Give some examples of everyday n+a ;:fnjul2 vvibrating objects. Which exhibit SHM, at least ap+lnvj; a2f:n uproximately?

Is the acceleration of a simple harmonics/8w4si**hy ,r xr6rw 5bjaxk oscillator ever zero? If so, where?

Explain why the motion of a piston in an 7hq gj9np7 k+lautomobile engine is approximately simple harmonic77gq+kj9l nh p.

Real springs have mass. akt,xv2, ht*n)ccy4ef: +p3yek5 y ua 3ndp-oWill the true period and frequency be larger or smaller than given by the equations for a mass oscillating on the end of an idealized 4,k t 5f-hk aec2,napyv* tnc:e3pyo 3)uy+d xmassless spring? Explain.

How could you double the maximum spu -i)l3z z;+vi* dv2ort alz6bm:6 kceeed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring sg 6)m xfe,ok5kcale, and then is released. Describe the scale reading as a function ofmo e,fkg56 )kx time.

If a pendulum clock is accurate at sea level, will it gain or lose time when takv bfqvr:d2x30 en to hifd2xb:qvv 3r0gh altitude? Why?

A tire swing hanging f/e5-tc3nnq y 3xn4pfulzcxkfh:) 0a 5 rom a branch reaches nearly to the ground (Fig. 11–48). How could you nef yh 3aql)zf5t 4:p nxu53cxkn -/0cestimate the height of the branch using only a stopwatch?

Why can you make water slosh back and ch +*wn frf-j.xsj09.)vs awmtfz l 26forth in a pan only if you shake the pan at a certain freqvltf 0 fjn9rcha wfws m*)6js.+2.x z-uency?

Give several everyday examples oqtrbxnv2cp.h s- ht57vjj3q :f (.4,xwqcm1 cf resonance.

Is a rattle in a car ever a resonancexr 9p6cp0it3s phenomenon? Explain.

Is the frequency of a simple periodic wscgw t) y588(s wxnpi9ave equal to the frequency of its source? Why or why not8cgs8ypnx)wws 59it(?

Explain the difference between the mb)bl7gq18yx,bfzmi ;q, y1e speed of a transverse wave traveling down a cord and the speed of a tinb) qim,,8mgyb7q 1b 1xy ;flezy piece of the cord.

Why do the strings used for the lowest-frequency notes on a /2)n)n dgzijjtt 6tf/tz/ p7npiano normally have wire wrapped around /fitp2 g n)z n)jn7tdt/tj/z6them?

What kind of waves do you think will8q8 rglqpg t3: travel down a horizontal metal rod if you strike its end (a) vertically ftg8r3qq l :8pgrom above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase in(6zqdij(ymsb7 /f :js8 w.lmt temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves in air to vary wi/: (wfty i ljbs68mjqm(sd7.zth temperature?

Give two reasons why circular water waves decrtu./zvrc r.q** jza j/ease in amplitude as they travel away from the sour /r/trzu ..jza*c*qv jce.

Two linear waves have the same amplitude and speed, and otherwise are irk)f+c t 2j1e ly3v2pidentical, except one has half the wavelength of the other. Which transmits3kvl)2e itrcy jp2f1+ more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sections of cordw5(*xsk5ez zdao s;o aze,m t )/s6*dp as in Fig. 11–33, the frequency does not change (alth/)tsw e55azeo m*d s6adk;o(x*z,zs pough the wavelength and velocity do change). Explain why.

If a string is vibra.w pt19(e( /iwzp0kdsg(o wb pting in three segments, are there any places you could touch it with a knifodit. (/9w1pkp (p(wgsbz w e0e blade without disturbing the motion?

When a standing wave existwo;t;z;(i wdn pkx))es on a string, the vibrations of incident and reflected waves cancel at the nodes. Does this mean that energy was destroyed? x )(;int p;wed owk;z)Explain.

