Give some examples of everydayp gpg176u 45iio p;wvl vibrating objects. Which exhibit SHM, at least app 5gpp p6livwgo 4;iu71roximately?

Is the acceleration of a sx (tk8/y sne2/h jzq)vimple harmonic oscillator ever zero? If so, where?

Explain why the motion of a piston in an automobile engine is aosh1gx. 3p7atpproximately simple harmon .17pts3hgaxo ic.

Real springs have mass. Wil 3f* (n p;l95nz2y*gu +ylebnxsd (vtel the true period and frequency be larger or smaller than given by the equations for a mass oscillating on the end of an idealized massless spring? unt3g 92ledvpxls;nn ( (*yzf +*b5ey Explain.

How could you double the maximum speed of a s9oajt52ba :dph2j 0ooimple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical springgf-l cwh lc5rk- *;q3q scale, and then is released. Describe the scale reading3 cwlc q*lhgqrk f-;-5 as a function of time.

If a pendulum clock is accurate at sea level, will it gain or lose time st jr0yvn70kjv; nvz,t(,1lgwhen tak, vl;(y 7t0jvr s,0vz tkjn1gnen to high altitude? Why?

A tire swing hanging from a )qvc.: 7nkufs branch reaches nearly to the ground (Fig. 11–48). How could you .q:c7) fsnk vuestimate the height of the branch using only a stopwatch?

Why can you make water slosh back and forth in a pan only if you shake tu7;sp ;ppi5h the pan at a certain frequencysiu57 htpp;; p?

Give several everyday examples of reso8quk9 jekex -2nance.

Is a rattle in a car ever a resonance phenomenon? Explain5 zc5er2dq 0sdstl11 a d-p(pw.

Is the frequency of a simple periodic wave equal to the frequ5g ,m+qewvivu ;v77kor9lg cm ju( 7n8ency of its source?jumgm uk;5 e 7vqvr(,gw +9ni877 cvol Why or why not?

Explain the difference betola 9kpp6:x,cween the speed of a transverse wave traveling down a cord and the speed of a tiny piece ofxl 9akppc,6 o: the cord.

Why do the strings used for the lowest-frequency notes on a piano normally have 5h/ btg1zaj 8iwire wrapped around tta/1b gi5zhj8hem?

What kind of waves do ygu ji;kdux+- ;tve(.m 6l tjm9ou think will travel down a horizontal metal rod if you strike its end (a) vertically from above and (b) horizontally parallel to its lelt9tvmim(+ jdu;uk e-x6j.g;ngth?

Since the density of air decreases with an increase in temperature, but the n6 zac 1,p7y0+ngk:y 8chmq70ew mkwbbulk modulus B is nearly independent of temperature, how would you expect y+ wapm bgk7w,mcn: 0e7c0q yk68z nh1the speed of sound waves in air to vary with temperature?

Give two reasons why circulnh m82mqg:l :har water waves decrease in amplitude as they travel away from the sourc8h:2 n q:glmmhe.

Two linear waves have the same amplitu ib3gc4pr 2pl6de and speed, and otherwise are identical, except og2 pcb3i 64lrpne has half the wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the bound+wd5z: shl;fph-a ) qbary between two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength shb 5z-l+;):ha fwqpd and velocity do change). Explain why.

If a string is vibrating in three segments, are there any places you could touchgseq+lxf :c76 it with a kls x:6+7gec qfnife blade without disturbing the motion?

When a standing wave exists on a string, the vibra3wjm o,o lbw 9,k3ngs1w 9nu6utions of incident and reflected waves cancel at the nodb 9lugj 9 s1nkww36m3,oow, unes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one por k1cw.wcwx ( (yr3zhs)/d ,wlace to another, how might we determine whether the energy was being carried by particles (wo,(zwwsw/ryd)xck1 3 ch.r (material bodies) or by waves?

  If a particle undergoes SHMlrk b7mj xkq-+ d2q/e+oo,j4 g with amplitude 0.18 m, what is the total distance it trav+ / 4rq+qkko7,g djej ol2-mxbels in one period?    m

  An elastic cord is 65 cm long when a weight of /dv3y5 h+ ibug75 N hangs from it but is 85 cm long 3+hv/5b dyi ugwhen 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 5.0 mm when its 68-6vit 96bixwkbi+gzm ey1+f-/ kg driver gets into the driver’s seat. If the car goes over a bump, what wil/bxf b tz wi1g iev-iy++6km69l be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2. 6n z.8iwls9awzw3:cd)afq o/7-kg fish hangs from it. (a) What is the spring stiffness constaz.6/saw98ficodwl) n3q: zw ant $\approx$    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 jp8kt0 (yu*8l,whk pvfrequency of 3.0 Hz when a mass of 0.60 kg is hung from it. Whpjl v(py80*h8,t wkukat is its 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(suc:a(*zplvj ( mbtr; am+bo r-(/uo = 0, blao /sb:p t(ra-mujm (+( ;*vzrco(ut = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 b b4ecr ex /dt*yq0e+7is caught in a spider’s web. The web vibrates predominately with a frequency of 4.0 Hzybcrt e* 7e4q /exbd+0.
(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. Wo;t6cz41l ppr*d/i blhen an additional 680-g mass is added to m, the frequency is 0.60 Hz. What is the value optbi/6l r 4zp1o* cdl;f m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per second with an a ub xpp* ib/hx*-p0x8z6ngq9gmplitude of 0.13 m. Detezgx-bpgb*p i6n*pq/x9x08hu rmine
(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 SHzxqgua2h1p8)kwm ,yg9,z ,p r xv d+/cO half the maximum valug,urvkz8 ma2/,x9qcyp ,x hgp1)zw d+e?$\approx$    A

A mass attached to the end arm sfyt8.9k ca6;4ebqqlv 92of a spring 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 s e g5/,(tspchxqb2n3npring 0.315 m. If the spring is stretched an additional 0.130 m and released, how long does it take to reach the (new),p/ctenq3(bx5 hs2gn equilibrium position again?    s

  An object with mass 3.0jdaq.s,t 7h)ud*xd 6,yj7 l kg kg is attached to a spring with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is moving with a speed of 0.55 m*ylx )duaj. 6gs7kdt7 ,j, dqh/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 ahkg0yr9 zw* ajcxhq3;bt: 11v toy popgun 0.200 m to “load” a 0.180-k3 1:bywj9h;cxg *ha 10ktzqvrg ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to one6ynf qge9kz3e(.g zk( end of a spring; the other end is fixed to a qzenk yk9ge3.fzg(( 6 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 a maximum acceleration of 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates according to the equation x = 0.45cos6.4t where x ivbv*t+ g+0g2eoh9p b k r+wb2ps in meters and t is in seconds. Determin29 bb2bvh+ t pwgv0r pkoe*g++e
(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 equi ylf/ecq6wr*25f 1asojda5 b3 0 4rraglibrium is the energy of a SHO half KE and half PE? ±c3f 05aorfa5b*serj da14qwy/lgr2 6    A

  If one vibration has 7.0 times the energy of a second, but their frequr(vz*aw4hp .h encies and masses are the same, what is the ratio of their amprvh4p ( z.wah*litudes?   

  A 2.00-kg pumpkin oscillates from a verticall,l xcq./dw8-evv)v p,r s+ zzey hanging light spring once every 0.c zsr +,el),ed v/- 8z.vxpvqw65 s.
(a) Write down the equation giving the pumpkin’s position y (+ upward) as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. y = (   m)cos($\frac{2\pi t}{0.65s}$)
(b) How long will it take to get to the equilibrium position for the first time?    s
(c) What will be the pumpkin’s maximum speed?    m/s
(d) What will be its maximum acceleration, and where will that first be attained?   $m/s^2 $

A block of mass m is supported by two identical parallelr v3fhti1(o;o vertical springs, each with spring1r;vhi(ft 3oo stiffness constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to tw2 cg2mvbn t38he equation x = 0.38sin6.5t where x is in meters and t is in seconds. Determine w bc3g282tnv m
(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/pxrytv49nm kntdu-;9fs:k.a9 3v nlabeled 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 r7zqhf r w;.w:c l(3eaagipo)(est on the end of a horizontal spring (k = 124 N/m) is struck by a hammer, which g f:z o rai(;). 7eqwph(g3lcwaives the mass an initial speed of 2.96m/s Determine
(a) the period and frequency of the motion,    s    Hz
(b) the amplitude,    m
(c) the maximum acceleration,    $m/s^2$
(d) the position as a function of time, x = (    m)sin(4.08$\pi$t)
(e) the total energy.    J

A vertical spring with spring s8 zu5 d eio:p.g;hp3f9ev3hgatiffness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equfiade3;83uzg9:p .5veop hgh ilibrium 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 twoh pfz )y4r0 wp8acmv95 springs, with spring stiffness constants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes dj w-xha+uz*4(,d 44wdiluk )urdsh- a 0.600-kg block attached to a fixed horizontal spring whose spring stiffness constantuzdjw 4r+hwd-dkxa,u( sud4 4) li*h - 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 bridgez+kj 1boyz6kbhs,l/ ;. After reaching his lowest point, he oscillates up and down, hitting a low point eigh/ josl1b;zh+,yz6kb kt 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 exactpn dq0lp*n- f::/- mfx+pm i )t.trso3hfr:an ly 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 t9-opuj nf em+a,99rd( s,ca9bbng;eone swing per second? (That is, one complete vibr n;ebru g-eda9bm,,o+n9jpc9 ( ftsa9ation takes exactly 2.0 s.)    m

  A pendulum has a period of ywkmrl3a3s5so-4/ /knudrb/xtz9g+ 0.80 s on Earth. What is its period on Mars, where thek t+ mu5s/azrd-g y34x3lbr 9wn sk//o acceleration of gravity is about 0.37 that on Earth?    s

  What is the period of a simple pendulum 80:)6 lyl*qj k a1peuhcx(ss8p 1 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 m, the pendulum bob hasv3 mlgpn:6rv1rt/ dtr6a9k1 u a mass of 365 grams, and it is released at lpd1: 93r6m vra61ntv ug/ktran 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 lvs q u- (k9rsg;m3j(0dw2o zulength of 0.9930 m. If the clock loses half a minu vwmj2;(ur0zk(du3 l-g s q9sote per day, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximum jtxawbouu6p* l w0oz1g m) j7,/-uz:h 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 ofktccm )l:,( gu 2.5 Hz. At it is released from rest starting at c gl,k( tmcu:)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 /gjn9zdxv*2zc4jn 1wn++j un*j*bix 3.0 s. He measures the distance between two crests to be 6.5 m. How fast are the wg b9z+xzw 4nj+**u1j2dn njci*nv/xj aves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels)scn(dxgr : k)jrx8/cbtp2*g 3pbnu / with a speed of 343 m/s How far apart a)jt*b (2n :xduksgx8 cg/ bcrnp)3r/pre the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 16n gp+d304lhe 7yh asi300 kHz (kilohertz) and travel with a spi ah3h3ldnp y+70e4gseed 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 (kl5dzz7scr (
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one is twice as dense as thd jgtb-i w 9)cu/s :le5v:)z9m:c dllve other. In which rod will the speed of longitudina-)lsg:v vud::j lbm 5t9l /dcwc9)zeil waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apart. If the ten4sk-pe mxg)c yb0.x,f) l*n ibsion in the cord is 150 N, how long will it take a pulse to travf*g,elx0.i4 xn )b)byps c km-el from one support to the other?    s

  A ski gondola is connected to the top of a hill by a steel car/pvoyry9 u1f3f82f h. 7 uisq9k0qlzble of length 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and sends a wave pulse along the cable. It is observed that it took 16 s for the pulseoz97 q3flsf1 82p kyv9r/iq.f0uuhry 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 shie*zizlj(i10b p just below the surface of the sea. He hears the echo of the wave reflected from the oce*z jb0i1(iz lean floor directly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake trpt2f-b s kp9yg :ggc+;avel at different speeds, and this difference helps in locating the earthqg:-y cf;kp2tg9bg+ sp uake “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 zos7uh my8g*,x6 glw+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? [Hint: Set the acceleration a>g] zh,* o86lgyu 7xw gms+   m

  What is the ratio of (a) the intensities, and (b) the amplitudes, of a 2 xn:qxq. xr7n5hzkf5n earthquake P wave passing through the Earth and detected at two points 10 km a5xknh2xnzf q57xq .r:nd 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Eal3 . y1m/wywys;uxy*t rth is measured to be tmxu 1yly*3wwy/.sy; $ 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 samefcs:m 0)vlf 6zab ge1 csczf1w( 72p8y portion of the Earth, but one is carrying twice the energy. What is t)m efzgc1cvf68 :lf1 zy (c27spba sw0he ratio of the amplitudes of the two waves?   

  Two waves traveling alom)g8n,sh( ewh ng a stretched string have the same frequency, but one transports three times the power of the other. (wesgn8) hm h,What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move up and down a total vemo9 kkj;m vbdl2/he (,rtical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. kd2;mm(9hj/k e lvb,o 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) Sketch tkf4(2dw qi f+bhe shape of the stringq(fw +2 ikfd4b 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. What has happened to the energy at this moment?

