Give some examples oey ms2jyfv */f. ph18vf everyday vibrating objects. Which exhibit SHM, at least approximat.yehm 2sy /*fv1f8 pvjely?

Is the acceleration of a simple harmonic oscillat.n6f 1 s,-fwp*dfntgq vl5 ok)or ever zero? If so, where?

Explain why the motion of a piston in an automobile enb;w4kcnh+fy )gine is approximately simple harmonic4n; h+)cfyk wb.

Real springs have mass. Will tto0(d*i* oq d-x si 0lhvvr8y;he true period and frequency be larger or smaller than given by the equat*d0 ysx(-ql ;rh tv*i voo08idions for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the gqk1xz* )+hqn maximum speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attac j4 7ypt92r7ku-lqzc lhed to the hook of a vertical spring scale, and then is released. Describe the scale reading as a functit77 r 4qlc9uypjk-zl2on of time.

If a pendulum clock is accurate at sea level, will it gain or lose/ x3,he:snycp xc vn-85 dbic: time when taken to high altitude? Wb e5v-/ccx,y 38:dnxin h scp:hy?

A tire swing hanging from a branch reach ajgr5ek;o6:i, nqik+es nearly to the ground (Fig. 11–48). How could you estimate the height of the branch using only a stopwatchgo: kijae,k; rq+ni56 ?

Why can you make water slosh bac,rf2r6t s tn5ck and forth in a pan only if you shake the pan at a certain fretrrct6n2s5f , quency?

Give several everydat dhnw0; h57oqfx44ab y examples of resonance.

Is a rattle in a car ever a resonance phenomenon? Explab h u)ly5c84wain.

Is the frequency of a simple periodic wave equal to f+8blz +agt(tthe frequency of its source?za (l8+f btt+g Why or why not?

Explain the difference between the speed of a tra i(g qh t969u-v(sjorknsverse wave traveling down a cord and the speed of a tiny pieceg - k69hiu(rosv(tjq9 of the cord.

Why do the strings used for the lowest-frequetm1j,b-yk*iqx) 3(fy zun )wg ncy notes on a piano normally have wire wrapped around them?qgw mxy13)t,)k bfn*iz-u (jy

What kind of waves do you 7kb 1 w2sn4ncmthink will travel down a horizontal metal rod if you striksnb2c147w kn me its end (a) vertically from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increszw.2 f4 w6hbzase in temperature, but the bulk modulus B is nearly independent of tempz sw4hbw62f .zerature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decreaki0.i vvl7xm* qzd)a0 se in amplitude as they travel away fromkx. izm0q a)ivvld* 70 the source.

Two linear waves have the same amplitude and speed,vpf 5 n*2 kq::usa)gqb0na0d q and otherwise are identical, except one has half )an ku:nqb fd2 0avg psq0q*:5the wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the;axjs* slc* a. boundary between two sections of cord as in Fig. 11–33, the frequency does not change (ala xs*s *aj;.lcthough the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there any places you couldi:7hxlzl ivc9mlqyj5ede : rj6: 7+.s touch it with a knife blade 9il r:z e:6l+m7i7.:hec5ldj xyvs qjwithout disturbing the motion?

When a standing wave exists on a string, thia0of 90d7ah be vibrations of incident and reflected waves cancel at the nodes. Does this mean that energy was de aoi0ad7bf9h0stroyed? Explain.

If we knew that energ6uk tf 8jk.mh4rppq-1pp67a hy was being transmitted from one place to another, how might we determine whether the energy was being carried by particles (material 8pq rp6p-1 kpthj4fhk m7au6.bodies) or by waves?

