Give some examples of everyday vibrating objects. Wh m zu9 zn919hdxju0up4ich exhibit SHM, at least approximateluj9p0mu1n zxh duz949y?

Is the acceleration of a simple harmonic oscillator ever zero? If so,zwol+f60 tgrbi(u* f(o maf.2 where?

Explain why the motion of a piston in an automobile engine wq6g3s.ug qi (m w;zol2;m:he is approximately simple harmonic hu; e(q3 w;izqm26l:.somw gg.

Real springs have mass. Will the true period and frequency tvukb6p/ n p6q2ewl r0jt,g43 be larger or smaller than given by the equations for a mass oscillating on the end of an idealized massless s kg rtpv6plten4w, 6u bq302j/pring? Explain.

How could you double the maximum speer.. hu/ v3k,jccivl7 cd of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of unyw)4274d dwlaw5y b a vertical spring scale, and then is released. Describe the scale reading as a function of 4 2ww4dy awnu7yd)lb5time.

If a pendulum clock is accurate at sea level, will it gain or ad+q 3-s8tmb0pde tw5rb6w +xlose time when taken to high al 3+mdt8bra50qt wp +wdx- b6estitude? Why?

A tire swing hanging from a vccv81 nt6: )j+jsr. rlzk z,gbranch reaches nearly to the ground (Fig. 11–48). How could you estimate the height of the branch using only a, +6vr sjz) r:8gzc.ln jkt1vc stopwatch?

Why can you make water slosh back and forth in a pan only if you shake the pan p)zdbl)kgr , cz6u8s(atb(gl )z8zc,)u s6 pdrk a certain frequency?

Give several everyday examplh yaz0rwh .8q2es of resonance.

Is a rattle in a car ever a resonance phenomenon? v91 hkak7m(lsExplain.

Is the frequency of a simple period w ,ekge:2ikxy+jt8pjpx+ f*iqfc31 /ic wave equal to the frequency of its source? Why or wp83 je/1+iix kxgq*ey +kfcpj2 tw,:fhy not?

Explain the difference between the speed of a transverse wave trav33bltd0o* 8mumx. vmieling down a cord and the speed of a tiny piece of thotimm *8d0u bl.v33 mxe cord.

Why do the strings used for the lowest-frequency notes on a piano normally jh f 0g0 pxug3nf7p9uiak2n;8have wire wrapped aruf39gfxn ju 70ng8 h kpi0a;2pound them?

What kind of waves do you think will travel do 6mkzo-mhh:d /c ;(psoh2l 1pkwn a horizontal metal rod if you strike its end (a) vertically from above and (b) horizont ;6dhm/chpkklpso- mohz2 :1(ally parallel to its length?

Since the density of air decreases with an increase in temperaturem5z7+0ys y vi/l(vjlt, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves in air to vary with temperature?i v+tsjl7yv/ ylz05 m(

Give two reasons why circular water waves decreasf i(ey z2:;u6seont+ji7f e/ re in amplitude as they travel away fj ez6fs+inoey(r ; i 2e:tf/u7rom the source.

Two linear waves have the same amplitude and speed, and gn0t ldrzcq94x:o,;px g 3s l vz,65nlwr3.hrotherwise are identical, except ont;x.pln ogrds:4qv6l33zrr, 9 chx ,n0l5w gze has half the wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two se:i3 j*zxs 1zuections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velociti s3 zu*z:1jxey do change). Explain why.

If a string is vibrating in three segments, are there any plau;mf hr)r.d(m2q(fnv ces you could touch it with a knife blade without disturbin f)u;v(rqf mdmhr(.n 2g the motion?

When a standing wave exiwn-;avv7f vx5 sts on a string, the vibrations of incident and reflected waves cancel at the nodes. D-f;a xvv nw7v5oes this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted frh;p9ot 6 2mdifom one place to another, how might we determine whether ot6 p2 dfhm9;ithe energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 yl:6au4i ev2f m, what is the total distance it tra:4ya6e il vu2fvels in one period?    m

  An elastic cord is 65 cm long when ahgph as(5uj- 6 weight of 75 N hangs from it but is 85 cm long w( - jpug6hash5hen a weight of 180 N hangs from it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0ab0)4im pfndyc d/;j. mm when its 68-kg driver gets into the driverbp.nj;4 if c/d)myd a0’s seat. If the car goes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm whenon+:5ggvvsyqp6.3t g*1 rv yq a 2.7-kg fish hangs from it. (a) What is the sprivqngyq*t5yo.vgs316v +p : g rng 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 off)ja: 2lc sq(h 0.60 kg is hung from it. What is iaqc(:sj )f lh2ts frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. 11–2 at times t q 56ejjl xxp0;wer(s+ m (dd2s (s5;j20dwe( jrxx6+lsmq epd= 0,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 sk sz7 u:/)ybr9wbaak7gzx y9 9pider’s web. The web vibrates predominately with a frequ99 :rbwyua79 xk)kz/a7g yzbsency 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. When an adueq +r ***l8ggmp *fytditional 680-g mass is added to m, theyugptf+* *q l r8*m*ge frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibratef b*9 * xrmx+hovajr6dh,ynid*s g*4 ,s 3.0 times per second with an amplitude of 0 r*ayhfmxg* 4didn,bjr+ 6o,9s*vx h *.13 m. 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 s1)jns+.r mdc0-k ovyc peed of a SHO half the maximum valur+ vj1ys )kdnco.m c0-e?$\approx$    A

A mass attached to the end of a spring is stretched a distajx8 ,:uwmn wgiin2e91kfg)c .nce $x_0$ 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 isgg:xsyimx0fg xpc58*/f ng- , stretched an additional 0.130 m and released, how long does it take to reach the (new) equilibrium positiox 0i mx, 8:ffgygsc -gg/x*5npn again?    s

  An object with mass 3.0 kg is attached to a spring with spc ;)r,xwm6ks0 jjn9 vpring stiffness constant k = 280 N/m and is executing simple harmonic motion. ,wj c9rnv;jsm60kx)pWhen 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 of a toy popgun+/ cx f0jcvotq)xt..r 0.200 m to “loafrcjo0 t)/vx.qt+xc.d” a 0.180-kg ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is att)npyrn )* 6a etp/ehh-t9ub2oached to one end of a spring; the other end is fixed to a wall. 3.a6n-uto2y/r9epe)) n hpbh t* 0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, the mass experiences a maximum acceleration of 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates according to the 2wh7lpv:ka 5gnye3yf tca ;:( t2y pe8equation x = 0.45cos6.4t where x is in meters and t is in : c:vaye8n7lg ta yk h(pf5w2ep32yt;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 equilibrium is the eners/ne:5 oy9gw j 8n4ycdgy of a SHO half KE and half PE? w4s yycg/n :j8d9on5e ±    A

  If one vibration has ratb-sdhc*q1(3 j . ji7.0 times the energy of a second, but their frequencies and masses are the same, what is the ratio o d*(q3ta h1sj .rcbi-jf their amplitudes?   

  A 2.00-kg pumpkin oscuwu8o1n3g x -xillates from a vertically hanging light spring once every 0.65 s-n xogwuu1x38 .
(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 sug +1cztr,.b-m lcvlqb4; yt j7pported by two identical parallel vertical springs, each with spring stiffness constant k (1.blmcl+qygt rjc -;b7v ,tz 4Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t where x is fxfh .9tu z1a;in meters and t is if. h1fa;t zu9xn 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 eachuwvf7sz4owg5wk f6 p :l4,z zm-/6mtt, 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 omq.f2sdv 4 qc)o+ym1xz /zx: kf a horizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial speedd sqmcq2/.:x1zz + )kfym4ox v 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/md y6u2/l 3 8lb; if:gswy7utd3z5syoq vibrates with an amplitude of 28.0 cm when 2s3oy :yysllb;d35 w/ud qzi7u 68fgt0.260 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 springs, with spring stiffness cdsdyc hn*jaqb)e846g h/7z5 qonstants $k_1$ 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 horizonta4b.bxe2z5 qtp l spring whose spring stiffness constan.pxeq2 bt4bz5t 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 mas ,k;f2trm4 iums 65.0 kg jumps from a high 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 levmm,24t fkrui; el 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 is it1iury; 7 nffhz:2h 7f:p,w-eo6gkp nys
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum, bb-0aj n,uze be if it is to make exactly one swing per second? (That is, one complete vibration takes exactly 2.0 s.),-nz0ba,j eub    m

  A pendulum has a period of 0.80 s on Earth. What is its per8h2v7orge8i m iod on Mars, where the acceleration of gravity is about 0.37mi e8h87o g2vr that on Earth?    s

  What is the period of a simple pendulum x-.wy /e793xjnzxakj di(f :c80 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 pendul;s:5ua8h cq;ct 0uahsum bob has a mass of 365 grams, and it is released at an angle of u5 h;8 ac:0;scqtsuh a12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’s pendulum has a length of 0.9930 m. If the eon mn-f wihspmw/3(6.mr0q4 clock loses half ap6n 4merqmh/wm i 03f o-sn(w. minute per day, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximum speed 7k 9bu8 pn,jn d,kw/b-svt:ok$v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscilla7+wmc de-nkv, tes at a frequency of 2.5 Hz. At it is released from rest starting at an angle of enk+v- cmw,d 715 $^{\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 h, fgfphh)ne 6wlh*2)mis anchored boat every 3.0 l*g) h,f) fnhempw2h6s. He measures the distance between two crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262lwc..rq,.satj qzpvv, c377 0q;a b vt Hz and travels with a speed of 343 m/s How far apart are the wave crests (compressions)? vtb7.s3 ,wcczv.; a .qq v,t0rjqp la7   m

  (a) AM radio signals have frequencies a., 7ictmu(o dm4r-h1m/ lw nq **skmqbetween 550 kHz and 1600 kHz (kilohertz) and tra(a- m1con*w i,lth.q74dum sr mq/*kmvel with a speed of $ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

  Calculate the speed of longitudinal waves in r/hc,rdb(uwju 2 w2yno+)rr+
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one is twic1 :ygrc5g 7mdge as dense as the otr751 dcgg:yg mher. In which rod will the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched bilm3th 0cv+ 2z:i6 sayetween two supports 28 m apart. If the tension in the cord is 150 N, how long w: 2asi l+v0y htzcm36iill 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 ca(c: qgmwl;70p u-5mwlgy 0n9 wfj ezs.ble 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 fl( cgzw9mw-fsg ;y5:l 0ju wnp em.07qor 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 his ship just below the surface of the se:cmbak,d / :e+3 zmddba. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. d d+zka: mde:3/ ,bcmbHow deep is the ocean at this point?    m

  P and S waves from an earthquake travel at different speeds, and thisj)xqme ; 6kwrt+c +o( e7sqsllnub:3 / difference helps in locating the earthquake “epicenter” (where the disturbance took place). )oj ter s3c+;w q :u(bq6k+l/mnl7sx e
(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 transve-fhlb(8 mal 5vrse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies),-(lm ab85fvlh 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, and (b) the ampl+-ex ,5e0;ghgfcjlfwgi fxrf5;/kq( itudes, of an earthquake P wave passing through the Earth and detected at two points 10 km and 20 km from the soge gf/w ;e,-x(cj f;5h grfk l+5qxfi0urce?(a)    (b)   

  The intensity of an eart-puts6l e e9.,fgi(dthquake wave passing through the Earth is measured to be i9gd. letpfs( tue -,6$ 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 throughpbhq6lw .j9 z0b 7wli) the same portion of the Earth, but one is carrying twice the energy. What is the ratio of the amplitudes of the two waves? 7 lpljhz bq90wi)b6.w   

  Two waves traveling along a stretched string have the same frequency, but f(m:x lo u,rq/one transports three times the power of the other. What is the rat fm(xul,:r oq/io of the amplitudes of the two waves?   

  A bug on the surface of a pond 54 2rs)ekyhri is observed to move up and down a total vertical distance of 6.0 cm, from the lowest to the highest poinhe)r r4 25ykist, as a wave passes. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each otheb+ 4kk2jd.y;in7a rkmr. (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 n4jkmd+ r ky ia2;k7.beach other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates af3w /i5: -cgz lozwx/ut 440 Hz as its fundamental frequency, what are the frequencies of the first four harmonz5ucxz: ol-i3w/fgw/ ics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what frequency will it v pn/i1dmxza,o:hfx2) qfk2.w ibrate if it is fingered one-thirdm12x.f,n: z /q f)ahwpk xdio2 of the way down from the end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string reson1 m0crb1e i8gpates in four loops at a frequency of 280 Hz. Name at least three other frequecmg11i0p8er bncies at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the frequency of stbgam9e/ nip1bz utw2 +2hr- w-5 mg-l4cek w;danding waves is 475 Hz, how far apart ar1med-9pw;lg5mbu-r+4-2ca k i2we /htgwznb e two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 350 Hm ipqsdj5 2lzr s)0m37z, what is the frequencyi5 0s)3jzq2mm p dr7ls of the fundamental?    Hz

