Give some examples of everyday vibrating objects. Which exhibit SHM, at leasawkn e z7m* *jh9wb36ht appr6bnaw ez**9mk 7j3hhwoximately?

Is the acceleration of a simple harmonic oscillator ever zero? Iffv md -wf3tm77t tzc.7 so, where?

Explain why the motion of a tvi: w: +hmk9dpiston in an automobile engine is approximately simpledw+:m:kh iv9 t harmonic.

Real springs have mass. Will the true period and freqwt( w nd0n .+5v3kmlgfq1fi5huency be larger or smaller than given by the equations for a mass oscillating on the end of an idealized massles h5f0n+5gk.mqw3 l 1tivdwnf(s spring? Explain.

How could you double the maximum speed of a simple harm1):/yxcdvd g6rzi h/zonic oscillator (SHO)?

A 5.0-kg trout is attackjm-n ue:1z x0( z2qzahed to the hook of a vertical spring scale, and then is released. Describe the scale zqmj:-x n zeu01k z2a(reading as a function of time.

If a pendulum clock is accurate at sea level, mzxk:s-c wek * h:o1fe8i(tq 06b,pfa will it gain or lose time when taken to high altitude? Wo (e *ksf- kz80pfhmbi tca:w1e:,6qxhy?

A tire swing hanging from a branch reaches nearly to the ground (Fig. 11–48). H8 tebhjtcha-fw **, (znj:ls:ow could you estimate the height of the branch(* hfajt:z w*t,cl8:- jbns eh using only a stopwatch?

Why can you make water slosh back and forth in a pan only if you shake tb*qx.a rh yzj; y706vdhe pan at a certain frvq*ab6hjzy y 7;x r.0dequency?

Give several everyday examplewvn 7vr6: b4c sla sm3*8dg1gts of resonance.

Is a rattle in a car ever a resonance phen2q /9.+ t9gk)yutjsvo,7x q6wex hh haomenon? Explain.

Is the frequency of a simple periodic wave equal to the frequency of its 9qqs qeag /d:y1c +n:bsource? Why or why nots:qgnc e: baq/+d1yq9?

Explain the difference between the speed of a transverse wave trv.1kc: zf ivr;e (7bvwaveling down a cozbke iv;f . v:wv(c17rrd and the speed of a tiny piece of the cord.

Why do the strings used for the lowest-frequency notes on a piano normally have 0 tyole.r7e/ psj bk1ob;i)v 2wire wrapped around th0vs1bloe o;r7j2ep/ .b k) yitem?

What kind of waves do you think will travel down ap,m*u0byrw* f horizontal metal rod if you strike i *ufy*rp0mw ,bts end (a) vertically from above and (b) horizontally parallel to its length?

Since the density of air decreases .x e.+qi4y sfyw,s*pj with an increase in temperature, but the bulk modulus B is nearly indepen . y4eiswjpqyx.*+,sfdent of temperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in amplidsf:g78 ;2ovwf5hf eugz-r,x tude as they travel away from :rwgdfv25;uef s oh,g7z8-fx the source.

Two linear waves have the same amplitude and speed, and otherwi;58 cpz2v 7ptwuk lpk4se are identical, except one has half the wavelength oft;u8v k 4 p2p5k7wclzp the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the bounc1,cp)yk 86utk,9l s*y/w* a2k5vr qrbanogzdary between two sections of cord as in Fig. 11–33, thuok pk5st,k6 q2b / *ycly*r8r ,nc1zw)9a gave frequency does not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there ansk l7g2 rb jqloe:9(r6y places you could touch it witbr79 ge: rl2 sl(qjk6oh a knife blade without disturbing the motion?

When a standing wave exists on a string, the vibrativ5 m, suhhhy ,jk:)j7 y3zix3zons of incident and reflected waves cancel at the nodes. Does this mean that energy was destroyed? kym)zj,iv ,yhh:7xj 3us h3 z5Explain.