If we knew that energy was being transmitted from one place to anothezwgb56;xo g6mfr /a thsw 4(s/r, how might we determine whether the energy was being carried by part;f/hb(5w66sg /zm sgwa rtx4oicles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the tow(k * uynm494cxu mp5baeyv- fl3rx42tal distance it trafv4x -c l 5x23m we4 rn*puu4(by9kymavels in one period?    m

  An elastic cord is 65 cm long when a weight of 7nh8i sshp ;5+s5 N hangs from it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” conssnihh +8; ss5ptant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg drive*c;3dcw teh. vr gets into the driver’s seat. e*c wd;t hcv3.If the car goes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs from ii)sm szc 9b*c2t. (a) What is the spring stiffness conss)cb c m*si2z9tant $\approx$    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 w cyz8p wu),1tstr*c/1qhsh h4 ith a frequency of 3.0 Hz when a mass of 0.60 kg is hun,th81s r )ctyw1 *pcq4z uh/shg from it. What is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. 11–srs0a 3ii/zm)+im3 pld iv)-p2 at times t = 0,t = )zidpm+-0vi simpl ai/s)3 3r $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 predomiu9; gcfww4ak *natel 4fk*;ua9c wwgy with a frequency of 4.0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a spring vibrates with a frequency of 0 3fvky/1jyn4(enb 5m zx-,f np.88 Hz. When an additional 680-g mass is apy-n f(5 nfybm,3zv4 xj/k1en dded to m, 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 times per seclzji1 8ic,ai *ond with an amplitude of 0.13 m. Determili8i ci1a*z,jne
(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 equilibrfp5wc7ne;1ek s;gqfbau uc,sv/ . (/ gium is the speed of a SHO half the maximum value7ue;,n5ba 1c;(s gfpeqfk .ucg//svw ?$\approx$    A

A mass attached to the end of aumgnw-9. s. chu9*pne spring is stretched a distance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretches a vertical spring rb8m9b rt pn:e)okq p232c-rk0.315 m. If the spring is stretched an additional 0.130 m and released, how long does it take to reach the (new) equilimbk:8er -cqr r9ppo t 2k32bn)brium position again?    s

  An object with mass 3.0 kg is attached to a spring with spring stiffness const )z-yyub4 c9t5gq*akh ant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is moving with a speedk)bzy ua*4y 95hcq-t g 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 cq 66ac4-wagqkompress the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will the ball leave tk46c 6wa-ga qqhe gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to one end of re ;tz46nzz-ea spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. n z-e4ez ;ztr6If 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 = 0.45cos6.4t where x .; n2mr w(vopzis in meters and t is in seconds. Det2;o( .vwrnp zmermine
(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 half KE an injfi x,c/7u.d half PE? ± iniu.7jx,f/c    A

  If one vibration has 7.0 times the energy of a 7px8ggz+0bg1bb 3dd fsecond, but their frequencies and masses are the same, whatbdg pb+gbfx3z g 7d801 is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light spring once every 0;l fzd:mhopc+51. owk.65 s. ho d1zk:5wmcfop; +.l
(a) Write down the equation giving the pumpkin’s position y (+ upward) as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. y = (   m)cos($\frac{2\pi t}{0.65s}$)
(b) How long will it take to get to the equilibrium position for the first time?    s
(c) What will be the pumpkin’s maximum speed?    m/s
(d) What will be its maximum acceleration, and where will that first be attained?   $m/s^2 $

A block of mass m is supported by two identical parallel vertical springs;-k0(fmxs7j;i8 2fi c+u) n cunkaprf, each with spring stiffness constant k (Fig. 11–49). What will be the frequencyf7usx-ca r2+ncf0n() mk;k 8fijpi;u of vibration?

  A 300-g mass vibrates according to the equation x io( l9l07o8skaee tgpf u) n*2= 0.38sin6.5t where x is in meters ande f(eugopa 9kt l )sni0*lo872 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 Sd-/d. jzmlda3HM, labeled A and B. For each, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest onturt.6n2 zcz ujbu- ;v u48lfzx5q2;n the end of a horizontal spring (k = 124 N/m) is struck by a . 2xq;unzutvzf 58tr c;n-2 b4uljzu6 hammer, which gives 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 stiffness constant 305 N/m vibrat ikp.3jo-jw89ro, th yes with an amplitude of 28.0 cm when 0.260 kg hangsy89pw ohr k-3otj i.j, 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; hkyou 3sc7hus*)0xx springs, 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 strikes a 0.600-kg block attached to a fixed horizontal spring hczhw,w/ +, ufyu 3 ):jsy7c7db1pxpowhose p)f/oupd7+7jzsbw,3u whxy: ,h1ccy spring stiffness constant is $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with mass 65.0 kg jumps from a hgk7;sjt g gq-.igh 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 jkgs7 .gtq -g;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 inr: o(h;mkcl ;z exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to mak 4,a h5.pqafwqe exactly one swing per second? (Thatp. waa54hfq,q is, one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Ea3 l7z+/gwao mbkp06*wbvt,ds rth. What is its period on Mars, where the acceleratio/ab0m6 gw,b* dl pt7k v+szw3on of gravity is about 0.37 that on Earth?    s

  What is the period of a simpleq4emvzr qm3;1u 51gg t pendulum 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 3dvj wu,6 b*pfk8mfji4cso+ ;4 65 grams, anb ,46i fu vwpcjd*m +ko4f8s;jd it 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 p5m yc*cu-. yxgs yye n,p+,.owendulum has a length of 0.9930 m. If the clock loses half a minute per day, how should you adjust the length of the pendulum? x-ucn.ymp,+wgoy *y.c5es y,shortened by    mm.

Derive a formula for the maximum spevcc+/ l-n gdl2ed $v_{max}$ 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 2.5 Hz. At it e4mghr ) 7;uwdis released from rest start g7 ;rw4me)duhing 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 booeh5 2wku(fw 8b 6it/fw of his anchored boat every 3.0 s. He measures the distance between two crests to be 6.5 m. How fasbo(ewuw26/ 8it ff 5hkt are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels wi d1qx,swkk 2u z2vl6f7th a speed of 343 m/s How far apartzf6dusw12klq,vx72 k are the wave crests (compressions)?    m

  (a) AM radio signals have frequencies ghoz70d ;8edb between 550 kHz and 1600 kHz (kilohertz) and travel wdb h 0d8oe7gz;ith 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 ofi i+9 -urnf lfe6obs*) 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 as inq8b8fzf n;, dense as the other. In which rod will the speed of longitudinal waves be greater, and by what f znnq8;b,if f8actor?   

  A cord of mass 0.65 l9sjm*yd4 d .fet7p)aj-,vh jkg is stretched between two supports 28 m apart. If the tension in the cord 9djdl.jvy 7a )esm-,jp4fh*t is 150 N, how long will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to the top of a hill by a steel cablev3j-( vjsvc 23ziet*f of length 620 m and diameter 1.5 cm. As the gondola comes to the end of 3ivv*vc( -ts2jfe z 3jits 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.
(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 akrmm+x3 td/r,..k djijb7p0 his ship just below the surface of the sea. He hears the e,j 7.x./t3r rmidkp0jk+m bda cho of 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 travel at dift-qs)ka tw npk w+(q-:ferent speeds, and this difference helps in locating the earthquake “epicenter” (where the disturbak-t) :qkw-nqp(wt +asnce took place).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced surface wave can be approximated by a sinusoidalz)*; dgot*: +qu l8jt7njtxs 4* phwvj transverse wave. Assuming a frequencyp js*zvg*jt8; wuq7j *l+n o)tdhx:4t 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) .t,nh 0oz)dijpv b,:f the intensities, and (b) the amplitudes, of an earthquake P wave passing through the Earth a.f0o tz)bvjh,pd,in: nd detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earba,p x dp 9/h(9b m5ay4jzcs5 g,6roxfth is measured to be 9 pgap6yhb9/ ,5( jxcrso b,dzm5 xa4f$ 2\times10^{6 }J/m^2$ at a distance of 48 km from the source.
(a) What was its intensity when it passed a point only 1.0 km from the source?(round to one decimal place)$\approx$    $ \times10^{9 }W/m^2$
(b) At what rate did energy pass through an area of $5m^2$ at 1.0 km?    $ \times10^{10 }W$

  Two earthquake waves of the same frequency travel through the same portion of tt-t:j aq(0ej+mnh i vn*xz*z .he Earth, but one is carrying twice the energy. What is the r+j0z z* :mev*qnt-h.antij( xatio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the s axc3re)k2p, jjs n2bktu3k (-ame frequency, but one transports three times the power of the other. What is the ratio of the ampl rtckekb -uxj,ja2pn32() 3skitudes of the two waves?   

  A bug on the surface of a pond is observed to move up and vg2url )5ws. 2yfb 4owp-opi 4down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm, by what factor doess4bl2pw y. u5pgwio2 )f- 4ovr the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each othexio4 c:rp-:.lu (;uchw sp mr5r. (a) Sketch the shape of the string at the moment they directly overlap. (b) Skem ou; .w xl5i(-c:ppr: r4uschtch 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 moment?

  If a violin string vibrates at 440 Hz as its fundamental frequency, wp4tyr z1k3 ync65 vbb)hat are the frequencies of the 1pk) 6ytbc 5vb 4yn3rzfirst four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibra(y ib 595 vt)hqu5rtpy-ky+q ltes at 294 Hz when unfingered. At what frequency 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 stan9yyqhu k+lpb5 ry (t5 -)tvqi5ding wave.)    Hz

  A particular string resonates in four loops at a frequency of 280 Hz. Nam*tecow 9 eba+gjq 9a0;e at least 9bq*+o we;g t90ea ajcthree other frequencies at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a stringg (ycg 90om2be is 92m/s If the frequency of standing waves is 475 Hz, how far apart are two adjacent nodes?0 ge2mbcg9o(y    m

  If two successive overtones of a vibrating sdg5mrc:e *v. j 0fi-hz-; ctmetring are 280 Hz and 350 Hz, what is the ;dmmfj-gie hctc0ez*5 rv-:. frequency of the fundamental?    Hz

  A guitar string is 90 cm long and has a massi n6b ju6 (wxcun;t4z( of 3.6 g. The distance from the bridge to the support post is L = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundamental and first two overtonetxibnu(nj; cwz(u 646 s?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, but it is measuredq2-o sk2vml 5o)/plgs to vibrate at 205 Hz. Bslqso22og-mk/5 )lv py 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 atv25di rxj(j1 nc46*qvy cp t4o 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to*i4jt dvpc5(nq orycv264jx1 correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-amplitude mechanical 60-4gtr.p* efpc05qs3 mpHz vibrator. The string’s mass per unit length3 40fp mqp.c*epr st5g 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 lengt4sa4 4 p-uncq+qh(qnwh of the string may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, hop -nqwns( +4hqu4q4c aw 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: qfnu183 rjxch in a tub at just the right frequency, the water alternately rises and fanf3:qrcu x18jlls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundary within the Earth bnqjy u7 277s+ +mlrcovetween two kinds of material. +c 7jsu qy n+ol77m2vrIf 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” whereqdq, dp6f x0auxb c-,,2l9xjp the velocity changes from 2.8 m/s to 2.1 m/s If the iq- pxupl 2daf,x j,,cq9bd x60ncident 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 x 9-awxc +mt5qair when it hits a layer of cold, dense air. If the sound wave hits the cold air interface at an angle of 2mxxwq tc95 -+a5$^{\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 typestp5,(h s i/6 okw,xhwe*xy rj; of rock at a 38 ewsi;oxh5 jy,xk6,* h wptr (/$^{\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 t e k0(m1u 9lbkj7hj7omhe user’s manual, the dish has to be pointed in the direction of the satellite, but an error of kj1 7l0b9j okh(mm7 ueabout 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 amy ;yi 2kjn(y.k;s0b2rr bi. qcross the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attrac;yi b yr;2nkmri2q0 y(jks .b.ted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness con/nu1 h)u p,hjastant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collides with a wall at a speed of/u nap1uhj, h) 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire n;p,0uk lo sb,get 18 m below, which stretches the net 1.1 m. Assume that the net behaves like a s ; kopbu,l0,gsimple 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 enrkiw wqove 3,x2(y ui0lg82b*d of a freely hanging spring. The mass then falls 33 cm before it stops and begins to rise. What is giuxlb*2,3o(2 8ykvqwei0r w the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 11–54), comp(pmpdt/f9 z-67df ogwressing the spring 5.0 m. (a) What is the spring stiffness constant of the spring?ffpd9-6(gd p7/ wzmo t    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of coffee (diameter 8 cm) at just the right:/gd v y7l4tb cldjt++l,u r6p pace of aboutl b7:+r 4/+jyutl gdtl,cv6d p 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 cer9 :6x8:akj bj(,si io5tp,z/im,mn zapomkq 2tain groove 10.8 cm from the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequency ozpa/ :ko:x mi9intiqmjoabp,kjz,, sm6 (582f the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cosq;q kl95w-jte7.40t where x is in metl59kqq-;w etjers 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 fv*f g qvcv*f;(9t4smarequency if it accelerates at 0.50g (;s*4ffqmt c9(vv*vag a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on -s4cwput3g dap5c rp3dmd49 4 the raft, it sinks 4.0 cm de 33uw pdpt9smr -445 cpd4cagdeper into the water. When he steps off, the raft vibrates for a while.
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a musical instrument ar baj f9l.i97whmds,k ,e tuned to play at 392 Hz (G) and 440 Hz (A). 99,ljk,hi as7wb d fm.
(a) What are the frequencies of the first two overtones for each string? G : $f_2$=    Hz $f_3$=    Hz A : $f_2$=    Hz $f_3$=    Hz
(b) If the two strings have the same length and are under the same tension, what is the ratio of their masses ($m_{\mathrm{G}}/m_{\mathrm{A}}$)   
(c) If the strings instead have the same mass per unit length and are under the same tension, what is the ratio of their lengths($L_{\mathrm{G}}/L_{\mathrm{A}}$)   
(d) If their masses and lengths are the same, what must be the ratio of the tensions in the two strings?   

Consider a sine wave traveling down the stretched two-part cord of Fig. m)6ml y2l:prf 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the: 2m)fplyr 6lm heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the tip of ep32 zl7oe:nd each prong moves 1.8 l3 oepde n2z:7mm to either side of center. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simple harmonzds* 66i*r ot5l0lb rnic motion of frequency 1.5 cycles per second. What is the max nizob6d 6slrl5*r0t*imum amplitude with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that end is attached to a ring .h-u9qrbufdy;4v+2 fz ylq n5that can slide without friction on a vertical porz ;nu5 h4vuy2bf+q-yfq9l. d le (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly34 1/w3dslrcgkrs i1qpyz 8. y 2.000 s — each one-way swing takes 1.000 s8 /k3dsly3gi 4 1 rz.pqrwsc1y.
(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 direcr ed6i9hm5e* ction 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, a 5heir*6cm9e dnd 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 tensio u1r141m7affxav4kjtbnt,8 m+0uei vn of 255 N. A pulse is generated at one end, and 20.0 ms later a seef ut j0fmv+1 11v4rt,mi4 87axnbuka cond 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 sq k8 di 407qcci7d/iubpring with spring stiffness constant k. A p /7bd qic8di4i0ckqu7enny 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 the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkfno-, v ce+.pgyard. The steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze startog-vec f,+ pn.s 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 af b4,bb1/vq lzge,-qilso gives the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins tbv e,b1 il-bg/qfq 4,zo 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