  A guitar string is 909m5k6 yvl;hw hve 8rt: cm long and has a mass of 3.6 g. The distance from the bridge to the support post is L = 62cm and the string mvt; k9r5v yehl6h8w:is under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is l(1n d-h rd8rlsupposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percenn-rh1r d8(dllt 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 st x7xwcj +:1s 1.d7xq8jpds gyut2 hwtpl l+,p2ring is supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in thec 1j7j2pdsx .qplg t1,wyh8xw:xs++tld u7p 2 string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a smalkrf v(yt1q a01tqvgzzg i455)l-amplitude mechanical 60-Hz vibrator. The string’s mass(tq5rt ivkvz1 5z4g0yq g1a f) 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 pl;3sve w hdc j0t 4)ze(ntj5i5ket8e-3i)rmpulley. If the hanging mass m is fixed at 0.080 kg, how many different standin 0je 8e5hi34tw em; pc-dkns)rl53)(ttizevjg 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 rightk89o78pnohv+0p yob*rs gvz) 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 0.85 Hz. What is th8k80vp sv9b 7+yr*go)np zoohe speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 kx9 x5 /;70xxv*h4fzyeaembrom/s strikes a boundary within the Earth between two kinds of mat/h0bze4 fxr5x 9m7yeav*;o xx erial. If 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 odu5e+j::8.r y au9jx:zlt xk“shelf” where the velocity changes from 2.8 m/s to 2.1 m/s If the incident wave cryu9t j:xk+ zj:ed. l 8:ou5arxests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air od(7pig3s;r8ilgk t6 when it hits a layer of cold, dense air. If the sound wave hitsid(p;s8 og6ilgtkr 73 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 betwee5 cql,mv l923md w;nno0ug ;rcn two types of rock at a 38 9,qwv0mgd ;c2 om3l5l;nr ncu$^{\circ} $ angle. As the wave crosses the boundary, the specific gravity of the rock changes from 3.6 to 2.8. Assuming that the elastic modulus is the same for both types of rock, determine the angle of refraction.    $^{\circ} $

  A satellite dish is about 0.5 m in diameter. According to the user’s manual, th; b/dl o-m2*y1tjrkmo3y zy3he dish has to be pointed in the direction of the satellite, but21k/y ltmyomr3*j;o z-ybhd3 an error of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 250 km and velocity 750 km/h travels across the Paci /sfw)2g8 +c+uqju m 5bp/mw mt:ilr5zy 5bn6zfic 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,5+y nfbmlu/qzr6)pw 8/25m t cugm +s z:w5bij some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness j7+prh 9ejhun5zn183:d grmaconstant 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 2.2 m/s (approximately 5 mi/h). [Hinn5+3gp18nd zuma97 errhh:j jt: Use conservation of energy.]    m

  A 65-kg person jumps from a window lvaa6:d+7 nsvo +zm :01f qg8mvlq a:lto a fire net 18 m below, which stretches the 1+vf no+l daqgm8s:7qa6lv :lv0zma :net 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 ooq,td-g *li-nn the end of a freely hanging spring. The mass then falls 33 cm before it sto*,tlno-i- dq gps and begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 11–54), compressilt)qjhm t /trjuy;gn 8/(y4r*ng the spring 5.0 m. (a) What is the spring stiffness con/hrr q8ty; 4)tnuml *(tjygj/stant 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 ju 9li -mnvnf-,tst the right pace of about 1 step per second, the cofl 9i-n n,ftmv-fee 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 certain groove 7ac6mgw,hp.e z8c5mx 10.8 cm from the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. pcc,5a m8x.6zw eg7hmWhat will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according toou-wi1r *:m etcss:0q the equation x=0.650cos7.40t where x is in mm0: - sie*woc tqrsu1:eters 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 oscillatehyided3p3*,dv+:h. q e*z x fks with frequency f. What is its frequency if it accelerates at 0.50g:exvyfip+ qe *h* dh,k33d.dz (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on0,/f2zax es9ehi*l g w a lake. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the r 9 azli/fh0,x2weg* seaft 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 ,epzy,bh r3i *are tuned to play at 392 Hz (G) and 440 Hz (A,3zh,rpbi y *e).
(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 s.4qi,kv lpo) :lnk)n ebn0n /etretched two-part cord of Fig. 11–33. Determine a formula (a) for the rat:,0/q n.) kloeilvbn)n nk4 epio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the tip of e)e cxjx;t( w1ef 684jywpbo +wach prong moves 1.8 mm to either side of center. Caycfbxe (p68jwo1t+wxwe 4j; ) lculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board osciluq,f mj9t (ds9;hyx b95csu8t lates with simple harmonic motion of frequency 1.5 cycles per secon s9d utxhq s(5fj,c8u9ym; bt9d. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that end is attached to a rnlmg u0b4,67yf8;x k2 wngikfing that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string wxfi lguw87yfk ;kb4 ng2m0 ,6nith one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each one-way swing u +t;n x(+roldtakes 1.000 s rlou; +n+(xtd.
(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 ver kug cjm )evs3;:4els67dtyc4tical direction or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontal swings, and by whas)ey e6d4g3mjtclkcvsu;7 : 4t 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 tens.rinj(m4z 0tc ion of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at the opposite end. Where wiltr 0.mcjz(4nil the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spriem49utp5:d *iw/s uo wng with spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillations that will allow the penny to just stay on top of the blw 94 sp:iuto w*5dmeu/ock? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at th *tkowx/e9 :a:,kpykqe junkyard. The steel crane cable 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 /a9*k,::eq ypowtxk kis the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shxow76*a glfw r)jq8u1own in Fig. 11–58 (which also gives the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back fr6aq7ow x )w8l1*g juand 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