If we knew that energy was being transmitted from one p nczj p)z 31 a-oj(l06-8vhyesxrgs1 mlace to another, how might we determine whether the energy was being carried by paa3)sr j -- n68jz pxsy(c1gh0meovlz1rticles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the total distance it 85gy8-kyefjp trajyfeg p8-y85 kvels in one period?    m

  An elastic cord is 65 cm longo5z.xrs.w 7g h when a weight of 75 N hangs from it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” con5x7.zr wghs.ostant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 6lxllq3 q-+-j r8-kg driver gets into the driver’s seat. If the car goes over a bump, what will be the frequency of vibratj-ql3+- lrlx qions?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hab(s3ojw9k /yg ngs from it. (a) What is the spring stiffness /g(w y39jobsk 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 q)+h ti hl);+c-rzccg 93waie Hz when a mass of 0.60 kg is hung from it. What is its frccic+9hqh+)a)e ;r w-z3tgli equency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. 11–2 at timf5kx3 d0venybukk 7qh(*(i o ;es t = 0k5 e3(*;q xvfnibuk dhy (7o0k,t = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

  A small fly of mass 0.25 g is caught in a spider’s web.o9 wv rah3x,e: The web vibrates predominat9 r,:h3xwaov eely 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 0.88 Hz. W1 6 mwwbh iwfiie1;h6;hen an add 1hfiw;hwi1 ;wi6m6 beitional 680-g mass is added 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 m-3e cv3y4w(q pje1 jewjj79qvibrates 3.0 times per second with an amplitude of 0.13 m.9je mwy- wq7jjjc3vp3 4e1e( q Determine
(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 vh:y956hkzpv4aw jpy1oz 2ar7 alu:p5 y rh26z7o19aya 4vzjph wke?$\approx$    A

A mass attached to the end of a spring is 5eu7k :p:b lt8e:o1 oucsc))ba2ohodstretched 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 ai2m qkk8u 6fm/ vertical 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) equilibrium positioku2/kqm if m86n again?    s

  An object with mass 3.0 kg is attached towaqkae8p e4mx82uv,d6 o g4f) a spring with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, itwkqux 8e) 6o8,md4av2eg a4 fp is moving with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compress the spring of a t5dt:tyqq wi/ 0oy popgun 0.200 m to “loa it:qq50dt/ywd” a 0.180-kg ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a hd;g 2n;fuwbv , ,kawud/. jovsq-c8(jorizontal, 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 iuoj nd-c vubq; sa,/fw.wg8,2(jdv;k s 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 equati0om3hrk;gv( w 4; w+dffa,w cton x = 0.45cos6.4t where x is in meters and t imcrw+wog,w4;3 f;h0ad v( tkfs in seconds. Determine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equio ddo-k6d+qu4si1x+ :.vod)z bvj n+m librium is the energy of a SHO half KE and half PE?o4di-) osnmq+o.+bd:zuk1v 6vd+djx ±    A

  If one vibration has 7.0 time3) rhoa -:.r4oyj 0,1 ;pxknxksuaefqs the energy of a second, but their frequencies and masses are the same, what is the 0 re :4nskjx yh u3qor)x1p .a;-,fkoaratio of their amplitudes?   

  A 2.00-kg pumpkin oso7meag;pw4 .*o 5 hnac0 c;ohg1 vh3imcillates from a vertically hanging light spring once every 0.65 o;7na 04*vggo hhwec aihpo. m15c3m;s.
(a) Write down the equation giving the pumpkin’s position y (+ upward) as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. y = (   m)cos($\frac{2\pi t}{0.65s}$)
(b) How long will it take to get to the equilibrium position for the first time?    s
(c) What will be the pumpkin’s maximum speed?    m/s
(d) What will be its maximum acceleration, and where will that first be attained?   $m/s^2 $

A block of mass m is supported by two identical parall(1x j/q zmgzpsk15o,,sa cdo: el vertical springs, each with spring stiffness constant k (k 1/o,mz1czj( aoqss :x5dpg,Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates accordi65yc ehwh19w +du1 k+je *bblvng to the equation x = 0.38sin6.5t where x is in metbe hywk1j++9hvel*w6c ubd15ers and t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows two examples of SHM, labeled A and B. For e0 p:38( rkc4e-rvt.pkq tc i4ykcmk/vach, 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 horizontal spring (k = 124 N/6cvi: hv6ecl+( wqps,m) is struck by a hammer, which gives the mass an initial s6l(6,:q vcvw ch spi+epeed 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 w s0 .,txse:at-9vtjokz;i3yes with an amplitude of 28.0 cm when 0.260 kg hangs from it zsi;x ykjvte sto.,:w-9 30at. 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 - 2bprk v(msdo.ppv*1two 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 apl t(l0u3 d6oto a fixed horizontal spring whose spring stiffness consta pl0o3tda l(u6nt 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 3da:ki:f obpqn5 22xkbridge. 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 maofq 5px: i2k3ndk:b2 below the level of the bridge. Calculate the spring stiffness constant and the unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrations in exactly 60 s. What tz nqvc26y6qb:2b; gs is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if if n:wd98i 6i4gc t u;rdizd()dt is to make exactly one swing per second? (That is, one complete vibratg:)wt d 8(;di6rdi9d4zcfun iion takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. rbwt h q;y nt/r:u()k(What is its period on Mars, where the acceleration of gravity is about 0.37 that on (htu y)wnrk;(qtr / b:Earth?    s

  What is the period of a simple pendulum 8/n*( g;lkrvctkzx 46 f0 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 mz(ek62f p 2yes, the pendulum bob has a mass of 365 grams, s22ez6 e(ypkf and 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 pendulum has a length of 0.9930 m. If+xs3 w dm1bs+l the clock loses half a minute per day, how should you adjust the length of the pendulum? wlsbmx+1 d+3 sshortened by    mm.

Derive a formula for the maximvi f zb l/ec.t-mye3c.0c b ,gu2kw+m(um 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 at a frequency of 2.5 Hz. At it is re-gmy3 l m(kse - n(05vpxqrx*eleased from rest starting aly q mep* x-kg(em-vsn3r5x0 (t 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 thz6 gj.eerkdcz s 6)3vsd22 :oaat wave 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 k:eoc 3z6 r2sz.dg62de) vjsawaves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with lpn(z*z. z.gza speed of 343 m/s How far apart are( gzz pn..zlz* the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (kilohertuw ( jmg2u- d7r17 idjqxig5r7z) and travel with a speg1id uq5 7ri2jd w7xg(ujmr-7 ed 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 longitudinal wabsarc72 fpih 5e c-lds4(2z0 zves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one is twkj( isdk/aima *qm h yy,:q1)8ice as dense as the other. In which rod will the speed of longitudinal waves be * / kh(kmqi)ysmiq,: jya18 adgreater, and by what factor?   

  A cord of mass 0.65 kg is stres/2 lu3hmi2k4* egbux tched between two supports 28 m apart. If the tension in the cordk* e uliuh42bsgmx32/ is 150 N, how long will it take a pulse to travel from one support to the other?    s

  A ski gondola is conssev +b1m,m 25a /ofa fayg4-anected 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 caso/g,sm+v4a51maf f-ay e b2able. 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 9bx2v2 qesc;h rl(m55 szf)udof his ship just below the surface of the sea. He hears the echo of the wave reflected from the x(u52cd5re zql v;)s 9s mb2hfocean floor directly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an ear0ci. kwxb , jufjg-m.4i gt,,bxj bh)*thquake travel at different speeds, and this difference helps in locating the earthquake “epicenter” (where the disturbance took place).fj..w*b-, )xgc,m0 tb jbk4ghijix, u
(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 approtynau,k; qh 38ximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude yaqu;3,ht 8 nkis needed so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amb9ag0,f4/npe4geq fe plitudes, of an earthquakqef bpg4fe aen /9g,04e P wave passing through the Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is measured q1a+k/ tk6fgj,jp/s 5 lr cii6to be ,j 6 6lak5f/c1kt si+qri /pgj$ 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 hhhx4 sxu563)r1q6gpj ekc3 cof the same frequency travel through the same portion of the Earth, but one is carrying twice the energy. What isx6)4q3s k c5xc1 hjhg h6reup3 the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched strf7r6uh ub9soa 7 +swnz **4e)z8ttm mhing have the same frequency, but one transports 76wb 9r+zuzoft*7he*m4 as )m8hunt s three times the 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 m0(/z mm* sqv km(d5glrbsp4v.ove up and down 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 dol*vb.s05z(gdvk 4 /qm(sm mr pes the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward eacb4 n )o7l4vuqke ib7+ph 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 straigh 44lbke7q i7 pn+uobv)t. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz :g ny2 0bq.rsyas its fundamental frequency, what are the frequencies of the first four harmonic ny20qs.:br ygs?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what freqq: +vl jz- men41;ubfwuency will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of the string vibratemlwj e+ buq; :4f-v1nzs as a standing wave.)    Hz

  A particular string resonates in four loops at a frequency of 280 Hz. Name at l+wza72k7ac1reo:j j+m3nqmvz, h ep0 east threeeojz,2c k3m a+ma177hev:nz +q0 r jwp 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. 0,rdo r3usj,o1srdr is 92m/s If the frequency of standing waves is 475 Hz, how far apart are two ,rds0jsrd3uo o, .r1r adjacent nodes?   m

  If two successive overtones of a vibr vp /*x6.odbp ,j 4qherg/9iuaating string are 280 Hz and 350 Hz, what is the frequency of t dpe4qgu/ih *.6 ,/bx9rvajop he fundamental?    Hz

  A guitar string is 90 cm long and has a mass oix7qb ep,c-,p f 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 arixpp-q 7b ,e,ce the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vib cn gpy+a-e11)y gm;hgn ls69rrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?So the r1glcp9-;amny 1 )6ns yg+hegthree frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar stringu ) ceysqcsh.+--s /-di 9ahqc is supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tensionisu -- ds.+ccqhh/9c)q eys a- in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string isq a;: (rir/wor attached to a small-amplitude mechanical 60-Hz vibrator. The string’s mass:rqriw(/ra o ; per unit length is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of the string may be adjusted by moving the x yc*gr2 52 3z:ixcw lvk6ffv4pulley. If the hanging mass m is fiz3:c 2f*5 2v ylkcr4 gfixwv6xxed at 0.080 kg, how many different standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at just the right fra3:mo9q s5/(0 j 2i6j uo*.djg/uwbdwmep wdqequency, the water alternately rises and falls at each end, gu pjo06 o: 2u9*wjabwj.q3/dwdqm/s 5 ( imedremaining 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 Eat cmc6lg2;4vzrth between two kinds of material. If it approaches the boundary at an incident an2mlvgc t4; 6czgle 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 undere owz v37)y4tso-gtd3p5 cr;dwater “shelf” where the velocity changes from 2.8 m zv 74dotc3-eyd;sptwro 5g)3/s to 2.1 m/s If 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 air when it hits a layer of cold, deg5z3a ypbi*.c nse air. If the sound bc3 pg. iz*y5awave 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 typl8cy7xmtv n )/es of rock at a 8cl/v nm)x ty738 $^{\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 abc zlie9n9le 9u j/i+copv3 +t*out 0.5 m in diameter. According to the user’s manual, the dish has to be pointed in the direction of the satellite, but an error of a+jv9i9cotn*3elezl /i cu9p+ bout 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 m asz44 whgsi0b+,a) eacross 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 war b) 4ss+ehm ,z40wiaagning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper hasvc6psq*.k(yr jcp 6 84ybs 7as a spring stiffness constant of 550 kN/m Find the maximum compression of the bumper if the cars6 pcb48js(ycy7vs*a 6r qp.k, 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 tooya*cz(q9jx11za+ f op n;om6 a fire net 18 m below, which stretches the net 1.1 m.6zmoc1(q9*fzxa1 p oo ;anjy+ 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 7uag2k ,(kb--hmu5 xjm9m piea freely hanging spring. The mass then falls 33 cm before it sgh9x u-5p-mm7,j2ak kubim (e tops and begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a e+ xey6ico7,sek af8a5wq .w5huge spring at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0i5,ee.x78a 6ewoyk fw5cq+as m. (a) What is the spring stiffness constant of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup ogpgm6wt8 p.ag:6hkp6f coffee (diameter 8 cm) at just the right pace of about 1 step per second, the coffee sloshes more and more until eventually it stap.g6 mg pg6katw8hp:6rts to spill over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the center w8 b25tmbjoj 0/kb3wzyp- 8 flof a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequebmopbw l tjz03k-wbj/8y 28f5ncy of the sound emitted?    Hz

  A 2.00-kg mass vibrates22zw 30s td n tab/;vq 5:hfj1xjsrqr- according to the equation x=0.650cos7.40t where x is in meters and t in std r 5fhbwxj0na;-j/ s1 :2q2s z3qvrteconds. 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 oscilmu,8sg cf5+u elates with frequency f. What is its frequency if it accelerates at 0.50g (a) 5u+mfg, u8cs eupward,    f
(b) downward?    f

  A 220-kg wooden raft floats on 1nm7 8 *jaq kwrpbqhz ,y:o7e7a lake. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he srhbj:wm p17 zkn8*aq o 77ey,qteps 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 instk5 p g-+zafu8xa6br m6rument are tuned to play at 392 Hz (G) and 440 Hz (A). ra xza+6-up km 865gbf
(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(gmwx-j6q : mu. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Isx :(m-mqgw j6u the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the 1ofjev (rs ,4hg +slt+tip of each prong moves 1.8 mm to either side of centerlsrv +,(4+gse1 j tfoh. 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 mo 4fjr yz/7m.eb e7 md)-r,zbtption of frequency 1.5 cycles per second. bb-j 7d m,.r7fyp)et zz/emr4What 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 contact with the board during the oscillation?

A string can have a “free” end if that e 5 w5+i.2xrd wcuzgmi*l*n0zend is attached to a ring that can slide without fucn*xzme0.rl5 +2i*gi5d w zwriction on a vertical 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 65wszievu :d* a period of exactly 2.000 s — each one-way swing takes 1.000 5s du*zei w:v6s.
(a) What is the length of a seconds pendulum in Austin, Texas, where $g=9.793\mathrm{m/s}^{2}$    m
(b) If the pendulum is moved to Paris, where $g=9.809\mathrm{m/s}^{2}$ by how many millimeters must we lengthen the pendulum?    mm
(c) What would be the length of a seconds pendulum on the Moon, where $g=1.62\mathrm{m/s}^{2}$    m

A mass hanging from a spring can oscillate in the vertical direction oxp e; gf3mal.k( mx*6lr can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period of the verticak;.6l3mf*p(g axlmx el oscillations or the period of the horizontal swings, and by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

  A block with mass $M=5.0\mathrm{kg}$ rests on a frictionless table and is attached by a horizontal spring $\begin{pmatrix}k=130\mathrm{N/m}\end{pmatrix}$ to a wall. A second block, of mass $m=1.25\mathrm{kg}$ rests on top of M. The coefficient of static friction between the two blocks is 0.30. What is the maximum possible amplitude of oscillation such that m will not slip off M?    m

  A 10.0-m-long wire of mass 123 g is stretched under a tension of 255 N. A pul9bke mkqm (od ,zz+r(6se is generated at9(6(kz oezkmq d+,m rb one end, and 20.0 ms later a second pulse is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spring wix/1/adq ofdbxbf0 ,o1th 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 d bo10ab /1/dx,fqfoxtop of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel crane cable is tvp)g1s *u rsdd 8x98a22 m long and has a diameter of 6.4 mm. A br*sx18 rv8audts p)gd9 eeze starts the car bouncing at the end of the cable. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (which also ge p3)k3kbom 7ntn:u1dh bz8+fives the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrpzt 3b b1d fk:+n7u3ohkn )me8ate. 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