Give some examples of everyday vibrating objects. Whic0/-r7j zabame/hqa,e h exhibit SHM, at least approximatel0ajmezqb -e,r7haa / /y?

Is the acceleration of a simple harmonic t2;e 5w mv6n,trh :-u83ednfhcf7 nc d6v)vyboscillator ever zero? If so, where?

Explain why the motion of a piston in an automobile engine is r 9o3tj8q/ kpuapproximately simple harmonic pu8/jorkqt39.

Real springs have mass. Will the true period and frequency be )p pf w0or:9l ,x-ry dv0m/mnflarger or smaller than given by the equations for a mass oscillating on the end of an idealized massless spring? Explai)/ 0f opwrl9 df:,mpymvn-x0rn.

How could you double the 9v zd6 ,,+s-nw bqbmqbt,: luxmaximum speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring s0fbjheqh -e7 -cale, and then is released. Describf -jbq7-he0h ee the scale reading as a function of time.

If a pendulum clock is accurate at sea level, will it gain or lostv,;cct(m ;zve time when taken to high altitu(;ct t;c vz,mvde? Why?

A tire swing hanging frombvlq l- u5;4dtq iovh.op71/y a branch reaches nearly to the ground (Fig. 11–48). How could you estimate the height of the branch using onltou 51 / lpv4. ohqy7biv-;qldy a stopwatch?

Why can you make waterz0 arc;66wmg j slosh back and forth in a pan only if you shake the pan at a certain frequg0c 6wj6a ;zrmency?

Give several everyday exampl,8 awl01tw*f(yefamfmg 8 df h9* /jples of resonance.

Is a rattle in a car ever a re2q a jjf do39q:r5cve0sonance phenomenon? Explain.

Is the frequency of a simple periodic wave equal to th ;idl 38itb52i1k;mmvp fqpb6e frequency of its source? Why oqp i ;bpdm1b5v l8im;6fik2t3r why not?

Explain the difference between the speed of a trani8c6w -el4 ha cy+(m u,hkwp4gy kl-i0sverse wave traveling down a cord and the speed of a lgywlpm ckh-0+4 hc ,k 6a-8iuiyw(4etiny piece of the cord.

Why do the strings used for the lowest-frequency notes on a piano normally hav1sy3r*dl ;d f;/lntiye wire wrapp;3d / y*dily;1fnstlr ed around them?

What kind of waves do you think will travel down a horizont/t4 y;b+re8a 3x t1a2h )ejh kdck5gtpal metal rod if you strike its end (a) vertically from above and (b) horizontally parallel to ix +k;hh 45pd y/arte3c e2kta)8gtbj1 ts length?

Since the density of air dei 2c*zq8m i: fdpsiv5hjd9;g.creases with an increase in temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the sjz:*im fc g59.v d2;si dpihq8peed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in amplitude as thgj-m,g hij4g68tqd z5 ey travel away from the source. dzj,h6gjg5g8tm q-i4

Two linear waves have the same a/d .tjragbo*;mplitude and speed, and otherwise are identical, except one has half the wavelength of the other. Which transmits more energy? By w jat d/*;b.rgohat factor?

When a sinusoidal wave crosses the boundary between two se lkcv5o)5ezuw fa)v8ahp .**dctions of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocity do change). vfak)va* pz u55 oledcw*8h. )Explain why.

If a string is vibrating in thret5*dew0 w/wscol3 :qge segments, are there any places you could touch it with a knife blade without disturbing the mo5tsdg :l03q co/e*ww wtion?

When a standing wave exists on a string, t,bar.wtw2v*e/2u9 ez a,*nolqfg l 8r*9egv yhe vibrations of incident and reflected waves cancel at the nodes. Does this mean that energy g wzqa2nt,r9u el8yv r,*a .9ef*ov/gl2*bew was destroyed? Explain.

If we knew that energy was being transmitted from one place toxo:dobo30+/ rt/fgb sdv 1vk/ another, how might we determine wt v :f/x+rosoodb kvd//3b01ghether the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the total distartxxens,)n):t+xx /h :ym2p tnce it travels in one2n:re)xx/ x,x m:thst+)pyn t period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it but is 85 r (ci+o igf6tb*0 zp88neqok i0+m+tmcm long when a we0m6 qfgko0ir++8ti8be *nopz c+mi(tight 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 ok12 qi99vxprfojb; 3 mm when its 68-kg driver gets into the driver’s seat. If the car3kj obqr1992xvp; fio 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 fispbyxfmq *ty03 0kf3q,h hangs from it. (a) What ,003m kyqq *ypf3tfb xis the spring stiffness constant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates withth/vuzecr+1 h1 a2xm 2 a frequency of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequvxz1c221hhe+au rm/t ency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the m1hud/o ;w+rury swww esc408, ass in Fig. 11–2 at times t = 0,wu,wo ud y4 chs 1;rs+/80werwt = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 caugesf rah6/ 4wd0ht in a spider’s web. The web vibrates predominately with a frequency of/eashwf r46 d0 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 viwo * 4gnt4/oxfbrates with a frequency of 0.88 Hz. When an additional 680-g mass is to/g 4n*f4 owxadded to m, the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of s;/*vja c*7s yqr,sffa spring vibrates 3.0 times per second with an amplitude of 0.13 m. Dq *s,sfa/ f*7crvjsy;etermine
(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 speediuwkb -c*-g ,k0ytey . of a SHO half the maximum valuue tyk-kw0i,c.-* gbye?$\approx$    A

A mass attached to the end of9(sv(hd2i6py;i w d gwg6qjm6 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 sprin )3dj70g4sxsahcr*8amc 0lk gg 0.315 m. If the spring is stretched an adldgca mkr*j s 80c73x sg4)a0hditional 0.130 m and released, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached tbp/ria9gf;z8;ffr mtph 5y j.ug84k - o a spring with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is pr8y/ ;z.kfpj h8ui9g-5 mg4;trabff 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 popo(b8 bkob 7p2uv d/43ci g9mqzgun 0.200 m to “load” a 0/b3 c84vgko 7mopb b2(qidu z9.180-kg ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horiy3xtjk 67l5kqj*t1 egzontal, frictionless surface is attached to one end of a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, the mass experiences a maximum acceleratkle15 kjqytj7gtx * 36ion of 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates according to the equation x = 0.45cos6.4t whu3gws* 4 lh.hqvg5ahjg3fp/ 6ere x is in meters and t i5u .wp gfvl 6jhsh3/hq4g g*a3s 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 ftuo69pnht )/urom equilibrium is the energy of a SHO half KE and half PE6/thupto n9u )? ±    A

  If one vibration has 7.0 times the energy of a seco:h:p* 2fjjzrg nd, but their frequencies and masses are the same, what is the ratiorp h::jj2zf*g of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hang/rum bey7v4e7ef +kj 9ing light spring once every 0r ejmu9 efb7e/v+47yk.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 para,d t,b ,idq5feg+g i5g cl6kr5llel vertical springs, each with spring stiffness constant k (Fig. 11–49). What k,g5t,bi decdlr,gi 6f5qg 5+ will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.i -ayijwb(o pr9ccg .0 nak-9.38sin6.5t where x is in meters and t y ncga wk.(9.rpi 9ja0b-ioc-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 eacr, p8p ltzzal1qu+:f6t ; bx1hh, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on the end of a hos 1*+mqg3 hmxwrizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial spee mg31 xqhswm*+d of 2.96m/s Determine
(a) the period and frequency of the motion,    s    Hz
(b) the amplitude,    m
(c) the maximum acceleration,    $m/s^2$
(d) the position as a function of time, x = (    m)sin(4.08$\pi$t)
(e) the total energy.    J

A vertical spring with spring stiffness constant 3a:le lvw/ra 5kp* h3m205 N/m vibrates with an amplitude of 28.0 cm when 0.260 l* h3k2lwm raepv/:5akg hangs from it. The mass passes through 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 stiffkq *ncb *hnr; :-zru9jness constants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes a 0.600-kg block attached to a fixed :xks4* wzn6jm horizontal spring whose spring stiffness constant imns6j:wx *4 zks $ 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 reaching hisn-xsvpw9pxt 4 s -yov+b569is lowest point, he oscillates up and down, hitting a low point eight more yxi-s54t6s9pob xp s+ vw-v9 ntimes 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 exactly 60 s.b/ h:uey.vtl8 What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly one swing per sh9xbi+u/t inc(zel*) econd? (That is, one complete vibration c+it eiu zl(h nb/9*)xtakes exactly 2.0 s.)    m

  A pendulum has a period of mpq5 my7b bxa3u01x0 d0.80 s on Earth. What is its period on Mars, where the acceleration of x5ypxa1m3b0umb d 7q0gravity is about 0.37 that on Earth?    s

  What is the period of a simple pendulum 80 cm long mfr0h ;x i)x(n
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pencj5i3:0jl mh1 s aj) ;n3stadzdulum is 0.760 m, the pendulum bob has a mass of 365 grams, and id:shc1 j ln03za;tjm )i ja3s5t is released 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 pendulum has a length of 0.9930 m. If the clock lo hfafuia8s-h4x+n( axba;a .5ses half -.ia+a uh a;fabxx48a( 5nfhsa minute per day, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximum y xjkw en00.6*k k*hctspeed $v_{max}$ 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 ofi 7s*ttw w0 r t3okeumf5t.u*r9fv. q: 2.5 Hz. At it is released from re5*otftuwr tir7u90s* fm .: vtq3k e.wst starting at an angle of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests pass the bow of his anchored boat every+ jdtu 3v0q/ 2fyh:qvk 3.0 s. qqy/dh2j ku:0f+v3t v He measures the distance between two crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with l i yeup94 quk2kg8 gz9y99en-a speed of 343 m/s How far apart a 9-zq2kn8iyguuk p9e4egl 9y9re the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (kbvbc3+d7 /fc sbam0:wilohertz) and trafsbwmcb:cab 0d v3+7/vel with a speed 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 oy awwf:(+q 3f jhsjh 7cl4*ftq4cc:9jf longitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one is twice ; /yw8he-e e s-oh yrq(nisgdd9y- 2u/6y*iopas dense as the other. In y us /i-dphod*;9(qie8e-erg6 - ynyow/ s2hywhich rod will the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is so arqv:4 efa62p* /jfctretched between two supports 28 m apart. If the tension in the cord is 150 N, how long will it take a pulse to tr/2*a4 qfjv :aecpr6o favel from one support to the other?    s

  A ski gondola is connected to the top of a hill by a steel cab9m j,0t;o;sf5byrxm r le of length 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and sends a wave pulse along the cable. It is observed that it took 16 s for 0 m;xot9fy; jm,5srbr 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 ofbun 28t1epm .79duzjjc(j8hz his ship just below the surface of the sea. He hears the echo o bj82 u1e8c7thjzn.9p(jmzu d f the wave 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 earthquake trfb-eyu-bz vqq )7t nw1k,.c w/avel at different speeds, and this difference helps in locating the earthquake “epicentqey. 1 wc zb u7bnf)qtk-w-v/,er” (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 app8ht89 n zz(oko:gf x2j9n rlr9roximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), wfohr92 9z g9orxjt n88kn lz(:hat amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplispfp47 zotm -5co i*v3tudes, of an earthquake P wave passing through the Earth and detected at two points 10 km and 20 kmo *o vis7zt-p 5p34fcm from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is measured2ffjme:a a2e f+3y+lz to be a22ma yfe jfe +:fl+z3$ 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 portgx* ,4 lg2k9ud: iwxluion of the Earth, but one is carr,l*wg2:u9i kx4xlugd ying twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling alongb:;q;nqd p,f b a stretched string have the same frequency, but one transports three times the power of the other. What is the ratio of: ;b ,dq;pnqbf the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move up and down a tbk;gzg scxfu3 7:rtanz. 5( ;xotal vertical distance:gr kubnt xf.gz; xa7; 5scz3( 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?   

The two pulses shown in Fig. 11–52 are moving toward each other. :b:t)xpp5 mup8otr2 x*y(fp q(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 moment the pulses pass each other, the string is strao*: u8ym()p:xr 5tbftxq p2ppight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundament 4wx6- toyph)/:ugy yial frequency, what are the frequencies of the wxioht g-:yyu6y4/ )p first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what frequenpcf-5ek f )sz7cy will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of the string vibrates as a standing wav ecfk5sfp7 z)-e.)    Hz

  A particular string reseot*g ac8z3*o8rke 1ronates in four loops at a frequency of 280 Hz. Name at least three other frequenciescro881ot*rz eke3 *g a 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 standing wavesaqzez5v 6 992cy5)n yfxo2gqk is 475 Hz, howca gqy n2k 59qv59z6 y)oe2xfz far apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz anda kazj6l1s)4*tj r9pt,u,wi z ww*r1l 350 Hz, what is the frequency of the fundamentalar, , zatiwj)jwlt4p*krlz6 w9us1* 1 ?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The +yoaku. g v8/zdistance from the bridge to the support post is L = 62cm and the string is under a tensio+y k8. gvoazu/n of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar striycn7)mkwb at5m3/5z b ng is supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?So the three freq7mny5 cb3 b5tma/zk) wuencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hz, but it is meas:vc eyc1w3p3p .xz-f mured to vibrate at 205 Hz. By what percent should the tecfvxy:3wec . zmp-13p nsion in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached pm,-.-yjjb ycpxdp,1(k u:3svhgz7k to a small-amplitude mechanical 60-Hz vibrator. The scj .pm-7: yk (,1,-vhgbuzjspy3xp kdtring’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 be adjusted by moving the pulle)4cxr jy,da- my. If the hanging mass m is fixed j mracy)-4xd,at 0.080 kg, how many different standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water baa-wk. .zg(zt ock and forth in a tub at just the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wid.-tz.o a (kzwge 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 boundar(gw h4(5awm+ve vbis/ y within the Earth between two kinds of material. If it approaches the bouiwb+v e/hma54(gs v( wndary 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” wherthjc*r+( ,ean5a7 t/tp1 zzx ge the velocity changes from 2.8 m/s to 2.1 m/s If the ina1 px*tnt(jh7/5geac,z t zr+cident 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 when ivr le rt3p.*. 5)papwvt hits a layer of cold, dense air. If the sound wave hits the cold a*w aevp.)v pp5 rr3tl.ir 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 boundap d5 ew0q hwgzwk3.a;)ry between two types of rock at a 3 )gkw0;5hw3adqp. ezw8 $^{\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 dianq gh+ lr :qsien51 3i *l xhk0ifrk+l3qs9:m;meter. According to the user’s manual, the dish has to be pointed in the direction of the satellit q +13ilxh:nln3l q gs 5 :qrkek*90f+ri;mhise, 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 vvtql1-mxh 0p 3elocity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, p3l-mtp10 qhv xeople observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness con ug ms/zhdyk p04l7:n*stant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 4mu spkz 7dn g0ly/:*h1500 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 jumpsy9y-fp- .nb.eler- iy from a window to a fire net 18 m below, which stretches the net 1.1 m. p. lf-9yb-e- iyer .nyAssume 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. Thqx n: o0lco2ex:ul73 we mass then falls 33 cm before it stops an7:e :lol0o2q ucx3x wnd begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. ,;. gzxhj*u- ne g/.hwm azxq(11–54), compressing the spring 5.0 m. (a) ;aguh x- *( .xnzjgzhwem/q,.What 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) qrab cw6r94k4hu1m xom,76 zq at just the right pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill ove9h6uqzrwqcoarm4 b m x46, 7k1r 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 33-rpm phoni-q, n+lofscgh ;(7d kograph record have a wavelength of 1.nh7qc fd s;kog,(+li-70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos)s tcc g+(3u: bi1mbav7.40t where x is in meters and t in seconds. Deteru sb)3ab:c1ig(m+ tvcmine
(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 frequpktjx 0no586 :zwji26h(j xquency f. What is its frequency if it accelerates at 0.50g (a) upward,6 jjoin5:6 xu hjp 8qzw02k(xt    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man slvlo/mt,r+1 )p8vi.q zslkl ( +s6yp stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the raft vibrates for a while. rsvls+lloi()/z+lsp1 6.m p8,v kytq
(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 tu6n,dgql q jj331:dpokned to play at 392 Hz (G) and 440 Hz (lg,:q6n pjjd3q o31k dA).
(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 cor shlf(. l(:iond of Fig. 11–33. Dn.so(:ihll(f etermine 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) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibraty h77vn -)o2..z wcr7 c4tnflb 9a+f yo+asxmdes at a frequency of 264 Hz, and the tip of each prong moves 1.8 mm to either side of center. Calculat-l. 7on+ 49cnv)7hfbyrc.+d2z w7m a sxyofta e
(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 frequency 1k*g*a;d evxw7po2kl /2s yt- u.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 losy-gxakvk d **27w;2 upoe/stle contact with the board during the oscillation?

A string can have a ahi, 4 2s0/x5gqkb9 l:fllp ud“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 the0lq fd2ukax 5:4lp gb9/s,hil resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period o ot -7 4gn go c)lni,gpv.7(swrd:s1wyf exactly 2.000 s — each one-way swing takes 1.000 sct1w)vwsd,gr s.oi7:gl g -(on yn7p4 .
(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 verti* zf h*mae9l;0dxq; 1lq gj.:lp(heyucal direction or can swing as a pendulum of small amplitude, but not both at the same time. Which oneq l*ule 0e.qa;;(gh:1 ydmfjzl*ph 9x 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 tension of 255 N. A p+ uvuut dbaa+ 7fv6:0hulse is generated at one end, and 20.0 ms later a suvv6+au 0tu7d+fbha :econd 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 spxt4mu n9vsd kc zc()71ring with spring stiffness constant k. A penny ok9xcumz7)s vn4dc (1tf mass m is placed on top of the block. 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 je4pif 1zb.t / h9 inc(nj2q-ljunkyard. The steel crane cable is 22 m long and hapqi 9znfjn / tc4.l1e(-2bjihs 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 (which also giv7efqg2f8 tzixil,,j sdc u )wh*,i52q9r a +goes 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 thi*j+q t5,2fl9, 78gz,wgfih)aodqri u esxci2s 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