  If a particle undergoes SHM with amh)6nbj9hdacsvk 7/( zsu26 er plitude 0.18 m, what is the total distance it travels in one period? ka/ d(uhhsz b6 nc)s7j9e2r6v    m

  An elastic cord is 65 cm s ./+udvrylw rqha6 /-long 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” constant qarrd s/w/hu l.-v6y +k of this elastic cord?    N/m

  The springs of a 1500-kg i+fh7fvt5fa.bs1(ud +b5e w pcar compress 5.0 mm when its 68-kg driver gets into the driver’s seat. If the car goefha(+b utbff7 w5v1. ds +5ieps over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches cl: 54 / j-hxk1nxq4w zod)zn h qa:1*ktd-ejo3.6 cm when a 2.7-kg fish hangs from it. (a) What is the spring stiffness consta- kqq dx4e1zkn:ho-wj4a l5nh ztoc )/ j:x1*dnt $\approx$    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 frequ4c 6dbevj.g54hfvx+tu2n yc: ency of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency x b4vje6 n5c4v:y+u dct.g2hf if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fi)u(*k fwh (dieg. 11–2 at times t = de)fw(i*kh u( 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 spider’s web. The web ou1i l3-vvr5yfyr5 n7z-w8e91urxqv vibrates predominately with a frequency of 4.0 Hzyuvei795r 5 r-1yxvfonq zuw1-l8r3 v.
(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 vib4y-iupl p5e4o ya0 2i-wyxr7u rates with a frequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency isyixare5u p4y4opy-w0u7 2 i l- 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibpy//43vf/wzkyt(x pgrates 3.0 times per second with an amplitude of 0.13 m. Deteg4zpy /wvyf/x3 /k p(trmine
(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 ma9ch ;o8ohn 15clhqx (xximum value? ;1oxh8qxoh c cln95(h$\approx$    A

A mass attached to the end of a s)bark) jw 1t0jpring is stretched a distance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretches a vertical spring 0.315 m. If the spring is stretche/bfa wy(u* mw(d an additional 0.130 m and released, how long does it take to reaafw(ym u*/w(b ch the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with spring stiffness )i5yy 3l+w /vp1f gxcrb -4njeconstant k = 280 N/m and is executing simple harmonic motion. When -nplbv/xyf+ 4irg1eyjw 35 )c 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 pqlw4p7)iuv c,uh onoh8,i2vb h t3/m+opgun 0.200 m to “load” a 0.180-kg ball. With/7nh), hhoum4ol ,wivt b8 v iucq2+3p what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is a mof) 43ngi.juttached 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 released from rest with the spring commfi)o3ugnj .4pressed, 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.zizmp i7 +5 z8)hrfc:c45cos6.4t where x is in meters and t is in seconds. Det:5pmc h8zi+ f7 z)cizrermine
(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 enerk.fg /sxv/apwrtiolr():p6s 2 hic:x(p/ 6jl gy of a SHO half KE and half PEv) ils past6xpihrol2(/6w(: x/r:pg c/. j kf? ±    A

  If one vibration has 7.0 times the energy)rb, hi .hqx4l of a second, but their frequencies and masses are the same, what is the ratio qi)x,. hrh4bl of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging lig1p5 wp6kjoei 6ezg wtwm:sx g86:1n3 pht spring once every 0.65 og 5es6:imz6 p6 tp:nxpwk 81wgw31 ejs.
(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 tw30etf x:fd ajelql ;69o identical parallel vertical springs, each with spring stiffness constant k (Fig:f36l9t l;ajexq0e d f. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t whep.0 2u mawmnybb78 a8xre x is in meters and t xwpan.y bub872 0amm 8is 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, l:bidg/tn,e*arxfz km7 91*w qabeled 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 mfloikb99 rx -lph* e 7)wl29ktbr.n3 end of a horizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.96m/s Detfr 9)k*3x 2bi9r9obmn7e tl -h.kll pwermine
(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 vibrates with al(*kr 4v)baf,zx 4npwzlle-4 n amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) with positive velocity al* ,nkl)lzwrxa 44 z4v( p-bfet
(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, wit 7z8pq1k g;iaph 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 blnnzvc w6i hjmx 80,v/(ock attached to a fixed horizontal spring whose spring stif0h8xwz / mni(jcvvn6,fness 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 jumbukjt8fwa j y) ()x57wps 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 level of the bridge. Calculate the spring stiffness constant and the unstretched length of the ba)wk tw7 byj(fu5x)8jungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vsfqj-t;xf:l + ibrations in exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if p q6d8kptu2j ;l-mh9v joc6.z it is to make exactly one swing per second?j qhtlupo668.k ;9-zcjdp 2m v (That is, one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What ij6g; zrie)+wxs its period on Mars, where the accelerat+)g ejirz6;wx ion of gravity is about 0.37 that on Earth?    s

  What is the period of a simple pendul2tce5+ 5)(iag:loj tt -9zi (rhlkpu lum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pen*o.t5g4qn3.vxihb0s3 v*d ecy r*xyp )f syh 1dulum is 0.760 m, the pendulum bob has a mass of 365 gq )*sch13ye5 dynvs f3h*gpxx*.0 rv.iobty4 rams, 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 lq b/1v b),tgzh gvbs-/ength of 0.9930 m. If the clock loses half a minute per day, how should you adjust the lengbs/zv vtbbg/,qhg1 -)th of the pendulum? shortened by    mm.

Derive a formula for the maximu4d id-jpsnww2j ruk(2,/i je;m 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 i:rji0vhj;iy3v o7rftw.yl p5 3/ gip1t is released from rest startinyfpy i h;0it7l /1ov i3w3jjrrv:pg5.g at an angle of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave h1ksriq. c+xas3nw(cb6*+6zrynn:; q8uac wcrests pass the bow of his anchored boat every 3.0ya:xsiwz s.kr 38+ b1q(q6*ch6 acnncnwu r +; s. 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 *hh2 ty0 ou z;uf-dh+la frequency of 262 Hz and travels with a speed of 343 m/s How far apart arlu *+ 0h;ohyzduh-f 2te the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 k t de/ei:j8 sthni6;cgs- j80frlz30kHz (kilohertz) and travel with a speetii hns8kejf cz /et:;lg 3dr s080-j6d 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 wfn rgz;-xj6 fn2 yyd:0aves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modul s)6mmm f8sc,x 5atnhs(b-.fxus, but one is twice as dense as the other. In which rod will the speed of longitudin bf smn .t,msxxfs)5h8(ca-m6al waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 289 cik euv y8i)-ypqb9qu5pm37 m apart. If the tension in the cord is 150 N, how long will it take a pu-p ii7)yuvm 8p 9byq5c9ku3qelse to travel from one support to the other?    s

  A ski gondola is connected to the top of a hill by a steelw7j 5arj77.ew1cc :q6ag /wnjmjt; fz cable of length 620 m and diameter 1.5 cm. As the gondola comes to the end za;w 5gj:n1 tjc 7q76jmj.7fra/c w ewof its run, it bumps into the terminal and sends a wave pulse along the cable. It is observed that it took 16 s for the pulse to return.
(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 sh u9 7oget, z 6g3+swxfsrt/c1dip just below the surface of the sea. He hears the echo of the wave reflected,6t +fw7 3 u/t1szexd9gog src 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 earthqteq/s ):gve3 zuake travel at different speeds, and this difference helps in s3 /vze:gtq) elocating the earthquake “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 sinusoi;hw 529i;qeommknms 2tnp y)1dal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin to 2smqhm 9t;i15;pwk 2 mneon)yleave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) tw.)wm r4p i.5u lwxhp*he amplitudes, of an earthquake P wave passing through the Earth and detected at two points 10 km and 20 km from theprp wm)h.5w.iwx*l4u source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is measurep/g+n7r z g3wsd to be npsw g+3rzg/7 $ 2\times10^{6 }J/m^2$ at a distance of 48 km from the source.
(a) What was its intensity when it passed a point only 1.0 km from the source?(round to one decimal place)$\approx$    $ \times10^{9 }W/m^2$
(b) At what rate did energy pass through an area of $5m^2$ at 1.0 km?    $ \times10^{10 }W$

  Two earthquake waves of the same frequency travel through the same portion 3/wpzg2nfl v8 of the Earth, but one is carrying twice the energy. What is the ratio p83l2wg /zvfn of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same frequenb,nl kdwqf2 5,cy, but one transports three times the power of the other. What is the ratio of tdl2bw,k n,5q fhe amplitudes of the two waves?   

  A bug on the surface of a pond is observed to mojb8 i*s(g)fcjf8z 2uz ve up and down a total vertical distance of 6.0 cm, from the lowest to thgjszfi)(uj2 z8cb f*8 e highest point, as a wave passes. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each other. (a) S / 4ui)bo;w:3j iaeigyketch the shape of the string at g;i 4oi:/e3yawi jb)uthe moment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its funda:m+ry ) xvawnzmwg84 )mental frequency, what are the frequencies of the first four harmonics ay m:8n+)) gm4wrwzxv?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz kutrm;9fi5i /7 686jbka/dst zk2glu when unfingered. At what frequency will it vibrate if it is fingered one-third of the way down from the end? (That is, only k2kmf/rildb akguiju8tt7sz /;9 56 6two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in zeliei9 3eu oa66cs7: t/*gvzfour loops at a frequency of 280 Hz. Name at least three other frequencies at whi e 7to /gzsi6cz9li*63eeuv a:ch 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 n:tn)ff2gj0o2il96z,zou q zx+hrh 4 of standing waves is 475 Hz, how far apa o2x f+ig u:4zthf,q)9z6j02onz rhnlrt are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 350 Hz, w x lv.-oh)+ a28ysi rzxfpx4e(hat is the frequency of the fundsf ilr-z xvxo+4pex8yah )2.( amental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. 8v. mll, lja8tg+/xshThe distance from the bridge to the support pog.xsm88ll t,hv/la +jst is L = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate xu1f)7 zz8e ceev;ih 7at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension i)c1 77f ;evzhuzxie8e n 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 atf: qd. sri w*xf6f6lo8np8+d e 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correc6ldqpw*8f+ x. f:ne ri6ods8 ft the frequency? decreased by    %

  One end of a horizontal string is attached to a small-ampfmauvyk9lw5;s x8w ex7 p481 ulitude mechanical 60-Hz vibrator. The string’s mass per uni71m;afwywv85x8 pukelu s 94xt 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 pemgxq 1wf-lbl (w 7mwu5*;t. jj8qn x*ulley. If the hanging mass m is fixed at 0.080 kg, how many different stand tbxx njmw1eq* -;f.j l78lq *5w(wmguing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forthi .jdkkuxd:;* in a tub at just the right frequency, the water alternately rises and falls d:;xkud. j*k iat each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave tdbt3q9sp4oqxz/m48 traveling at k.0 km/s strikes a boundary within the Earth bb z8px st4m49q/d3to qetween two kinds of material. 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 “shelf” where the velocity changem3.zhd,8b43qjlavjgb dh1 c dpui. m+ 9aga1 +s from 2.8 m/s to 2.1 m/s If the incident wav1dzd3+. lhgmavd 3juq jc.g+, 8bbpham94i1ae crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm ln/c/gn+wkb1 air when it hits a layer of cold, dense air. If the sound wave hits the cold air interface at an wb/1nn+c /gklangle 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 boundarjk645 2xpdue*dr m ap(y between two types of rock at ak2da prdxj*p6 (me4u 5 38 $^{\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 m ;r;afon5ocg 6 ,gic,):kp vjbanual, the dish has to be pointedn k ,cbp6,if)o;o;5 rjv ga:cg in the direction of the satellite, but an error of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 250 km and velocity 750 km/h travels ace3)o ha g,mp7kross the Pacific Ocean. As it approaches Ha)g3pok7a m,ehwaii, 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 attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has*1jtvxy7 ;o( lpa c7qg a spring stiffness constant 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). [Hint: Use conservation of energyy;jqx*1v 7 agp(7l toc.]    m

  A 65-kg person jumps from a window to a fire net 18 m below, which stretcyww5zg bo+;np7c jwjy 02im 72hes the net 1.1 m. Assume that the net behaves like a simple sprw2yon;i7gzc+2jmbw w 0yjp 75ing, 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 spxghgax /f24u(o q5pz; ring. The mass then falls 33 cm before it stops and begins t24qxp zxo5/ug;ag(hfo rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (90 i/jicn6 kzhs*kggr)w cr.7Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring /rk9g6s0wz*jcrih)nc.kgi 7stiffness 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 of coffee (diameter 8 c:jyzvo+ ud 5d(m) at just the right pace of about 1 step per second, the coffee sloshes more and m ozv:du(j+d5y ore 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 10.8 cm frjdl n6fm,kr w-j vx--d+mi8/d om the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequency of tx+,mm- rj-inj6/ kvd 8ld-f dwhe sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t where x is i u4m , jmwotl6:*vdte*n meters and t,**me6vjdttw4o ul: m in seconds. Determine
(a) the amplitude,    m
(b) the frequency,(round to two decimal place)$\approx$    Hz
(c) the total energy,(round to one decimal place)$\approx$    J
(d) the kinetic energy and potential energy when x=0.260 m.(round to one decimal place) PE$\approx$    J KE =    J

  A simple pendulum oscillates with frequency dx;kou5m r7r.f. What is its frequency if it accelerates at ;dk5r.x mru o70.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats/aqb /f35iwwr,e jo 5t on a lake. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps of /ro,if ja5w5bw e3qt/f, 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 musi0-4 mzb44 ekvowba4bh(ed w )ccal instrument are tuned to play at 392 Hz (G) and 440 Hz (Ac em4b4)4wewab vh-d 40ob( kz).
(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 kox u+ax1-o8m) wc *rrof Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lig1uo r*x m+xckoa8)r-w hter 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 d s (knezwjni.(s 38y65;aebmat a frequency of 264 Hz, and the tip of each prong moves 1.8 mm to either side of center. Calculate 3k;5 6(.8(m szwyj n bdsaieen
(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 frequency 1.5 cycl7; 1fml x ba-b7aurzc4es per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) willc-fb17a7; zl 4x mbuar not lose contact with the board during the oscillation?

A string can have a “free” end if that end x f34wo0z +3hex n1f.m -ersifis attached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determif3 fxf sn10-oemei xwzh .3+r4ne 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 one-way swing takes ptz-dp)ofjj5-j 6 xd-1.000 s.)5z-jx -jt-p pojdd6 f
(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 springz,*o*y1rm vlqtt 1 , a,sw)mkb 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, the period of the vertical oscillations or the period of the horizontal swings, and by what amou osqt am,1,kty1,w *lrvzb* m)nt? [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- e3zin xadbf.y 9tlwlhj( a.7uw ,l39 123 g is stretched under a tension of 255 N. A pulse is general elhay. aw 33l,-nz7.wjtdx9f(i 9bu ted at 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 fo. w)1)xec,yt kcle+ xh/pxc 5rom a ceiling by a spring with spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum ampliy pe ckot h1+c)x,x5clwx./)e tude 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. (p)mdbkneo r(0e s-0pnnild* p:0d/sThe 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 is the period of t:p0 )ppm0 * oeissrlednn0d-dbn(k ( /he bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–5ns b uz+rzoat6/ us/.a657ywn8 (which also gives the dimensions of the block). You push it sideways as shown, and 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/6 7ana+65tz.uyo znsrsu /wb that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz