Give some examples of every-a8ym1xbj aq0wcdqs/ o1g2/b day vibrating objects. Which exhibit SHM, at least apybs -//0jcdxqg owq am81 21abproximately?

Is the acceleration of a sif mjmt q8udri0 1u. b8,q(5hvzmple harmonic oscillator ever zero? If so, where?

Explain why the motion of a pisjq/o8*o/ wvvg,mp 3buton in an automobile engine is approximately simple ha ov,j vp8 //u*owgqmb3rmonic.

Real springs have mass. dwce8vq+p1. b, :ej7 d/8cxks6uza csWill the true period and frequency be larger or smaller tq:jkess1euca / dw c6+zb d8,.v8cx p7han given by the equations for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a s sxgdsz 5sas8 (,h a,gtu te(-)cosaz5(ax6i*imple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hwjwuo2id g*+ly y+b*;ook of a vertical spring scale, and then is released. Describe the scale reading as a func dylw;+ g*ouj2+b iyw*tion of time.

If a pendulum clock is accurate at sea levele*.up*1 *tmturz8+(qntx zf tnznm)5, will it gain or lose time when taken to high altitude? Whnftqzzmnnr+ tm()uxtz* u85t** pe.1 y?

A tire swing hanging from a branch reaches nearly to the ground (Fig;v b 5g/( s*phrl-v xm.pokiov3*0iim . 11–48). How could you estimate the heig-mg ko .hro spi*vb/ vi3(i5*px;m0vlht of the branch using only a stopwatch?

Why can you make water slosh back and forth in a pan only if yosy6 vu* ebgvga(mt/9hi 6-ns.u shake the pan at a certain freyn.vt6ae9/h-b*u sg i(m6s gv quency?

Give several everyday examples of resonawh1 np9;yo4 evw 6x:tlnce.

Is a rattle in a car ever a resonance phenomenon? Explain.t5 6p240iib9 v:+viqpyox(kbgkf n0pw* l0 vv

Is the frequency of a simple periodic wave equal to the frequency of its source? sb9t2c 7*p.3glps xqv Why x 9*ls3cvt7p bs2g. pqor why not?

Explain the difference between the speed of a transverpe .*njv 44jnkse wave traveling down a cord and the speed of a tinn pvj4k.ne*4jy piece of the cord.

Why do the strings used for the lowd5 -47nvhsnz oest-frequency notes on a piano normally have 7hv5-dsz n4no wire wrapped around them?

What kind of waves do you think (.:opdqy qyl: will travel down a horizontal metal rod if you strike its end (a) vertically from above and (b) horizonto l::y( p.yqdqally parallel to its length?

Since the density of air decreases with0i;q1yht2ija t 0 m-mb an increase in temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves in air to vary w q0t; 1j0i ahyb2imm-tith temperature?

Give two reasons why circular water waves decrease in ampliu6cdo*w73k, j rhpa1 otude as they travel away krcou3 jo1h*w76d pa,from the source.

Two linear waves have the same a ie j/jej8lv17mplitude and speed, and otherwise are identical, except one ha7/1lv eji 8ejjs half the wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the ycgrms 3(),fi*jnb b :6tmmcja w1/u, boundary between two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and vbc1b cfu /,a*, jjmysn3 gr:6m)tmwi(elocity do change). Explain why.

If a string is vibrating in three segments, are thereogqag 9g40i l: any places you could touchqgg9oial4:0 g it with a knife blade without disturbing the motion?

When a standing wave exists g5x0qyyg ef c)(y 7c/pon a string, the vibrations of incident and reflected waves cancel at the nodes. Does thi py5 0e(cgxyfgcq7y/) s mean that energy was destroyed? Explain.

If we knew that energy was being transmyn9 v4qct ciby))(9v oitted from one place to another, how might we determine whether the energy was being carried byn 9( ci v)vq)bctyyo49 particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0qp abnaw8c 3 07n94z jf,nuz5b.18 m, what is the total distance it travels in one pe 3n 4af n0jz,975qz8uwa bpnbcriod?    m

  An elastic cord is 65 cm long when a weight of 75 zk/pran, d)r/N hangs from it but is 85 cm long when a weight of 180 N hangs from it. What is p)zkda/ nr /r,the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg driver geto-)aiqohc.2:j vil 7qs into the driver’s seat. Iqiv- .a:h l72icjqoo) f 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-kg7ox0c-81m vd(zx, n q*kvbcsv fish hangs from it. (a) What is the spring stifx7scdv*cq z8 v1xb0 -(ovnm, kfness 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 axllmy(mv,4u+ frequency of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency if olv ,my4um+l (xnly 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. 18i3d,,z,h,oke bjb lk1–2 at times t zlo3b ,kei, ,8dhjk b,= 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 spider’s web. The web vibrates predcz0gkqg+v l ),ominately with a frequency ofcqgk,)z+g 0lv 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 j2 j4-4a;yso6o ekdn uan additional 680-g mass is added to myj6 o dseuno-44a;jk2, the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 timmn6j3tsz-q l3 ;ky hnnw.-xs1es per second with an amplitude of 0.13 m. Dzjq-lntn s;3-3w6n .xkhm1 y setermine
(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 eqd dscqnqpij06ud ( ,x49-zl b)uilibrium is the speed of a SHO half the maximum valun d u6qjiz s 9d0,p)-d4(cbxqle?$\approx$    A

A mass attached to the end of a spring is stretched a distance id/:j minz)2p xf12mc3fo v l7$x_0$ 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 0.315q (1g m v0*fcv ry+.j qoa)l0k.kdau1m m. If the spring is stretched an additional 0.130 m and released, how long does it take to reach the (new) equilibrium position again mqgy(. 01)r a* 0okkv1lqu+fjcdav.m?    s

  An object with mass 3.0 kg is attacjroz;g h0/+uuhed to a spring with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the objecg rh0 uzu+j/o;t 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 the spring of a toy popgun 0.200vv y;:pdmvon 7.)/qh 5 o3ydpw m to “load” a 0.180-kg bal.3;h/n7:mpwvv)qpod y5 v od yl. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to okh:sn /hlgqjbe5*dsz x1/7: sne end of a spring; the other end is hks /e:xgzdq 7 /51ns hjbls:*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 equ .c9q w8x7bhu8ffhq*m yy-yy+ation x = 0.45cos6.4t where x is in meters and t is ih9y8.hff*wxu qb -yc87+yqym n 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 the energy of a SHO hanz64w0x0,se4 em 3y pdv;ncw 0n mhmz-lf KE and half PE? z x,-ndn46e4w0m0scve ;0 n3zhwy pm m±    A

  If one vibration has 7.0 times the energy of a second, butqt xmprqzau3 63;e.cv ln g/*z.4e*ut their frequencies and masses are the same, what is the ratio o*z3mt*/;et.n q4l p36 czr uexg qa.uvf their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertic)ejq6 i si wx68i3k8gb7il6rqally hanging light spring once every 0.65 siseq i r378jbq6ik6x6i)g 8lw.
(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 paraowxtu4t;hc8nl)exhxxg hf6 +o ;7 -,illel vertical springs, each with spring stiffness constant k (Fig. 11–o; it; 7xh-u 8,hoxhe4fxw+t)xl 6n gc49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5p.1*dhxbf w0n z5a+qp t where x is in me q0 ppdfz. 1anw*+5hxbters 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, labeled A and B. For each, wxs,qub h5-0rbs )zdp/ hat 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 r2r2t*wu4rqo 73 crtz= 124 N/m) is struck by a hammer, which gitr rr w2c or*72tq34zuves the mass an initial speed of 2.96m/s Determine
(a) the period and frequency of the motion,    s    Hz
(b) the amplitude,    m
(c) the maximum acceleration,    $m/s^2$
(d) the position as a function of time, x = (    m)sin(4.08$\pi$t)
(e) the total energy.    J

A vertical spring with spring i*,ul0j8.l: psuf1e 7 39td1yyc 4welwdkxes stiffness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes t :ytlk1ej 9 d71si4xe30yupw.* s,8edfluwlchrough 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 consi)gl)1(upm wstants $k_1$ 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 atpp 7b-b6pmi5 fixed horizontal spring whose spring sti76 mbiptpp-b5 ffness 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 high bridge. After reach/k9 d:/lrj g gh2zp:bkjd +h*wing 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. Calculat:+kg/z29 *kbpl:hj rdjwh/dg e the spring stiffness constant and the unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrations in exactly 60 s. What i99nzv 9 mla(bts its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is uwnone.3ho09 to make exactly one swing per second? (That is, one 0en uh9w .o3oncomplete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on Mars, where2rf g/m/qag+k kpt;l/ the acceleratil gr+g/;m2 /faktp/qk on of gravity is about 0.37 that on Earth?    s

  What is the period of a simple pendulum 80 cm longp78.ujdowu 2 s
(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 pen(r7xx/f; ll1q ct- axwdulum bob has a mass of 365 grams, and it is relc1x ft(llxx7rw;/ - qaeased 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 cloc q x cgeut /bi9o3u(;ew-f78ckk’s pendulum has a length of 0.9930 m. If the clock loses half a minute per day, how should you adju cfuubwoke9gc3e-/x(; 7 qit8st the length of the pendulum? shortened by    mm.

Derive a formula for the maximum speed nh82 : wmz3uea$v_{max}$ 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 r5oa :-ec vzn3zx3g g62.5 Hz. At it is released from rest start3-c zg5 : ago6z3nxvering 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 bowl(( j : kllzmu5p2bal5 of his anchored boat every 3.0 s. He measures the distance betweek 2jp5lu(l(lz5 mal:b n two crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequencyi4ox*ewsg3e (c *w:jy of 262 Hz and travels with a speed of 343 m/s Ho4gxc3(:ews* j weyoi* w far apart are the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between:pcsh kz) w n,:;d2hpf 550 kHz and 1600 kHz (kilohertz) and travel with a speed of w):pfpdshz :cn ,h ;2k$ 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 longit q l70qy ubk:+lo7fht.udinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but on 3tr3, mn/hpa8iy 9paee is twice as dense as the other. In which rod 9/8a,re3m h yit3nappwill the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 2ag j;gr)bu9rlagti gd, q-,2/ 8 m apart. If the tension in t,jtda9agq- gug)br/ l, 2gir;he cord is 150 N, how long will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to0/pyzlb.*qd4 o4 5agh9oucje 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 hd/u gc oje9z0 4y*qo.4b5lap the terminal and sends a wave pulse along the cable. It is observed that it took 16 s for the pulse to return.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

  A sailor strikes the side of his ship just below the surface of the sea. He hg:,2 kqtax, dt+cqz5argko crqmo/4u,5z -0h ears the echo of the wave reflected from the ocean floor directly below 3.0 s later.q2+z du g5 ttgq/5a:m0qh- orc,oark x,z,c4k How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at different speeds, and this diff6g)j0djkj )1knlfql0xs/jg 6erence helps in locating the earthquake “ep0q sjnk) jx)66gf/1 ldkjl0jgicenter” (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 ap 4 4p7j*h2chkha o:gzyproximated 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 th7*ky h:4gcop2jz h4ao leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (wo4vj q ;*keu1x;r :aia) the intensities, and (b) the amplitudes, of an earthquake P wave passing through the Earth and doj er;iuv ; akx4*w:1qetected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth ivyu-)m9qbtl x*bt5;wwx u92b s measured to be 9wxqu)9-t* vb2mx ly ubt;w5b$ 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 ofko2sp2f9 bk qgeqa+)enm2x 5. the same frequency travel through the same portion of the Earth, but one is carrying twice the energy. What is the ratio of the amplieb2mk2 2qfe9 anx.k )5og+ qsptudes of the two waves?   

  Two waves traveling along a stretched string have the same frequency, but uh8g0 r0idh wl,5uzvnu2z 4s(one transports three times the power of the other. W0 unzwszvh ,2g 48ih5l uu(dr0hat is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is o *r/vdt us. 5px k;b8pz0fjclsp1w-( tbserved to move up and down a total vertical distance of 6.0 cm, from the lowest to the highest point*sjw.dl85kt-vs up1 x c;0b/zp ft(rp , as a wave passes. If the 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) h(7u(rvy6qq4jsqhct ;joq). 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 Figt j)47cqhhsqjv(qqr (y o6 u.;. 11–36a, at the moment the pulses pass each other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at s6y;sa(tvs8,m6tji h 440 Hz as its fundamental frequency, what are the frequencies of the first four harm (t6 v6mtj8,aissy s;honics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what frequency will il4scir s ut(d/ -sv0f9 dqfn:1t vibrate if it is fingered on:c-did1snfls90vu / rftsq4(e-third of the way down from the end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four r r5tae:68pn mx:cqp6loops at a frequency of 280 Hz. Name at least three othnc 8mx6rpa:qre 6 5:tper 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 the 2g8jkbyn qy4l )tgbzs : *,xb3frequency of standing waves is 475 Hz, how far apart are two adjtj)n3,g* 4:zlsx g8 b yk2bqybacent nodes?   m

  If two successive overtoliyp -(v 4zl8ones of a vibrating string are 280 Hz and 350 Hz, what is the frequency of the fundamenti-p loz84lv y(al?    Hz

  A guitar string is 90 cm lonb.m)f+ggl8 nrz d7 8k+ssbt +qg and has a mass of 3.6 g. The distance from the bridge to the support post is L = 62cm a+ .+drsb 8bk+nf q tzm)g7sl8gnd the 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 te d;u nt)g 0m)fom /gl+;rt;eno vibrate at 200 Hz, but it is measured tmtm rt0dgn;) n/)elg;fo;e +uo vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hz, but it iscyn 0oht/p79n-yis5 l measured to vibrate at 205 Hz. sy5th-pcin9yo 07 ln/By what percent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a,mpddno4c tw /i :m(9)u dzoj/ small-amplitude mechanical 60-Hz vibrator.ooc4/j9dw mimn/(d,u : )dpzt The string’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 ofrawgst4r(e+8x flq) 5 the string may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 rr + 48qg5tfxas(elw) 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 fort*az(76f .oa xjru hl+hh 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. h 6(hazojx*+7ufla r standing wave in a 65-cm-wide tub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling a8 2mm j-:ygbylt k.0 km/s strikes a boundary within the Earth between two kinds of material. Ifmm-8jy y2g:lb it approaches the boundary at an incident angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “shelf” where the velocity changes from 2 o7yntcfr,oha*ry 0+4 db -vu1.8 m/s to 2.1 m/s If the incident wave crests make -orfr y0 +*yo74baucht ndv1,a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air when it hits t h)0:+yakh*hcs9 utw a layer of cold, dense air. If the sound wave hits the cold air interface at k ctwa:sth)hh9u0*y+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 3bgqxoyw6 kg(-f 1 jr.a 38 k3g f(yq 1b6j. x-owrg$^{\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 dipc( 7erj p0wi8ar -oz7ameter. According to the user’s manual, the dish has to be pointed in the direction of the satellite, but an error of abor0zp8erjo(i-77 cwap ut 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 acro. dwrj,ctn*8h tu.90kqqp h -oss the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in. *rpoj-qth,n9 h0 c twu.kd8q the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness constant of 550 kN/r)t0di4c1.1 xa2jtfm+b jjgsm Find the maximum compression of the bumper if the car, with mass 1500 kg, colx j g0cabt.djrtjs2141) m+iflides 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 3tgv g* s-,*q blzo)m+k 3sptia fire net 18 m below, which stretches the net 1.1 m. Assume that the net iomgl)t v*pb* 3k- gzts+s,q3 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 sprq0 :m4w(txyfn ing. The mass then falls 33 cm before it stops and begins to rise. Whaqn t4yxm:f( w0t is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a 6s3f*( ;cbtd skvz)wrspeed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffness constant of thzs rvkd)sw ;(bc6*ft3e 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 cob0.cdx p gj36wffee (diameter 8 cm) at just the right pace of abo pbd 3wj6xg0.cut 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 gcu q4q3a *ls)cm from the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequency of the sound emittuq 3aq*l)4 cgsed?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t where x is in dfwmeiq6z,t3by,j u 1ue8q .7meters eeq1yjimzutd f87. 63, wbq,u 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 it acc 2-q2zpmvnaz- elerates am-zna 22pv-zqt 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on 2 u:qygn 6y1o/q8m 0g)lrqmxia lake. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the raft vibrates for a qy1mm 8lq g/:2 yrin6oxg0q)u 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 instrumev3bt25ac + ;xsg ci*m.o:wqqent are tuned to play at 392 Hz (G) and 440 Hz (A2e5moc vc:qg .+3wa; qxbtis*).
(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 (8o9e g7; uhghj5ix 6qug y( 1j(khangstretched two-part cord of Fig. 11–33. Determine a formula (a) for the 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) hgjg8q ui(k5e;1((hjg yo6a xh 7n9guIs the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequ dys/ljra4 ,3vency of 264 Hz, and the tip of each prong moves 1.8 mm to either side ol d,a/r3j y4svf center. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simple harmonic motion of wo o;;2 dnli5wfrequency 1.5 cycles per second. What is the maximum amplitude with whi l;ownio;w d25ch 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 oscillation?

A string can have a “free” end if that end is attached to a ringjoj( kb, g; e uhz8z-v+0kei7p that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a strin jg;,e-ij8e0u pk (+z7obhvkzg with one end fixed and the other free.

  A “seconds” pendulum has a p( fb4 t2(px i(qhibem2eriod of exactly 2.000 s — each one-way swing takes 1.000 s. 4f22hiq(bm (txpbe i (
(a) What is the length of a seconds pendulum in Austin, Texas, where $g=9.793\mathrm{m/s}^{2}$    m
(b) If the pendulum is moved to Paris, where $g=9.809\mathrm{m/s}^{2}$ by how many millimeters must we lengthen the pendulum?    mm
(c) What would be the length of a seconds pendulum on the Moon, where $g=1.62\mathrm{m/s}^{2}$    m

A mass hanging from a spring can oscillate in the vertical direction or can swki0s t :qslg/chuky3nul0swl2)f 1 5:ing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontal swings, andfyu0c1ss w5gql3)0/l i:: u tk2shnkl 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 tension of 255 kwhji4-a22w 8kl9dzen i(e6 p N. A pulse is g92ep(6i42- wk8 zw akeljindh enerated at one end, and 20.0 ms later a second pulse is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spring with sprih8uc6b3+ bpxbu c31y7 xl .fnfng stiffness constant k. A penny of mass m is placed on top of the blocbcp3buu6cnf xxb+71.3lh 8 yfk. What is the maximum amplitude of oscillations that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. Tc t7zo+,j), (v7kymwmdqc6njhe steel crane cable is 22 m long an7,d6,j cqwk+ vcozj(tnym 7m) d 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 Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (wh/,snzwsldm. rdkx, s41j3p3 nich also gives the dimensions of the block). You push r1 sdl d4n/,km,ssj3z3. nw pxit 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 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz