ured to vibrate at 205 Hz. By what percent should the taue)zbnawr9u9hv4 +5 :d v y0kension 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 measured kv -b.*nrlyo9gk./jyto vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequeb. ./9yyng- jk l*kovrncy? decreased by    %

  One end of a horizontal string icb+f-f 0.4.oa99yyhm jzfdey s attached to a small-amplitude mechanical 60-Hz vibrator. The string’s mass per unit lenomcfj hye4da f9 0by 9.y+.-zfgth 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 len17llxpkx6rgj8 yi 2.c gth of the string may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patternscxll kx1 .yrpi2j87g6 may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at justx rlml.mg/lplg3(0 v) 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.lpgml03x) lr gv.m(/l What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a bounddw ybqwj) vw55y:its e)d9c t5 c6.q/iary within the Earth between two kinds of material. If it aptyid9)e cww qb s5 vc t5/:5jqw6y).idproaches the boundary at an incident angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “shelf” where the veloci8e2l es 7+/rgyuks y;ity changes from 2.8 m/s to 2.1 m/s If the incident wave crests make a8 guyeyr;72se+s k/li 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 lag-57qa .mmzgb5n ,b.*8bv , szkzrvl dyer of cold, dense air. If the sound wave hits the cold z,gavz.n - bm.7,q m vb8zbr*5 5sklgdair 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 rock at qs*2) ns*)b jhcsfe 1va 38)) f2*shvjc sb*qe1ns $^{\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 manxv xo(t a80r*i w4.p9te b7jvjwc(l7 xual, the dish has to be pointed in the direieww(xx8txpbc* 4lt0 (v 7.v9ajj ro7 ction 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 travels across li /:zg+9jsm 09 8 o8c2kzcghwtso 5xtthe 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 knogih: 8cjowxsz z8/k t9lcmgo +20t9s5wledge 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 t cz)lqxq31u7Find the maximum )qtlqc z 3xu71compression 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 from a window to a fire net 18 m below,zja /.2 it.kz1kn e7 jpw9,cdeyixj/. which stretches the net 1.1 m. Assume that the xz 2 ,ne.tkce. p9/i/w.ij 1jjyz7kda 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 off8(z qlh 0(klk a freely hanging spring. The mass then falls 33 cm before it stops and begins to rise. What is the fr(llh0zkk(f 8qequency of the oscillation?    Hz

  A 950-kg car strikes a hug7-as yg,zym r9e spring at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) Whm,rga z9yys7 -at 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) at just the right pac3+8+if o4f :juuoa3.hmm:ulecav9.( qxa ekfe of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11 k :ijfofuu8cmla3e(q4+3ah.afmo : u v.ex+9–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from tt7cy-re tt+1j paq s1t85 h7irhe center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What wihr+7et ip87ctqsy j tt-ra1 51ll be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates acc(b2zprtk i1r( ai0qd. ording to the equation x=0.650cos7.40t where x is in meters and t in seconds. Determ.2 iztp 1kdb0q(r ia(rine
(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 fprvpum j:jem+9*,i.y3l f ) kj. What is its frequency if it accelera.p m3:*pjrf luj9 )vk+iemy j,tes 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;*2dpfee:r:0tzj l -,dy8tb *0z *d o yvuulsx the raft, it sinks 4.0 cm deeper into the water.0b,fov z p;ulz :*yyd:r d-e0j2 xues*t8d*lt 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 instrumentno-2 md:3it9v n : :,+m6oqvsbwd slot are tuned to play at 392 Hz (G) and 440 Hz (A). b:9:w n2vmtis:+3s,n6t-ov o d mqold
(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 dowlk a6(z)tj bo.n the stretched two-part cord of Fig. 11–33. Determine a formula (a) for t j zkb)alt6o(.he ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a freq.x ssep1y j8*mvsoy, 1uency of 264 Hz, and the tip of each prong moves 1.1vy1s8y* s mjo.xes, p8 mm to either side of center. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simj gveu5vv0 f;mi4j, 5sple harmonic motion of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board during the oscifuivg0j5ej v 4m5v;,s llation?

A string can have a “free” end if that end is attachsxsh) m;qj4;p un; ,( sjlrnt*ed to a ring that can 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 rh;msuxjn q4s);(ns, jp *;lt the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each one-way swin- xi ,ffw+f*xz5pkq,qs+ 4aa sg takes 1.00afi5,p +zax+,f *x-s w4 fqqks0 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 dirxvq on*r-(rgvb1 zg)n unuk(,),pg )tection or can swing as a pendulum of sxg),oqg(rv )t)g , * pnv1bzknrnu -(umall amplitude, but not both at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontal swings, and by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

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

  A 10.0-m-long wire of mabk, oj9 *9bs1jz49az wyij vg4ss 123 g is stretched under a tension of 255 N. A pulse is generated at one end, 49gjwoa9k,jb jz s* bz yv941iand 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 suspen7sh9 t. g-e.dbnb ig.rsjlr14ded from a ceiling by a spring with spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillations th hjrbl1t.b 9iegrns 4d. g.7s-at 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 cy(x;eift;u4 ts;, ylc rane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. What is the period of the bouncing? [Hint: Refer to;;;t 4ul,i (xytfcesy Table 9–1.]    s

  A block of jello rests on a plate or*q iiw(1a97p 0w( +zzlkjf uas 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 springr0+qz*jwi(7 u(w 1if zlpao k9s 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