Give some examples of everyday vibrating objects. Wh0l5ev8zp6qbv7 py u,mich exhibit SHM, at least approximatellup 8bmv5 qy 0,7epvz6y?

Is the acceleration of a simple harmonic oscillator eveyrkvyqf;;d (-id. fu* r zero? If so, where?

Explain why the motion of a c5ft,p-eulwx)r;+t d *6i tl9ysl r5s piston in an automobile engine is approximately simple harmonic6psurx-l crte*wy5 tlt)f,l ds;i 9+5.

Real springs have mass. Will the true period (mh:)ocg:wgsy/0 f ad and frequency be larger or smaller than given by: gmd:0f(go/a h s)ycw the equations for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximw65ozc8b k7 moh (w,tkum speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached humq+col:(5g:uc6 jhto the hook of a vertical spring scale, and then is released. Describe the scale reading as a function cq g:cmh( l5oj:u6hu+of time.

If a pendulum clock is accurate at sea level, will it gain ow4rs9 g5m ycu3h d0u2 wsto1h7r lose time when taken to so 5cw1umu3r7 4h h9wy20tdsg high altitude? Why?

A tire swing hanging from a branch reachdn:(q)ot t lce x1mpo(cr43x,es nearly to the ground (Fig. 11–48). How could you estimate thetc,dpm1:c xoe4l ro(t)3 xq (n height of the branch using only a stopwatch?

Why can you make water slosh back and forth in a pan only if you shake t8jgn5cq e 6x)m8(c tomhe pan at acm(t5 c)n8x eo6mq g8j certain frequency?

Give several everyday examples of resonanq v.ryk/l ;k1kce.

Is a rattle in a car ever a resonance phenomenon? Exp7oqpn uv 1+7folain.

Is the frequency of a simple periodic wave equal to th1 -8 bmvrdap3ke frequency of its source? Why or why not?v m8-ak b3dp1r

Explain the difference between the speed of a transverse wave travelin ab1xl9c* a5bqy2 gebfc) (u:yg down a cord and the speed of a tiny piece o (b)uc2:gbq l cyay519efb*axf the cord.

Why do the strings used for the lowest-frequencyfa fg ;4vq2w7d notes on a piano normally have wire wrapped around 2;7vw d4fg qafthem?

What kind of waves do you think will travel down a horizontal metal rod if yqhs,6 +-tsfboou strike its end (a) vertically from above and (b) horizontally parallel to itsb+f-ht s6, qos length?

Since the density of air decreases with an increase in temperature, but th:l;xlk xowz: z.+bce-.x js/l0e9p c te bulk mbw lpk9+0o:lsce l:/t;zjx xe.c.z x-odulus B is nearly independent of temperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water weu+:re. e+v2qu f w) c7p(uaj yvvwb/5aves decrease in amplitude as they travel away from th52r+ f7:evwe(v a+/vu) p cuqy.jwube e source.

Two linear waves have the same ampli(euv7z(mr l + u;7veqatude and speed, and otherwise are identical, except one has half t auv7qlu+(e 7(z;evmr he wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sections of cord a;f 2-2bv1vh sa bz7lays in Fig. 11–33, the frequency does not change (although the wavelength and velocity dbfsvh2 a a;1-zl y72vbo change). Explain why.

If a string is vibrating in three segments, are there any places you could ty l*1w tordd22x( b5yjouch it with a knife blade wit*ld2d2w1 yjyx5 tr ob(hout disturbing the motion?

When a standing wave exists on a string, the vibrations of in ci1rjc73ef(w 5;3voh t9fucx ip2r1q cident and reflected waves canc3r(p1frvx oftj 7 i ic53 e;wcqc91hu2el at the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being tru-gn( q.h6v/f ucawi5 ansmitted from one place to another, how might we determine whether the energy was being carried by particleh-vaw(nu c.f/g 6ui5q s (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the tot)et0kn4dp 8o( k,iz syal distance it travels i ye inkotk,4z(8d0)spn one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs8tb w,tl-g o+:swi,q or4 v*jvqtk6b- from it but is 85 cm long when a weight of 180 N hangs from it. What is the kb6tl w:+o4oq-r v,8 visjtbgt, wq-* “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress o+ 8mhjflxisvx dj( 1r53dn84 5.0 mm when its 68-kg driver gets into the driver’s seat. If5jjio8v dhs(3r4m8 xdl f1+n x the car goes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6.egq5,lnlfu cn:9 bz. cm when a 2.7-kg fish hangs from it. (a) What is t5znl q,:b.. efl gc9unhe 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 with a frequency of 3.0 Hz when a mass of 0.60 kg i/p gk1c9 jis:ls hung from it. What is its freli9 spg /:1jkcquency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position n1 cu/+uel3v jx of the mass in Fig. 11–2 at times t = 0,t = n+ue/v 31clju $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 6w 1pre;+su n;/g:v gqevghv; in a spider’s web. The web vibrates predominately with a frequency of p6+vuwrh;ge1e:n sv /g ;v q;g4.0 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 fre px tkabz h8*6im1k/1 (r7jcwzquency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is 0 khmca78/zbp xr*wkz jt61(1 i.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 second wj *n7 zhuaj)ka y52(gd w;v i-*y8jtcoith an amplitude of 0.13 m. Determ i*jdk a)ytguo7aj5(wvzcj;n 2y-*8hine
(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 hayg u1+jdpdre sf311(e 7qrz4 qlf the maximum valf (dz3sje1d+g4yr1eqq up1 7rue?$\approx$    A

A mass attached to the end of a spring is stregeb+l(k( no*uq7co jp m* 5xj: k-hgmmvw-;6ptched 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 0.315 m. If the spring is st* -sr7-zf,gug wzntu.kmel.)retched an additional 0.130 m and released, how long does it take to reach the (new) equils *egug.um)lr-,.kw-7 tfnzz ibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with spring st2 7 gggdl:k/kniffness constant k = 280 N/m and is executing l2gg7kgk/: d nsimple harmonic motion. When the object is 0.020 m from its equilibrium position, it is moving with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compress the spring(/9jr p t r(zi2pvguyhg8z49n of a toy popgun 0.200 m to “load” a 0.180-kg ball. With wuj8r/ zp2n9 (y(4t ghrvp 9zighat speed will the ball leave the gun?    m/s

  A mass sitting on a horizonuj+pk j7/neah14 i-wg tal, 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 rel+7hewp iua - g41n/kjjeased 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 wherp ,9nyj9mha;q e x is in meters and t is in seconds. Det9h,;ynq 9ajmp ermine
(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 tzo vi;2 xbg-rldw7i2md6s*; m he energy of a SHO half KE and half PE? ±w*xd;iv or;6lgm72zbsm 2i -d    A

  If one vibration has 7.0 times the energy of a second, but their frequencvfvv a3 cy*b5ztr8b- 820llf-gvqy0oies and masses are the sfvv v3lab82rq0 glvt5oy-z -bcy0 f 8*ame, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates fror3 f :nnpl.c ,qu;3lzvm a vertically hanging light spring once every 0.65zv 3f;nuqnpr 3 ll:c., 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 suppjb-: c0nwmx 6rorted by two identical parallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What will be the frequencyn6r -x0w :bjcm of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t w ,udd3nla ,-zxhere x is in meters and t i uxndda,z 3,-ls 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 ozh1wvga4,m vy c,wy 2(f SHM, 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 on the end of a horiz*ucslecp - )j*c)0weeontal spring (k = 124 N/m) is struck by a hammer, which gives wc0)*ujes*)ce-clp ethe 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 303s4el g6 uwfyp5g/ lq1 /ngfc45 N/m vibrates with an amplitude of 28.0 cm whenu 653esy/ wgl1f/ lg4qgp f4cn 0.260 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 spri :y8y-z5w ogvkngs, 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 attachd- as1f2rt n8ved to a fixed horizontal spring wf8r1dsn-2 a vthose 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 high bridge. After reachihqqp-*q *chi,ng his lowest point, he oscillates up and down, hitting a low point ehq qh*cq,pi* -ight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibratioeb (*awtb+jlm9 q/i m6ns in exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if g:rli-rh r; s;it is to make exactly one swing per second? (That is, one complete vibration takes exactly 2.;hlg;: - isrrr0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is itsm ozh-32t uzbzx--i/ s period on Mars, where the acceleration of gravity is about 0.37 t-smoi-- /h u xzz2zbt3hat on Earth?    s

  What is the period of a sim) darom+: , ebsne()qwple 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 365 er,/ojmz4h5i grams, and it is released at an ang e/ rh4mijo,z5le 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 penbr+ 7vtzet;:wdulum 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? show7ztr:+b vet; rtened by    mm.

Derive a formula for the maxiqmh4 gvwd1fio 36)ewhr50j2dmum 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 oscillatey,npc l,mr1s4s at a frequency of 2.5 Hz. At it is released from rest starting at an angle oy ,s4c1l ,rnpmf 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 z*oo,s g18w+agjrzd) boat every 3.0 s. He measures the distance between two crests to be 6.z jrg+1osd z*a),8wo g5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency 3d 4)twugx a0oof 262 Hz and travels with a speed of 343 m/s How far apart aretx3wagu0 4o)d the wave crests (compressions)?    m

  (a) AM radio signals hazb umgwp sg6 .y4(7:zgve frequencies between 550 kHz and 1600 kHz (kilohertz) and travel with a speed of g7 y:w s4 z(gbg.z6pmu$ 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 longitudinal kr ;dhnb cj* )fugh93p,6 xb0n5d/zncwaves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic x)8*maemf scvis1 1 w+modulus, but one is twice as dense as the other. In which rod will the speed of longisacm m+sx1)iw1 fev*8tudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 j ow3g6 /a(nbl6n ddf;m apart. If the tension in the cord is 150 N, how long will it take a pu6(6/jfno d l3wad; bgnlse to travel from one support to the other?    s

  A ski gondola is connected.,7wr zi5)stteaa,7wdptrb 1 p ,c)qe to the top of a hill by a steel cable of length 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and sends a wave pulse along the cable. It is observed that it took 16 s for tp a1te 7w)eq p.c)t rd5r7z, ta,w,isbhe 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 (kmlwp y l/)*uv/cp/(2iyz nyof his ship just below the surface of the sea. He hears the echo of the wave reflecteypl(m pnv w/i ck/2lzy)y* u(/d 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 spes s8e-6-dwcnq eds, and this difference helps in locating the earths 86wq- e-scdnquake “epicenter” (where the disturbance took place).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced surface wave can be approximated by a sinusoidal tran(q1 pf1-l-errnmik ;q8bb 3ohsverse wave. Assuming a frequency of 0.50 -m-oh1f n8iq rkqer b;p31bl(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, ar qb, f1 oop 4;-9btwuvptg*1xnd (b) the amplitudes, of an earthquake P wave passing through the Earth and detected at two points 10 km and 20 km from the sourc1p 9g1q-prbov *t 4twou; b,xfe?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is melt(/ne,t.i xo asured to be e.ixt /,t(oln$ 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 m/ a-3k) p/fixr7wpvs:aug5q travel through the same portion of the Earth, but one is carrying twice the energy. What is the ratio of q3rfa px)/:m k 5wg7u/vips-a the amplitudes of the two waves?   

  Two waves traveling along a stretched string have th)i 8 uao0fu3wne same frequency, but one transports three times tfwo8auu)in 30 he power of the other. What 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 u6wj )*)mwa*qa/ ngag:9hbpc adddu ;h/n.v: vertical distance of 6.0 cm, from the lowest to the highest point, as a w6 d)da*w .j9hngap)q;uh/g c:ba*/d :aw vmn uave 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 ek ((wgjc( ui5tj8l ;mwach other. (a) Sketch the shape of the string at the moment (ukjct;mi((ww5l 8 g jthey 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 moment?

  If a violin string vibrates at 440 Hz qxuum9*0.rq05a c cp9g s a68l9gjtbxas its fundamental frequency, what are the frequencies of the l c5ux9sgb609mx9q*pc0u8q j.atr a g 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 f0 qqv mnc25*9zh82/hj ikex pcrequency will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of the qv /k5*x0zmejh82n qcih2c9 pstring vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequency ofn qgf j:1j0 iyk8rez18 280 Hz. Name at least thrrk1 :j80 znjy 81iefgqee 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 string is 92m/s Igh)p:*h3b5*tw kpq1te v hd82 kpur1cf the frequency of standing waves is 475 Hz, how far apart are two adjacent nodd8)*rp:k* 3ucept 125whkp bth gqh1ves?   m

  If two successive overtones of a vibrati dqql5u,(0pht 4l qfs*m3 rrh(ng string are 280 Hz and 350 Hz, what is the frequencp*3r(5rqsh(hl d q0 umf4lt q,y of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. (s(.- j8azl1mz,3vt yvwdn; 5 ndsysu 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 thu lwnj3m-av( vsdzytn;8,.1dsys5(z e fundamental and first two overtones?    Hz

  A particular guitar stry 5 ynqc/ln;oi:q3k- hdox :(ejvq++zing is supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what per (:oq3v lq :khn;-xo jz+y/+d5i nyqcecent should the tension in the string be changed to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hz, but itgj7up o/iy5/q,: zd :kv.plx8c8 eckq is measured to vibrate at 205 Hz. By what percent should the tension in the stzx:j:l7p, .cg y/qk8qvu p/8dic e5okring be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-amplitude mecm. n8mlt+e9 6/rembl6hp ip +shanical 60-Hz vibrator. The string’s mass per unit length +/p69 mnhrtlm8eep6 m+lb i.s 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 strin *j2*vpzffsi:g may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying L between 10 cm and 1.5 m? i:svp*j2f f*z  

  When you slosh the water back and forth in a tub at just the-4tz z)m b3nt)wxv z/e3mo gd) 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-wide tub is 0.8e))3-bwz4 ng)z3momtt / v zdx5 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at kb1gnyr-haewq6va y 4+: y0jq7.0 km/s strikes a boundary within the Earth between two kinds of material. If in6r :bvyj w+ heyaqgy1q 0-a47t 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” wpgo-s+x,) 3frap+ +dtf0g jdwhere the velocity changes from 2.8 m/s to 2.1 m/s If the inc j) tdfr,xo3g-sw+0f+gd+pp aident 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 m:x9ivs-a;y v.p z8zs7jpx1l3rk1 imwhen it hits a layer of cold, dense air. If the sound wave hits the cold air ;:8vaz17 y9xsr .m silkmpp jiz 3x1-vinterface 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 earthqua qbk (uhh+lr.tk yy -o*zk0y,2ke wave strikes a boundary between two types of rock at a 380hk2l*b ,-oykr.t( +uzqhyk y $^{\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 dia0xdpqcj2 ua4ag p6**k meter. According to the user’s manual, the dish has to be pointed in the 4pqx0 2ua dj gp*ak*6cdirection 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 waveleng t3zief-1(qx*z)u b jnth 250 km and velocity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attrat1 f(-zieuq)j xnb *3zcted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness constant of 550 q.n*at * 6kdk7usetfow6(nb/ kN/m Find the maximum compression of the tbtk7(q 6a*won6ek.f u*d/ns 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 window to muap /fg1h8 2 b1mtdacv(9fc8be w 3(ra fire net 18 m below, which stretches the net bu ac1g9pbwmaf8ehd2 ((3 v8mfc/1tr 1.1 m. Assume that the net behaves like a simple spring, and
(a) calculate how much it would stretch if the same person were lying in it.    m
(b) How much would it stretch if the person jumped from 35 m?    m

  A mass m is gently placed on the end of a freely hanging spring. The mass the0:c 9loly1 ;xmkiq/ f(n2z z(bpmegx89oc he7n falls 33 cm before it stops and begins to rise. What is bf8m ly9 ioz cohqc:n19l(e07(g z x;ep2xk m/the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 2ijq-2ntt 0-hgxk ,ywm94fsf+r6*n o s2 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffness co, tg nfi-jso k*nhrs0fw2-xt 9qym6+4nstant of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of coffee (diameter 8 cm) at just the righ+ 32c3 dy iz;keobfug8t 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 coffudgy2e8 ; o33zcikbf+ee.    cm/s

  The ripples in a certain groove 10.8 cbqy /9xsi2 3jnbf 3st/m from the center of a 33-rpm phonograph record have at3bq/x2 9 nji y/bsfs3 wavelength of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrar 4y yg8j7 2 c9muqb*bg5kr70qnh6bp ntes according to the equation x=0.650cos7.40t where x is in meters and t in seconbq brq6p r7*2ujb5nyngk4yc 8h 7mg 09ds. 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. Whatr 4x*ufdw8tajc62 c025 /i c nqybba0k is its frequency if it accelerates at 0.50g (a) upward,qxa/wdk2a uj8 ty40n5b*2b ci6c rc0f    f
(b) downward?    f

  A 220-kg wooden raft floats on a lakesupqjq-+j3: -bogr7x. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the raft vibrates f q: q-3b+pugsj orx-j7or 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 inskeg*;5y s3 zertrument are tuned to play at 392 Hz (G) and 440 Hz (A yz see3;g5k*r).
(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 f )9-0s4 vj* qpmvlzggthe stretched two-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds ofgjvflm* )v0q -4ps9 zg 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 vibrates at a frent+ 4bw fin;5/grfu s;quency of 264 Hz, and the tip of each prong moves 1.8 mm;+i4sfntr/5u nfw ;gb 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 harmonic motion of y ;bc6z3u)mgoyz(- b shwa 9+xfrequency 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 th(gsm;cz3yba 9 6obhwy)x-z+uere (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 rm;bno0 ujfol;; (d:wm ing that can slide without friction on a ver:; owmn;u0o bmfdl;j(tical pole (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 exactly 2.000 s — each;; gqku65c9nndq b.s i one-way swing takes 1.000 s.9bnis 5g.ucq q6kd; n;
(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 os ;+ibk8d 8w-yzt)if a spring can oscillate in the vertical direction or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, th;o wzid-fsb+ 8y 8)ikte 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 2+5mckyd/ gq*qsyrc3 . 55 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at the opposite end. Where * /y3cd+ 5k. rqcgysqmwill the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a sp,ppn) np, zd3zring with spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maxi ,n zpz)ppd3,nmum amplitude of oscillations that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel crane amj/gn)4t/ dwdzm 38 ynik;*8h vcnj 9cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. What is the period of the bouncing? [Hint: Refer to Tablk3;w9mznjad mc y* vn/) ig8ndt48j/he 9–1.]    s

  A block of jello rests on a plate as42c(0tfxs e 4q/pjc t bs*5rqm shown in Fig. 11–58 (which also gives the dimensions of the block). You push it sideways as shown, aqt/4bm(psx cj4 q r*5scef0t 2nd then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this vibration, given that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz