Give some examples of everyday vibrating objects. Which exhibv:a2ggw3et )vrl6 qg3it SHM, at least approxim2q3vggtw:rg 6)3vl eaately?

Is the acceleration of a simple harmonic oscillator ever zero? 9dlzvb ;zg/1a If so, where?

Explain why the motion of a pistom9 hybgus (2t:n in an automobile engine is approximately simple harmonicyht( 2sug 9:mb.

Real springs have mass. Will the /ajmwgoslvs uwimnd c2 *m34 52a)e:*true period and frequency be larger or smaller than given by the equations for a mass oscillating on the end of an idealized massless sprin j:5la2w/m*2 mdsmao4g )u vince*3swg? Explain.

How could you double the maximum speed of kp.1 4j7f) rc0ivfdea a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spritv+5,icirej) 2ju 8tpng scale, and then is rele 2tujii,c5p jte r8v)+ased. Describe the scale reading as a function of time.

If a pendulum clock is accurate at sea leveln14v/tb-mq +ir segt( , will it gain or lose time when taken+s1b-eq m vg4/i (ttnr to high altitude? Why?

A tire swing hanging from a 9wavdiq 83w2xbranch reaches nearly to the ground (Fig. 11–48). How could y 9a 2q8wwdvix3ou estimate the height of the branch using only a stopwatch?

Why can you make water slosh back and hq637gc c-kxq forth in a pan only if you shake the pan at a certacqq 3 x6gkch7-in frequency?

Give several everyday examples of resonrvb,paqq50c7b7(u2l hn 2bw l ance.

Is a rattle in a carghb3pil ;2 xm-jy+y(k, oor +e ever a resonance phenomenon? Explain.

Is the frequency of a simple periodic wave equal to the frequency of its sokjg4 )b2pqqp.hw o;: vurce? v khg)2qpwqj.:ob ; 4pWhy or why not?

Explain the difference between th,cmj3yk;ql3. uwssy yx*f5k k zl86l7 e speed of a transverse wave traveling down a cord and the speky8 yssqc xlwm*7jkl ,zl6y3 53 ;ukf.ed of a tiny piece of the cord.

Why do the strings used for the lowest-frequency notes on a piano normally have(fg, v bgx1+gh wire wrapped around txbfg gv1+(gh ,hem?

What kind of waves do you think will travel down a horizontal metal rod if you szxmz2y-hfc)q mm*t* d nx;e. ,trike its end (a) vertically from above and (b) horizontally m*xc q,m xzdf ;e.-yz)t2*nmhparallel to its length?

Since the density of air decreases with an increase in temperacpp gukw6nh62 vt 7f8)nq+il(ture, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves in air to vary with tni 7q upn2f)t8ph6 +cgwvl(6k emperature?

Give two reasons why circular water waves decw)- np6zi3bc t b+i)pzrease in amplitude as they travel away from 3zbznwpi )tc6 b)pi+- the source.

Two linear waves have the same amplitude a7slg .k(2o on8utlrv. . gde2hnd speed, and otherwise are identical, except one has half the wavelength of the other. Which transh2.dr7 ls okglou e tgn..8v(2mits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sections of cord qv 2qh50ih uc9 re(9lvas in Fig. 11–33, the frequency does not change (although the wav59i lhr qh2c(quvv9e 0elength and velocity do change). Explain why.

If a string is vibrating in three segments, are there hfsa,s 3sy1 cuvkh*(5 any places you could touch it w3(hcvy, 1fas*s skuh5ith a knife blade without disturbing the motion?

When a standing wave exis1/ 1*d10zaxdi va eyspts on a string, the vibrations of incident and reflected waves cancel at the nodes. Does this mean that enera1 1xeas v/1dz pdy*0igy was destroyed? Explain.

If we knew that energy was being transmitted from one place to an5zog9,0d+wpwpap ,jyother, how might we determine whether the energy was being carried by particles (material bodiesg, ,p+zww9a0ypp j 5do) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is thy:koda 2e. wvb 13drx3e total distance it3dewv b:y1 3rx2oa .dk travels in one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs frpit- gns 5:)spom it but is 85 cm long when a weight of 180 N hangs from it. What is tp-i:t )5gsspnhe “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car comprh89l.2zwwe.+ifuvu bf *: rnqess 5.0 mm when its 68-kg driver gets into the driver’s seat.r892 :nwvuu+e.hb ff*qz. i wl If the car goes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretchewrr3nxs ( s/;c8 32+szu6:y r dpqkqsbs 3.6 cm when a 2.7-kg fish hangs from it. (a) What is the spring stiffness constantn8sbs d:/p 6xkzy(r+r3q; ss23cu w rq $\approx$    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 frequenf 0s (bjlfz-x m8(8)paqqhdw 6cy of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency if onlpq)z d bm8qwf 8s( jh0ax(-l6fy 0.38 kg hangs from it?    Hz

Construct a Table indicating,xla.an(9n e h the position x of the mass in Fig. 11–2 at times t = 0,t.e9an xl,(na h = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 rq s81h 9m)xyqvn-2ii vibrates predominately with a frequency of smq2y81q9in rvx h)i- 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 vibslim p/6e,z1qevx;l9 rates with a frequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 Hz. What is the value of m?ezl lspx,1/6 mq eiv9;    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 ,a9 ez;apxd2gtimes per second with an amplitude of 0 9;xg,pez2ada.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 speed of a SHO half the maximumbad:wk*+l 7 my+.rfr 9j vpow( value?.vfl +r (bpw:aw*ydjkm7+ o9r$\approx$    A

A mass attached to the end of a spring is 3ft tp e5j*0gqstretched 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 stretch yt 1f9sue+i m2bms57hes a vertical spring 0.315 m. If the spring is stretched an additional 0.130 m and released, h1mts u yhm e9fs75+bi2ow long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with spring h2swjo d j)l/7stiffness constant k = 280 N/m and is executing simple harmonic motion/2dj)h7jl ws o. When the object is 0.020 m from its equilibrium position, it is moving with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compress the spring of a toy popgun 0.200 m to “ltpp3 /np; yvv4+rm wi*oad” a 0.180-kg ball. With what speed will vw*;r34 my/it +v ppnpthe ball leave the gun?    m/s

  A mass sitting on a horizontal, frictio(j:p p1u ud)xtnless surface is attached to one end of a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, the mass experiences dxu)pt:pj( u 1a 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 = 0mt 5fo-p:o 4f 5t zuu.ir1rpj7f7rd-r.45cos6.4t where x is in meters and t is in semfour1:u-7 7- rtftr pjdopi5frz.4 5conds. 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 energy of a SHO hr; ci7m qknze)+72d,ysku9 maalf KE and half PE? c zsuyrdm,7ea2;+mni 7)q 9k k±    A

  If one vibration has 7.0 times the energy of a second, bu+aokdx i.xapt;c i*(*t their frequencies and masses are the same, what is the ratio of their ampop.c+d** kxi ;( taixalitudes?   

  A 2.00-kg pumpkin oscillates from a vertic)ll4 ge8ap+c/k :ejreally hanging light spring once every 0.65 s. g+lel:8c4e/)j a pke r
(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 twpiq.m yna:-y n9mp2i 4dzwls)xf d53;o identical parallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What will be the frequency of vibrq5z4l i-p wm2i:;.y3x ns)dn 9pydamfation?

  A 300-g mass vibrates according to the equation x = 0.38sin6.s4/y7eyznyo6d5 be;04w e wyj5t where x is in meters and t is in seconds.j y;4d04eo bzyseyww6n7ey /5 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, lab*:kli377 cvpyn vof t4eled 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 5+q3:ch kmu +lfttx5jrest on the end of a horizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial sp uj+cqht 35l5 kmx+ft:eed 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 vibrates with 5q hyw.b *dnm1an amplitude of 28.0 1n*.dybwq5h mcm when 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) with positive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two springs, with v2tf/ou u8e6z 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 0.60mtaly2iir0e4 -0 sd.j0-kg block attached to a fixed horizontal spring whose spring stiff 0.asmijl4t-d ie20ryness constant is $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with mass 65.0 kg jumps from a high br3)h e8)hlqvo+z ce)h9xq3sebyzc 5 /nidge. After reaching his lowest point, he oscillates up an)y9 bl35 ncqeohq z8)e3+s/zvxhhc e)d 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 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 ex6 bggb 4tu36lcactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly one30/:ajzix8 w xp2no 13cpwdph swing per second? (Thn2zd:apwpp8 / 3wc3 0x1oh xijat is, one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on Mars, where eq (hpp -t.i(wthe accelewi -(p.tq( ephration of gravity is about 0.37 that on Earth?    s

  What is the period of a simple pendulue)0-*r -tre j:lo czl2tex(hw6q g; wzm 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 m, the pe o)rs9d)n ;q78i fsta3 nqpir)ndulum bob has a mass of 365 grams, and it is released at an angqno 9nr) qs;fd)i)a 3ripts78le 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 length4h q2dgrxou;. of 0.9930 m. If the clock loses half a minute per2ohru;x.q dg4 day, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximum ahm5+1u6 jxhs 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 Hsg 985,sdk b hoci2p:fz. At it is released from res sgp b82isdcfokh9,5:t starting at an angle of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests pass the bow of his anchored boat every 3.ow30)64vpp;mtb x nno4 b2sgt 0 s. He measures the distance between two crests to be 6;pgxwt0s )mob6t bnv44 opn23 .5 m. How fast are the waves traveling?    m/s

  A sound wave in air u:*( ex *bd dzm-tn( 1kjutx-pcn68r bhas a frequency of 262 Hz and travels with a speed of 343 m/s How far apax1m8bu uj6d:(crtexztn dk-n* p-(b *rt are the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 k ut-v+gyzkx-wn.* x3bHz and 1600 kHz (kilohertz) an+.nu3 txk xyz-w *-bvgd travel 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 d 5pyk5y7k*i(mp dbpk( 4uy7gvc jj;.g9 zd3dwaves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have th /0:f5 wmfe+xei5o/m /0bmynyw pi: wxe same elastic modulus, but one is twice as dense as the other. In which rod will the speed of longitudinal waves be greater, and by what factor? y/ fp ef:ew5 0 05m/mwni/x i:b+xmwyo  

  A cord of mass 0.65 86jg0yu d5xm x/7jw;ro g8o orkg is stretched between two supports 28 m apart. If the tension in the cord is 156;xmxjyg/ ow 0u grj8r 5o7do80 N, how long will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to the top of a hill by a steel cable of leddy q y;z.f74s vy+r2pngth 620 m and diameter 1.5 cm. Aspv; r74f+.z dy2ys dyq the gondola comes to the end of its run, it bumps into the terminal and sends a wave pulse along the cable. It is observed that it took 16 s for 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 belo2(vqzijhhp: 0ot h.) 3a wp-atw the surface of the sea. He hears the echo of the wave refp-h zt.j0:ph3 vqwao(2t)ih alected from the ocean floor directly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake trafrheh *c6p9py:1lhw:vel at different speeds, and this difference helps in locating the earthquake “epicenter” (where the disturbancl 1:h*9rypchwe:f6hp e 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 sun b:/wzg bz, qcy b/(0otv 0zig-den+(rface wave can be approximated by a sinusoidal 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 leave contact with the ground? [-w(o:cznzbzve0 ,0n/byd/g(bt q+igHint: Set the acceleration a>g]    m

  What is the ratio of (9p78x ic d c0r7bm6hfta) the intensities, and (b) the amplitudes, of an earthquake P wave passing through the Earth and detected at two points 10 km and 20 km from thexbhcc 8t76m0rid7p9 f source?(a)    (b)   

  The intensity of an earthqua)p5b +tf 9,b 9wpih lvxq(t2teke wave passing through the Earth is measured to be +pt9txwp9 vq)f(i ltbheb52 ,$ 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 samee j j 2l,azu71xd3awk0 frequency travel through the same portion of the Ew37j a0jl1 ze2 ,xkdauarth, but one is carrying twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string z2urv4jm jj )/1yg0qn have the same frequency, but one transpg4qjn)/2vru01 j zyj morts three times the power of the other. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface o*v o4yw7c0o1:2zvoqfc3bu vh f a pond is observed to move up and down a total vertical distance of 6.0 cm, cbv v*3cho 21o7q0 fo4:wzuvyfrom the lowest to the 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 ea4721m e20xdhn.8(dtwlui dbglr 3wd xch 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 straight. Whaed1g 8b lx73hn2 utd(4l2w0m wd xid.rt has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundamental frequency, b8h mmg ;,zm* m .wyiapp/;wu;what are the f8.,am*z/w ug; m;pbw; i mphymrequencies of the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when uf8.6nyg/k qz, tnv9b +fl)sre nfingered. At what frequency will it vibrate96nkg rlf )en. b tqv/,y+sf8z if it is fingered one-third of the way down from the end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequency of 280 Hz. Namy ,1xj4lmqv g e71r9bwe at least three otherjmxyevw17 9r 4,gbl1 q frequencies at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92f3aodk 92lbg+f4(uq o m/s If the frequency of standing waves is 475 Hz, how far apart are folodq faub+g2k(94 3two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 350 Hz, what k +yhk62al-d:qg r*fn is thag nk2 y*:k6-fqd hlr+e frequency of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distance ijh0; qja yz;41ep ds)p2/vut from the bridge to the support post is L = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundamental and fi;jhza t;/jqi4p 2pvd1) u0y esrst two overtones?    Hz

  A particular guitar string is supposed to vibra0z)kh9.f7m hbpg/u uh9g0 ilf te at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the )/ug9p bkg.zi h0ffu9hh7 ml 0tension in the string be changed to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hz, but it /29bdz-q(2abi-ggjj+ekznobo -g )i is measured to vibrate at 205 Hz. By what percent should the tension in the strin -n2gz g2dz(/bbkaooqe ij gi- +b-)j9g be changed to correct the frequency? decreased by    %

  One end of a horizontal string is att:.gaq): dvet+p. bdcm ached to a small-amplitude mechanical 60-Hz vibrator. The string’s mass per unit leng:m..tvpc: e addbg)+qth 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 m i6 ,9h( 63otjfx)gvgm s)1ze2 uddfithe string may be adjusted by moving the pulley. If the hg 2thmxi66) v mdgz3e(df)j,i u9fo1s anging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at just the right frequency,k- whiibj w/ad8s1/p + the w1s/d+hwi w-j 8pib ak/ater 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 the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundary within tr 6a1 k-py:qmohe Earth between two kinds of material. If it approaches the boundary at an incidenyq:r- a 1pom6kt 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 “shb1t3+(iyhnz jw0 9byaelf” where the velocity changes from 2.8 m/s to 2.1 m/s If the incident wave crests make9bby(zw3n 0y+ih1tja a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling fe p5f; 0)dqekin warm air when it hits a layer of cold, dense air. Ike0fd) ; eqp5ff the sound wave 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 earthquakml;1dzpb v) y7e wave strikes a boundary between two types of rock at a 38ympd;1vzb7 )l $^{\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. s1pm q.gxo58c5 m in diameter. According to the user’s manual, the dish has to be pointed in the direction of the satel5sx q m.o8cgp1lite, 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 across the Pacific 6 (uob8d/ue bhOcean. As it approaches Hawaii, people observe ando b(e8u/hub6 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 a spring stiffness constant of 550fy5o b6ywbxbzwulh2p-8 3j /+ kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collides with a wall at a speed ohbobly3w yp+2 85z ubxf-wj6/f 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m be 5wod *a0o(eyqlow, which stretches the net 1.1 me *d (q0ao5wyo. 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 tm,3t2(ruwq pach y 0y,pfwj*/ he end of a freely hanging spring. The mass then falls 33 cm before it stops and begins to rise. What is the frem wp/tq*2 f3wy (0yh,rpjcua,quency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed ocsas;zo5 v.+z f 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a+; s5voazzs .c) 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 of coffee (diameter 8 cm) at jus2dp znn;j,ak 69f /+j bvvjuf(t the right pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the sv ,apfnvkz(fb2;j +j u 6nj9d/peed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the center of a 3k4+;lapbl n-:c ne t;s3-rpm phonograph record have a wavelength of 1.70 mm. What wills 4la:c;p;nl bnt+k -e be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.652jw gn,vd .tl)cm - *aulsxm;b7ld3n80cos7.40t where x is in met g) ,tcb;ldw3ln7n8-vjx*dml2.au m sers and t in seconds. Determine
(a) the amplitude,    m
(b) the frequency,(round to two decimal place)$\approx$    Hz
(c) the total energy,(round to one decimal place)$\approx$    J
(d) the kinetic energy and potential energy when x=0.260 m.(round to one decimal place) PE$\approx$    J KE =    J

  A simple pendulum oscillates with frequency f. What is its frequency if sgp4;y15orxait accelerates at15 4ypasgxo r; 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. 1r5.dk7 brstix)pf 3s When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he st5i3.r t s7)srb1 fxkdpeps 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 musaue7ucler8z :4,s2 w7lw0 pft ical instrument are tuned to play at 392 Hz (G) and 440 Hz (A8wspe,4a c t 2 fl7:l0eu7zurw).
(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 stretcf,jo5s,/ql zu(sae a -hed two-part cord of Fig. 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) Is the wavelength greater in the heavsq-f(aa/z ,jl5su o,eier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and tyu0 0ub :kswu7 vm+skhp u7k06he tip of each prong moves 1.8 mm to either side of center. Calcu kk us7k6swuvby0 7+:h0pmuu 0late
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscilb d3;oq4e9(; dwcqfd2 vruqj 3i: /)xogp.bl hlates with simple harmonic motion of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not ibxjq 4;g;def povoq)(u2h d9 q/w33dbc.lr: lose contact with the board during the oscillation?

A string can have a 9rq za,am h r:nxhj5a+ik: m62“free” end if that end is attached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Detj9h:rz hnq5r,xk m+a2ama :6iermine 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 exactl r0w1hfv a g.:fdry/-dy 2.000 s — each one-way swing takes rd f0r/hwg:.yfvd1 -a 1.000 s.
(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 oscfwhq(5x *.dy9,q*j t;dksjgt illate in the vertical direction or can swing as a pendulu,5 (hj9t*tk;qqg df y s.xwjd*m 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 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 go8jcy b. xd;h 9c4e/nd is stretched under a tension of 255 N. A pulse is generated at one end, aoxbd .hdce n;y98/jc4nd 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 withm4jix+;qp0 r 077yvtd, am bqa spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillations tha4ammvj;7bdq 0p i rt0+q x7ay,t will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steesde +zmk:n x.vh39+bel 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+h: xmes n.bvzke9d3 +he bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shownl5zd3: elm.nl()rtu hzxvv-j:hr4ij lm 05o 9 in Fig. 11–58 (which also gives the dimensions of the block). You push it sideways as shown, and then you let go. Thei9o5j:lvvtrz m5-3lrdl.eu)4nm hz( :x 0ljh jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this vibration, given that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz