Give some examples of everyday v1i:vhft7nemj;+(;oogj o+ vg ibrating objects. Which exhibit SHM, at least approximately?v+ j n et(1vojg7;;g+ooi:mhf

Is the acceleration of a simple harmonic oscillator ev d 9;m*dv; *wojvjqlh2gi7mr3 er zero? If so, where?

Explain why the motion of a pivw8-0k p;mywfston in an automobile engine is approximately simple harmon8 fkwp-;v wmy0ic.

Real springs have mass. Will the true period and frequenc09k5rfvaucf+ +o ogq 3y be larger or smaller than given by the equations for a mass oscillating on the end of an idealized massless spring +c+3ov akqfg0f9or5u? Explain.

How could you double the maximum speed of a simple harmonic o 9p,pr-tnzo2ixg0 tl,9bh n)r scillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scal8kw*7j 1/ mcck. nptjws/zaowtd 35x4e, and then is releasesj/zwnam4j. 3xco/5tckk871p* wd twd. Describe the scale reading as a function of time.

If a pendulum clock is accurate at sea leveldkxc q,)w00pq, will it gain or lose time when taken to high 0 ),wdqxc 0kqpaltitude? Why?

A tire swing hanging from a branch reacx/yzi*d)n,+a:pfqhfbv 0 8k p65vnfj hes nearly to the ground (Fig. 11–48). How could you estimate the heightfnfnpaypx jf: d58vvq/k,z6) +0b i*h of the branch using only a stopwatch?

Why can you make water s ov/r8:m :kdcxlosh back and forth in a pan only if you shake the pan at a certain frequen8xvm r:/do:c kcy?

Give several everyday examples of resonevj 0yuw ,s5(9 ul8dhoance.

Is a rattle in a car evq*vxowz-v c8 5l pe-,ter a resonance phenomenon? Explain.

Is the frequency of a simple perio5 0j alk v::2v lxuj/ge.zjof,dic wave equal to the frequency of its source? Why or why notju2:lf/j,zovjxek :vl0 a5. g?

Explain the difference between the speed of a transverse ,jc4 u7x txqa2wave traveling down a c,c a4uq 7xjt2xord and the speed of a tiny piece of the cord.

Why do the strings used for the x55 z y*ucl7edlowest-frequency notes on a piano normally have wire wrapped around them?d57 * cxlezuy5

What kind of waves do you think will travel down a horizontalpzovhxi2-0py9nbe0 5c/nc w+ metal rod if you strike its end ipye+c 0o2hvn0bc9z/n p-w x5(a) vertically from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increan7+f+qjmjs xw0ijl )0se in temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound w+wj js )0il0j+q m7fxnaves in air to vary with temperature?

Give two reasons why circular water waves decrease in amplitude as e(mjxw.bt7cxd yl i,z a .:tg6:z. ql5they travel away f: y.dq.ewax5 tl(cl,mj tzi b x.:6gz7rom the source.

Two linear waves have the same amplitu s.et//uft -)p0xlh nwde and speed, and otherwise are identical, except one has half the wavelength of the other. Which transmits more energy? By what factorte xp /tl)/shfuwn0- .?

When a sinusoidal wave crosses th*hsy7, b*yb ()fe lrhae boundary between two sections of cord as in Fig. 11–33, the frequency doessb( fa y)l,ehy b7*rh* not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there any places you could t(rc u cg9:w7mc29;jeqavff + youch it with a knife blade withoutu2a:qvg9jr9ccfew+f7m (c; y disturbing the motion?

When a standing wave exists on a string, the vibrations of incident and r x;.u-eq hfm3ieflected waves cancel at the nodes. Does thi .x;efmhui q-3s mean that energy was destroyed? Explain.

If we knew that energy was being transmitted froidi6m 90i/:dq xk2xg mm one place to another, how might we determine whether the energy was b i m2d: xdkim/qigx096eing carried by particles (material bodies) or by waves?

  If a particle undergoes SHM z aj4dcubc 8) zf+w;vu7bp.mo 6.)3dewyb(gq with amplitude 0.18 m, what is the total distance it travels in onew+ mp g .qvj8z4e;d)ub(b z6fay.3obuwcdc )7 period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs fro -zg:kw0ma) ky.l4ao hm it but is 85 cm lok4mkwzg.h)y o- :a0alng when a weight of 180 N hangs from it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car c *y/,kyi efrw pq*rn8+ompress 5.0 mm when its 68-kg driver gets into the driver’s seat. If the car goes over a bump, what will be the frequency y,q +in/p kw8*f*ryerof vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs from it. (akdd2clqwy1m07 wiz 46x7 t1ju ) What is the spring stiffness constant ykdq w7c201w4 t1iu mld7xzj 6$\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a frequeny ,f;cxvhr5x 6cy of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency if only 0.38 kg hangs frhfxr;x,y 6v5com it?    Hz

Construct a Table indicating the position x of the mass in Fig. truq6 jzg6 9wgc9fxov,u2o6- 11–2 at times t = 0,tg6u9fxz96u,oq-r6o wgjc tv2 = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 isi1;d 8 ei siv+tghyh3; rnka*5 caught in a spider’s web. The web vibrates predominately with a fre+y 5v8;hti3es r*ii hk1;ga ndquency 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 ox m/xyo407z5xz;o9 yo h uv1oof a spring vibrates with a frequency of 0.88 Hz. When an additional 680-g mass is added to m, the fr;yo yho0x/mox9x 4o5vuzz7o 1equency 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 times per 06fst d e )+gj:s kkc2aa/ef:zsecond with an amplitude of 0.13 m. Determinej sfadc:: g6/+0kt2)azs f eek
(a) the velocity when it passes the equilibrium point,$\approx$    m/s(round to one decimal place)
(b) the velocity when it is 0.10 m from equilibrium, $\approx$ ±    m/s(round to one decimal place)
(c) the total energy of the system,$\approx$    J(round to one decimal place)
(d) the equation describing the motion of the mass, assuming that x was a maximum at x = (0.13π)cos(  πt)

  At what displacement from equilibrium is the speed of a SHO half the maximum vailt 1.5*q tmcq7x. kb tbim;-pluexmb1 i*tqmt p.- lik5tbq.c;7 ?$\approx$    A

A mass attached to the end of a spring is stretched a distance w-3:kwdupywf k+*:am $x_0$ 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 vert5i;f;q8oh y auical 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)5o8;i hy;qfu a equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with spring stiffness constann/s.1ab 4cn y sya;z7yt k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is movi4a7z1 n;yysaby /s c.nng 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 0.200 m to “lo9./vod8qri- 0gcs uu7grhl(lad” a 0.180-kg ball. With what speed will the ball lcgrq70rh9o/ d-. 8l vgu(iusl eave the gun?    m/s

  A mass sitting on a horizontal, frictionltr0/daoaf ei2 6lj0) -md1duxess surface is attached to one end of a sf e62ud1 od0lxir/aj-0 a dmt)pring; 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 acceleration of 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates according to the equation x = 0.45cosjj9hfju.)t1/r mmxad 3 1t qt.6.4t where x is in meters and t is in seconds. Dete mqra tum jhdtj.f1391xt)j/.rmine
(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 ch y2.ojnv/ g1SHO half KE and half PE?y 1 hc/gj.no2v ±    A

  If one vibration has 7.0 times the energy of a second, but their fr5ddl 6(jwxuor:r mh+v *;8pdm equencies and masses are the same, what x6o+ m:5( d*; plwrruvddjmh8 is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging ligc5 um+; i89u2i0l:78wdqpdi qbsefu hht spring once every 0.65 d dsiqu2l ;7ueb9uq pf8+ci50i8 wh: ms.
(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 suppq j(5.qwfz (iefd3vz .orted by two identical parallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What.eqfw qvzd(jiz3. (5f will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.cuyf:jaa8c *2 5t where x is in meters2 af8caju* c:y 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 aoe ncp(m6 rg, x*5(sibnd B. For each, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

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

A vertical spring with spring stiffness constant 305 N/mu5 ,y tvhc gkr,/n(j-r vibrates with an amplitude of 28.0 cm when 0.26gn rct/yrj u-(v,5hk ,0 kg 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,uozk ::li;+ei; ld w-h with spring stiffness constants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikesd .w0 pxkhq+9d0 sz2uw a 0.600-kg block attached to a fixed horizontal spring whose spring stiffness constant is +w pd ud0s 0z2hw9kx.q$ 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 hi)mhda(7,j5/sid de ptgh bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level od( t/ )ddaispemj7h,5f 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 6 ,1hfecbh+9dnjvqxdo: ) l(7e0 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 y0d3c oa4wr;7zo m7mpper second? 7 ;dc34pmm7rwo0yoz a(That is, one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s o5twxkztq5 kol6sye( r-a 0s-2n Earth. What is its period on Mars, where the acceleration of gravity is about 0.37 that on Earth? s2yla k x5-sowe0 z(trt6-kq5   s

  What is the period of a simple pend fy rouo8 f98r1i7qet:5fyy vrvze* .(azwn43ulum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 m, the pendulum bob has a mass of 6s ne ui;gs2p(365 grams, and it is released at an angle of s6sn; p2(egui 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 ofncr2g8v 9d* 7fu1 qw*g soes-f 0.9930 m. If the clock loses half a minute per day, how should you adjust the length of the pendulum oeuw9gfv *r8-2n 7c1f dsg*sq? shortened by    mm.

Derive a formula for thcq0qq(6 mfc. le maximum speed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates a l p4uce4he*a/7;z zzzt a frequency of 2.5 Hz. At it is released from rest starting at an ang;74/hcapzu z4le*ze zle 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 wav-7ec e 9po*j x kxptsw:fv *q;7f3rqr0e crests pass the bow of his anchored boat every 3.0 s. He measures the distance between two crests to be 6.5 m. How fast are the waves travelikt 9*p qfp 7;0:*es-v erjx3w7fqcxro ng?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with a speed o jo5 .fb8xwf3en gqgcvc46p2;1np . zlf 343 m/s How far apart are the wave crests (compresg2q pvze .f5f61jn nwgo;pb 384c.lxcsions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 160zmp +,b58qcaq*lj ny 20 kHz (kilohertz) and travel with y qjmlnb8+5z*2 cqp,aa 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 of longykg/ v*1 k3 dwmvs:gz3+zvn+mitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the su :ct*9*hy dpf2 wd/rr+ii )mname elastic modulus, but one is twice as dense as the other. In which rod will the speed of longitudinal waves be g2c/mwt+d:*ri*yd)9 rnpi h ufreater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m)q+fdh(wt s/p c4en357tg(d-aq(jk6l asf ji apart. If the tension in the cord is 150 N, how long will it take a pulse to trafj (qlqa dst46(/c3e)gst nfda+jw7h-pi (5kvel from one support to the other?    s

  A ski gondola is connected to the top of a hill by a st ;ow/b/;1hza j mht18njj khb-eel cable of length 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and sends a wave pulse along the cable. It is observed that it took 16 s for the pulse to return.-b1 ;/ hjowjt m;h 8jb1ahnkz/
(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 n79xwqzqhka 604t u/;d-bgvrof the sea. He hears the echo of the wave reflectqd 4gxwbn 9vuq6/r7kzh- ;0 ated 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 travel at different speeds, anh uch*ook y14,-(ynr md this difference helps in locating the earthquake “epicenter” (where the disturbance took pla,k hoy4oc*hr(-ymnu 1ce).
(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 tra/66bm srae: 93h kcconnsverse wave. Assuming a frequenckhmbcna93 6eor:s / c6y of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, ant6gu dp3 9az2wd (b) the amplitudes, of an earthquake P wave passing through the Earth and detected at two points 10 km and 20 km ft zd2963 uapgwrom the source?(a)    (b)   

  The intensity of an efw8ogz qy5)* jx8.( wtod7hrr arthquake wave passing through the Earth is measured to be otfho87rd).z 8*rw qxyw5( j g$ 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 th3-.sopvgg r g n/0ou;ce same frequency travel through the same portion of the Earth, but one is carrying twice the enerv.cu og-r 3gp;og0s /ngy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same frequeu6ba juw82hb gy57wp7i-bob -ncy, but one transports three times the power of the other. Wha5jw iuu7--pbb2hobwb7a6 g 8yt is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move up and down a total verticrk:tq+6qh7 nmal distance of 6.0 q7 :mk nq6htr+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 moving2g(7ecy.q k 2rwxbxr6 toward each other. (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 straight. What has happened to the energy at this momg crw (262xy7xrekq.b ent?

  If a violin string vibrates at 440 Hz as its fundamental fr8xo:m.y 9qsej -ogja 8equency, what are the frequencie8ja-q.gxy jos9:o em8s of the 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 frequ h1mu 8cp6 qr1g1gc6snmovj ;,ency will it vibrate if it is fingered one-third of the way down from thegg,o181 vmh qsp;n6c16mujcr end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops idpsl4l) c*8/taz bb+ at a frequency of 280 Hz. Name at least three other frequen8bt+) zdcsp ba*ll i/4cies 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 frequenxx:cv 2bc )zmr.ly79h gbf8 2pcy of standing waves is 475 Hz, how far apart are two ay 8 m)x9cxz .b2rclh 7p2fbvg:djacent nodes?   m

  If two successive overtone iumf(j hqf4*d2 a uy.op0po*1s of a vibrating string are 280 Hz and 350 Hz, what is the frequo4f u *ifqyom0aj1* .p2dh(puency of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distance from the b0,8nft1mqevi u3 6 biqridge to the support post is L = 62cm and the string i 3e60,1bqqt 8fvmniu is under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string kd*i)wn, i v8fis supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. v8*ki ni ,dfw)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 ja/e 3:i myoekneh218 string is supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent sho 8oe2ye:km n3iej1/a huld the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-ai )8mmvkha /3pmplitude mechanical 60-Hz vibrator. The string’s mass per unit lemahi k)p/v8m3ngth 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 pulley. +m7z mr3tu si8If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying z8tm+m s u7r3iL between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a k9,wvb/f;(xi m t+tkktub at just the right frequency, the water alternately rises and falls at each end, remaining relatively calm at,(f/; m vtxkkbki9+ tw the center. Suppose the frequency to produce such a 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)n18 6re y8 9tyk2ogetkdd ujp .e.7vo at k.0 km/s strikes a boundary within the Earth between two kinds of material. If it approac.e. 6ed9pook d 7v)y yj8uk r1g8tn2ethes 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 2.8dbi3:wqu ha/;d. inp 6 m/s to 2.1 m/s Ifdw/: . ;di ahb3pinqu6 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 amsk49 bmo4*cvx zp11vir when it hits a layer of cold, dense air. If the sound s41vz9cmm xo*1v4 pkbwave hits the cold air interface at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave strikes a boundary between two types offs gi-nlg m j0gp 2 :9us*k4diqs1/)ya rock at a j *adsf/m : 9ykqg2nigi-l04)s1pgu s38 $^{\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( usfjvqazz*i ,r3x +9u2sy8g manual, the dish ha3r y+ u 9f(ju,zqszas g*i82vxs to be pointed in the direction of the satellite, but an error of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 250 km and velocity 750 km/h travels across 9kj9b5 uhfe.p*kmxaxq 58o6uthe 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 h8ph9 m*5xajfx6ek9qbo5. u kuave 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 550sl*fk*27nhj z kN/m Find the maximum compression ofj*lsnk2*h7fz the bumper if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a windoz lsj9pa -ok tm4f5tl 0c1:r7h in*hp)w to a fire net 18 m below, which stretches the net 1.1 m. Assume that the net behaves like a simplktsto-50rl :c fn )phazjp* mh19i47le 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 hang.ax3/ ed tuzr,ing spring. The mass then falls 33 cm before it stops and begins to rise. What is the frequency of the oscillation? t3/ dez,rau.x   Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 111xh.mt r(: wl(odqq3i–54), compressing the spring 5.0 m. (a) What is the spring stiffness constant of the spw(o. ql1qh(:dx3trm iring?    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) a11o+i r1dqyip t just the right pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the speed of waves in the cp r1q+1i dio1yoffee.    cm/s

  The ripples in a certain groove 10.8 cm from the center of ,) gh2ri58ycud k*qn mf;tdf:a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the iry2c ghkd )q8d t fmu5*,n:f;frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t where x is in t 2y.* qmu;hcemeters and tqutc2.* ;hey m 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 frejj ms8hnp8(n6i /s -vnquency f. What is its frequency if it accelerates at 0.50gp8-vmh is(nn /6snjj8 (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats ig8/2u*tljobr ua,+pon a 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 v ,g+u a2uji8lp*tbor/ibrates for a while.
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a musical instrument are tuned to play at 392 Hz (G) and 440 Ht-e+:wb ..ztup3 y/wcf f7m.ore/wcnz (/+p:yceefb .f73wztmc n.ur-to/. w wA).
(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 thx*d2a wxh : 6eo l7ju/p5kya2ge stretched 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 ax/j ouxh2 y6:kgpawle2d7*5 ) 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 msf9acz /:yb a7go3s 8c4l ;swof each prong moves 1.8 mm to either side of center. Ccaab /7:slmy 4c8sw9o;g3z fsalculate
(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 fr7a4d .cxid tc5blbkrz3b /3h0 equency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact3xiahd.7 0kt/b 4bzl d35 crbc with the board during the oscillation?

A string can have a “free” end if that end is attached to a ring thdas 36v ktzxzy/3(i7h ( f:cfrat can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with onzk6fs3ry t: (3f h7(/zcx diave end fixed and the other free.

  A “seconds” pendulum has a peri/ik 7 u:a*zeslod of exactly 2.000 s — each one-way swing takes 1asl eki: u/*7z.000 s.
(a) What is the length of a seconds pendulum in Austin, Texas, where $g=9.793\mathrm{m/s}^{2}$    m
(b) If the pendulum is moved to Paris, where $g=9.809\mathrm{m/s}^{2}$ by how many millimeters must we lengthen the pendulum?    mm
(c) What would be the length of a seconds pendulum on the Moon, where $g=1.62\mathrm{m/s}^{2}$    m

A mass hanging from a spring can oscillate in the vertic: 42yd a+7h/)lvtrwmfzc6joyal direction or can swing 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, and bjdw6f c/h 4yyzmat v)lro2:+7y 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 -br/puyre 06dig q y *y6j/t-x255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at the opposite end. Where will the two pulseb-jd/06pgi/ yq ye6r- txyr *us first meet?    m

A block of mass M is suspended from a ceiling by a spring a.l (. s-rs-byzj1ihe:wb ( yi/nxhk6 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 just stay on top of thheyha1:.biis/xr w-j-sbly .6 nkz((e block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel crane cable is 1u;u 1fye6 h2tzfcp r-22 m long and has a diameter of 6.4 pheft f zc;2u16-1uyr 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 bu/r-ru g0asv. 84pooshown in Fig. 11–58 (which also gives the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back andbo u-ogp0sua .4/8vrr 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