Give some examples of everyday vi1 jjj+rs/0ji dbrating objects. Which exhibit SHM, at least appri/jj j0js 1+droximately?

Is the acceleration of a simple harmonic oscillator ever zero? If so, u+.l3am6 tds* ssrw9f where?

Explain why the motion of a piston in an automobile engine c,l;k9sf w ;nris approximately simple harcfl; 9ksn;r,w monic.

Real springs have mass. Will the true period and frequency be larger or smalleh; :i) uup zkz:m4uro5r than given by the equations for a mass oscillating on the end of anpkzm 5;4:oi)ruh u:zu idealized massless spring? Explain.

How could you double the *dgfl .o8,sqn maximum speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scale, and then is rr.1;(6(dskqkorgkwd pm z6g3eleased. Describe the scale reading d mg qkogr6 ( ;(kpzsr631kwd.as a function of time.

If a pendulum clock is accurate at sea level, will it g- avt2 g8kd*t;gdy o,uain or lose time when taken to 2gt-8y kv,d*t oa;dughigh altitude? Why?

A tire swing hanging from a branch reaches ne(m32bral37yrz;rmf tarly to the ground (Fig. 11–48). How could you estimate the height of the branch using only a sto r3r(tb; rmz7flym 2a3pwatch?

Why can you make water slosh back and forth in a pan only if yo:8j )tc0qwfivv a0qu- i9kk+uu shake the pan at a certkwa0+cj0 vf ui 98uqq-k:)v itain frequency?

Give several everyday exam- h(( z/c;qet qvg6znjples of resonance.

Is a rattle in a car ever a resonance phenomenon? Explaine (m)m5voec o*.

Is the frequency of a simple periodic wave equal to the frequency of its s*wc, ; usmng6lource? Wh ;,cnw*g6su mly or why not?

Explain the difference between the speed of a transverse wave traveling down a ceqemxi6 8y00h4mef t z /.phy(ord and the speed of ayemhq(0ex fy.mpe h4/t06 iz8 tiny piece of the cord.

Why do the strings uh ux3;)k a-.nhyq8pc jsed for the lowest-frequency notes on a piano normally have wire wrapped arou j8ypxa;h3h -knc)qu.nd them?

What kind of waves do your4me qyl h5*e16:goa r think will travel down a horizontal metal rod if you strike its end (a) vertically from above a m6o e 4h*agreq5:1rylnd (b) horizontally parallel to its length?

Since the density of air decreases with an increasxe bh(wx ca:i0y9* ;yfe in temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of soun;e iwx9(yac0bfyh:x* d waves in air to vary with temperature?

Give two reasons why circular water waves decrease ifgssr ;yzd3l0 *q:3 ucn amplitude as they travel away fcd3z*l rs;:ug 3fqy0s rom the source.

Two linear waves have the same amplitu9b 7x 9rw4e,gn neo*fwde and speed, and otherwise are identical, except one has half the wavelength of the other. Which transmits more o9gnn *9b x w47we,refenergy? By what factor?

When a sinusoidal wave crosses the8n/pq8 0 ozujs boundary between two sections of cord as in Fig. 11–33njs80p z8q/o u, the frequency does not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three t4.pz(+ re dfd/vo ) b6ih+txxsegments, are there any places you could touch it with hv x(xd4+ f.p/+rzdie 6t)tb oa knife blade without disturbing the motion?

When a standing wave exists on a string, thiv,fr0la ,1m, 7vpsjge vibrations of incident and reflected waves cancel at the nodes. Does this mean that energy was r,,vm7 ls vg0,a1fpji destroyed? Explain.

If we knew that energy was being transmitted from one plazj(t 0o 0nk/y m*-a7lw,vzepzce to another, how might w/yoz0l- (w,0 em*n vt7zkazjpe determine whether the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 mcj* 8 ld 4fu-o1+wpuq1:clggo , what is the total distance it travels in o1gfjq8 *u4ou -cw1l:lp gc+o dne period?    m

  An elastic cord is 65 cm long when a weight 1 qwji /90enios-i) stof 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 elas1/9swje qoii s in0-)ttic cord?    N/m

  The springs of a 1502uiuj bgyq 4:/0-kg car compress 5.0 mm when its 68-kg driver gets into the drby/ q42:ijugu iver’s seat. If the car goes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs from it. (a)p4fov7a -ff 0fm5r4h l What is the 4m4aho p7r5fl0f fv- fspring 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 vibra49qxjh+nhm6 zk,fs( ates with a frequency of 3.0 Hz when a mass of 0.60 kg is hung from it. Whh94nhfm+qja szx k(6,at is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the possj69+i.a*o , .qk3 utagbz( qu i-tvxkition x of the mass in Fig. 11–2 at times t =a-i qb .j x tq6ug.kkvsi+z9u3,*a(to 0,t = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

  A small fly of mass 0.25 g is caught in a spidse inb; 1x8 d2 vdk6scyb(;5ix1+jsi ger’s web. The web vibrates predominately wiv+;in 8kcsx;be s ibjd16d yx2s5( 1igth a frequency of 4.0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a spring vibrates with a frequency of 0.88 Hz. When o ;*.qba zy21zoe+lhj 9e +*guosyi(j an additional 680-g mass is added to m, the frequency is 0.60 Hz. What is the valuezeh +qbgy*+oi o * zj;as.elu y92o1(j of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per second wib /3 5uh*tvqovth an amplitude of 0.13 m. Determine u*vb5h qtv3o/
(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 eyl6/kjrzs 3-9hog, /o3n 8waqkt(j ij quilibrium is the speed of a SHO half the maximum val6jy8i z(9s3r /tkogw onkaqljj,3/ -hue?$\approx$    A

A mass attached to th0 8m,tn htpz3ze end of a spring is stretched a distance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretchesd;f7o 0 z13augnsa2vb 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) equilibf20vgan z37bou1s;a drium position again?    s

  An object with mass 3.0 kg is attached to a spr7l/ /qr sri-v-y:niv7;j4an )fho fxying with spring stiffness constant k = 280 N/m and-7iyxn;f:a l 4sr)nfqr/ oi7vhj/v-y is executing simple harmonic 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 compres6mm9h14ub 2 ugraw7e is the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With wha mu2mh u7rg4b96 awi1et speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface ifjdy ah4ip,j5y9.xw /-gdr 7k f,h-rms attached to one end of a spring; the other end is fixe .fhxpf/gydrw-m y 9kd jah-,57, j4ird 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 accordineb:i1jrbz4 gl( u0hs5g to the equation x = 0.45cos6.4t where x is in meters and t ijhe 4u gs:5rbl(01 bizs in seconds. Determine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equilibrium is o/;ug ru* )jjgthe energy of a SHO half KE and half PE? ± )jg; * rjoguu/   A

  If one vibration has 7.0 times the ener6-j m1-,ysukmmiy p5n gy of a second, but their frequencies and masses are the same, what is the ratio of themum ,61 j5-pyskimyn-ir amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging lii2zo7 llf4zhxqoks3i ;6orvm g x*699ght spring once every 0oozlzim f; s76 l2qoxx69ihkr4vg3 9*.65 s.
(a) Write down the equation giving the pumpkin’s position y (+ upward) as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. y = (   m)cos($\frac{2\pi t}{0.65s}$)
(b) How long will it take to get to the equilibrium position for the first time?    s
(c) What will be the pumpkin’s maximum speed?    m/s
(d) What will be its maximum acceleration, and where will that first be attained?   $m/s^2 $

A block of mass m is supported by two identical parallel vertical pbkk0a+kutycr2)t05ms *qa5 ty*ko : bq;t6 ksprings, each with spring stiffness constant k (Fig. 11–49). What wib ;k*kat*uy q 6b:yrc5mk)p k5t0t0+2atos kqll be the frequency of vibration?

  A 300-g mass vibrates according t so02oxw(g-cxf*q jz4 o the equation x = 0.38sin6.5t where x is in meters and-j(c2f0o*zx4o s g qwx 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 Svvwlkh 9kk7(je 1tg:-HM, labeled 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 5fjp-lyi;k j*zq k1 7vrest on the end of a horizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.ivy-jjl ;zfp 15kk* q796m/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 spri- ln +ouxr-;opng stiffness 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) with positive vel+on l;u-xp-o rocity 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 sp9re.ad yqk7:i, jm+wtiffness 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 tomcx0zwhc 9) e 9k2)sit a fixed horizontal spring who0w9zcksche ) xi9 )2tmse 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.qq,row : bx/69rmii+c7qrur 80 kg jumps from a high bridge. After reaching his lowest point9oi + rr:,i qcwr6mbq/8r qx7u, 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. 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 exaw-v7 ud*zs 1oyctly 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 bpk;/2z zqtd+ per second? (That is, one complete vibration taq2p;ztkb /zd +kes exactly 2.0 s.)    m

  A pendulum has a peri8oavt 3vk45 rh e5jw;nod of 0.80 s on Earth. What is its period on Mars, where the acceleration ofhjkvw 355ret;v 84ano gravity is about 0.37 that on Earth?    s

  What is the period of a simple pendulum 80 cm long (p*qqtyq pr73
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 m, the pendulum bob has a mass of 36q.ca f u2tnyh b5:ulp98 gn/3g5 grams, and it is released at cn25ut.pflg 98nhyu:/ qgb3aan 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 pr k,g2jo)h;do endulum has a length of 0.9930 m. If the clock loses half a minute per day, how should you adjust the length odj,2rh);ko gof the pendulum? shortened by    mm.

Derive a formula for the maximu,nfq5 z)if3llj6dr (q m 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 a1 0ebyhs5. wjp14 shb.z1 svrp2*inzc frequency of 2.5 Hz. At it is released from rest starting at an angle of 15 be1jc p n5 r zshv1s.402y.bipwh1* sz$^{\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 anchoredw g5 1;m o/ay,u*axqcj boat every 3.0 s. He measures the distance between two crestac o, x/ ujmqwyg51*a;s 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 h27v 7 ejxaku:travels with a speed of 343 m/s How far apart are the wave v2:ah7kj7 xe ucrests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz9yuva yromfq 9n*s3 -3i7hor4 and 1600 kHz (kilohertz) and travel with a r umsi 9o yh37fyarn4q*o-v9 3speed 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 o v4xuu*/.ircz jhi-g +f longitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastcefbyg4u o2k*k (gor46 :ql y3;a9qvbic modulus, but one is twice as dense as the other. In which rod willy kr*ce9y: oqg;blfqu6g4v(k ao4b23 the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apart. If :vz gjq0 ;v,gtf)p9pg3p yx8pthe tension in the cord is 150 N, how long will it take a pulse to travel from one support to the other?p g8 pppgy )f tq3zjg:9x0vv,;    s

  A ski gondola is connected to the top of a hill by a steel cable of leng/ijy 5cmwqi 2+th 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and sends a wave pulse along the cable. It is observed that it 2w/ijqi cm5y+ 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 the sea. He d lwv* *gq/a6phears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is the oceand*6 a l/vpwgq* at this point?    m

  P and S waves from an earthquake travel at did9tf6qxj7k(mmww+9wwytv) d br c*.:fferent speeds, and this difference helps in locatinxr7.j:)qtv96 f*w w+t w(9ybkdmc w dmg 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 surface wave can be approximated by a sinusoidal tran) m)z xifpjnp,7x1,9mee0 ssp sverse 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 cszf 7s9 )p1e,0x)i,m jp mexpnontact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities +b.p nb6 kcy+08f;n )srmj0ucn -hoxs, and (b) the amplitudes, of an earthquake P wave passing through the n0c-xnh m cbr 6;.nos+f+s)jybk 80upEarth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing*waw/0q jlye/nlt h+) through the Earth is measured to be /0jqna w+y/) te*llhw$ 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 same portion o52 rgqky ,/)toh wk-w jvx1--s:yv vqpm3qx(pf the Earth, but one is carrying twice the energy. What is the ratio of the ampliq- xj,g - xkqm123(vpotvqsv-r) :ywwp h/5kytudes of the two waves?   

  Two waves traveling along a stretched string have the sam/oeje w4kq ej:6b9v(a e/n4nie frequency, but one transports three times the power of the other. W/:e4j qje/k we94 no(a6nbveihat is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move up and 4bqd.sz4y8f*nw(fou down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change(fufs*dwy.o q4bz n8 4?   

The two pulses shown in Fig. 11–52 are moving toward each other0 zjkvjb).lg 0. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moj j0gz0kvb.l)ment the pulses pass each other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fu*xbi 9,afkkhgvq )6j1vklg3 .ndamental frequency, what are the frequencies o lk3 ivxv*,k9fa.)jqg16 khb gf the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 29 qftx+i0 d30sz4 Hz when unfingered. At what frequency will it vibrate if it is fingered one-third of the way down from the end? (Td0ixfs0+tz q3hat is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequeuq-ed 7 7-wnwpncy of 280 Hz. Name at least three other fre--wewuq ndp77 quencies at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the frequency of c* iyqk 9 mo-jkwbt5ig7w7* +i td+/ktstanding waves is 475 Hz, how far apart are two adjacenik7kyiwt-/+jbcd +* k*7ttwio qm5 9g t nodes?   m

  If two successive overtones of a vibrk6x2bed9os kox e. .tf3hf +.vating string are 280 Hz and 350 Hz, what is the frequency of thd 62v .hfo9es.3obkx. fxtke+e fundamental?    Hz

  A guitar string is 90 cm long and hay( auo1s:xcv: s a mass of 3.6 g. The distance from the bridge to the support post is L = 62cm and t y1 us:ax:cvo(he string is under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibl0mrmp.k+qk (rate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed t.m0q +m(lkkrp o 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 meav-tyeqf,q+ v.sured to vibrate at 205 Hz. By what percent should .+yqf-eqt ,vv the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is atta ,99n:bmv agleched to a small-amplitude mechanical 60-Hz vibrator. The strmn, a :vlge9b9ing’s mass per unit length is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of the string may e4 3fwzftl6zm9sz2b2 be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how mae zs2 4bmft2 36fz9zwlny different standing wave patterns 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 just the right* b hrh0)za1eew9(tja frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standte*e (0wz)r b9aajhh1ing wave in a 65-cm-wide tub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundary withig.b hr-hbfr(j6+e vf5n the Earth between two kinds of material. If it approaches the boundary at an incidbfrrb6 5v. jh+f(eh- gent 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” whzubl a3:;a7,k p67 uv4gicm lfere the velocity changes from 2.8 m/s to 2.1 c7zml a 4v73 ki,6;faupul:g bm/s If the incident wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air wh61/ ;xcdw;l zf3 rhsvuen it hits a layer of cold, dense air. If the sound wavewul/6zvhfs3rc d;; 1x 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 wa3:,(s: cx h t-xohzwwqve strikes a boundary between two types of rock at a 38 zch:(hsxowwx -, 3t:q$^{\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 f a0*r)b4 ucfsmanual, the dish has to be pointed in the direction of t)c* fbr su0fa4he 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 75bn2zjg1rd 85tep34 iw0 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 to thed geinbj5z23r14 ptw8 shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a s+y-ymnjtd8;8 hso 8*i 0jo cqaf80j: pp cb8ifpring stiffness constant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (apprjf pq itja0ocos j;fn i8 *d0-y8:c88+ h8mbypoximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 rmhhhsp1 hnt8vt 9 t ++vq-f8 75r+dujm below, which stretches the net 1.1 +5dfr+p8v9tmq7thh1uj8tn+ h hs v-rm. 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 spring. The mass then *62xe5 f ktt /ztbpw1k: vv2xsr9xgb; falls 33 cm before it stops and begins to rise. Wxt5s;9ep2tbgv:1 kz62xfv/xt wrb*k hat is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 117h9 j-si gf xuqwgjf895ob9o88 tem p5–54), compressing the spring 5.0 m. (a) What is the springg98xo9spmejbtg8q7i f8 55ju- o w 9hf 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 pace o9kv9 .4aoxr04 n jqtljf about 1 step per second, the coffee sloshes mor09ljxv.on9qt j4ka4r e and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the center of a 33fesco1(lctkxhh ;s3;*erc5 . -rpm phonograph record have a wavelength of 1.70 mm. What will be the frequency of the sound emitted? ckts ;.sl3fro*1hec(h;x 5 ec   Hz

  A 2.00-kg mass vibratixdqt;c2o/ptz .ne7 ( es according to the equation x=0.650cos7.40t where x is in meq.(d c xnit ot2;/p7zeters 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 frequency if itp 30( bp+feicl accelerates ap( lpbi0+3 ecft 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on the rc3 ,panppvp*;;kvxg( aft, it sinks 4.0 cm deeper into the water. When he steps o*(ppvk,;3x p; a gvpcnff, 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/woxm c(utqqt(k)1zza 1lp8 8 440 Hz (A). zx(w)ac8 o1 klt 8z/qp( qumt1
(a) What are the frequencies of the first two overtones for each string? G : $f_2$=    Hz $f_3$=    Hz A : $f_2$=    Hz $f_3$=    Hz
(b) If the two strings have the same length and are under the same tension, what is the ratio of their masses ($m_{\mathrm{G}}/m_{\mathrm{A}}$)   
(c) If the strings instead have the same mass per unit length and are under the same tension, what is the ratio of their lengths($L_{\mathrm{G}}/L_{\mathrm{A}}$)   
(d) If their masses and lengths are the same, what must be the ratio of the tensions in the two strings?   

Consider a sine wave traveling down the stretched two-part cord of Fig. 11–33. D4z /u u o;go5ay.xu 37bh+n3rqa ih8iaetermine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that iu+ihno io 5;ugz/7xa.rqayua 3 348 hbn the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the tip : lmvelnr9g44tn/xh )of each prong moves 1.8 mm to9 nh/e :)4vl 4tgxrnml 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 witrq7 nx;ey;a26h -d jtdk wb-*dh simple harmonic motion of frequency 1.5 cycles per second. What is the maximum amplitude with which th-x2j;a67dtk e d w-bry*;nhdq e 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 oscillation?

A string can have a +o:t*4us 327l uz di,eibge jow5xx0a“free” end if that end is attached 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 onjs0ti:uoxex4lgu 3i2d*+ ea 75w ,obze end fixed and the other free.

  A “seconds” pendulum has a period of exactlyahspk fx;)* y8 2.000 s — each one-way swing takes 1.8spy f *)a;kxh000 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 os;.g2zlnyai :cv9; llx cillate in the vertical direction or can swing as a9;n;:i. a2yx llgvc lz 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, 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 tensi t4pcejsx wpk956 65td:ricz3on of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at the opposite enki95pew6t 4jdt5x6c p csz3r:d. Where will the two pulses first meet?    m

A block of mass M is suspende 7ne 2eq.wenz9d 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 that will allow the penny to j ze2 qw9ne7.enust stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junk-zr /s6iyv8liyard. The steel crane cable is 22 m long and has a diameter of 6.4 mm. A breiys-iv 6/8z rleze 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 plate as shown in Fig. 11–5groe voc *:zm,4mjqf(: 5p5 kf8 (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 mass vibrating on a spring, estimate the frequency of this vibration, given that the shear modulus (Section 9–5) of jello is 52ovemk:: q jzm,r5f*pg4of 5 c(0 $N/m^2$ and its density is 1300 $kg/m^3$    Hz