  If a violin string vibrz8 sp: y .0vabm8:hapgates at 440 Hz as its fundamental frequency, what are the frequencies oaah 0y 88.bz:ppvmg:sf the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what frequency will rc;/ ee7mncj3dq)nf9it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of the string vib)nfe3erq/ nmcj7d 9c ;rates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequency of a x6+;pczdyg5 6cq .nr280 Hz. Name at least three5p;. adcr+g6nxq 6yzc other frequencies at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves o 79gjx/ox 2m)sz4n5gzooob4i n a string is 92m/s If the frequency of standing waves is 475 Hz, how f4/zz sggm5xo b2no9j)o4iox7 ar apart are two adjacent nodes?   m

  If two successive overtones1rbrgz57xjj 5 of a vibrating string are 280 Hz and 350 Hz, what is the fjzbj1x r75rg5 requency of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.jn 2hjjv2(b h ak)ohmmxrmb108a ;rir;.:b 3m6 g. The distance from the bridge to the support post is L = 62cm and the string is under a tension of 520 N. What are the frequencies of th(ja3;ahbj1r 0 ; m8j xor:2ih.)rvm kbh mbmn2e fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz,rgy i2v w3g8)p but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?So ggp8v32 yrw i)the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibratei4.s ;hvg owj0 at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the; 0vhgws i.j4o string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-amplitude mechm6r(4 nea/- pwumx9jo*1yf chh d*a r;uzd 6w2anical 60-Hz vibrator. The string’s mass per unit length is p6 omx4ry(wcwade6ua;* /dr f2 -9 n*uhh1mjz $3.9 \times10^{ -4}$ 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 lefd72relo g 4o mmbu+:;ngth of the string may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.m2ob4 :7odl eurg m;+f080 kg, how many different standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the wateryvc r ojgm0r/*x7 )zxg0ml-h, back and forth in a tub at just the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a*c0o h yxm-vxr/70rm zggl),j 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 bymwi7g-iouy j *y9bn3bg, l8 9oundary within the Earth between two kinloibnwu7yiybg 39- ,g m*8y9jds 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 vef9 *u unpo1-nulocity changes from 2.8 m/s to 2.1 m/s If the incident wave n-o uu1n fu*9pcrests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in1 qaxh*1 b(bhnchkvmog09 y5* warm air when it hits a layer of cold, dense air. If the sound wave hits the cold air (cmvo*hnab*h gyx9 kh511b 0q interface at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave strikes a boundary between tzn /7js*gh*h vwo types of rock at a7*g*hn zhvsj / 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 manu6;eph;,my mw yl/wq 3ial, the w 6yl3qp,wye ;i;m/h mdish has to be pointed 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 travel goo u cc2r6m.dp,sc+(s across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsuco,gc.dc6 upo sm+2 (rnamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness cgdrnyzqlke 3 i5334;fonstant of 550 kN/m Find the maximum compression of the buqz3rndiy353; g lkfe4mper if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps frod1p ol+n+ic7q o1w rm5m a window to a fire net 18 m below, which stretches the net 1.1 m. Assume that the net behaves like c5+wl71 npq o+ir mod1a simple spring, and
(a) calculate how much it would stretch if the same person were lying in it.    m
(b) How much would it stretch if the person jumped from 35 m?    m

  A mass m is gently placed on the end h*ipqv/b hu0fj)07nd b. croe::g me7of a freely hanging spring. The mass then falls 3q/7.0b gu vph:bor e7 hemfc*idn:0)j3 cm before it stops 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. 11–543 t9(*xmnda zv), compressing the spring 5.03dz9xva m*n (t m. (a) What is the spring stiffness constant of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of coffee (diameter 8 cm) at just the rightwju3 w.zh/qc8s+e jo- pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11jw-o w8zc .qj/+h3su e–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the center of a 33-rpm phonograph .p :ifzyd(v wi8ok0gtao +f(/ record have a wavelength of 1.70 mm. What will be the frequeop azt .(i:8df+ k0iovgwfy(/ncy of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t where x is i65;gd6mex4uh;et d ft n meters and t in secone dh4tfeg6; ut;dx56mds. 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 fgp6i2j thh4b 3requency if it accelera46jh2phi bt3gtes at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-k 9w6j/h2gz, br0.y o(6hsffrny1 ruwmg man stands on the raft, it sinks 4.0 cm deeper i2 orf /hhr9 fs zj .0w6b,wrg1umyn(y6nto the water. When he steps off, the raft vibrates for a while.
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a musical instru,ljo9qc ,/ b8ym wjq(t)7; gwd lfpwq4ment are tuned to play at 392 Hz (G) and 440 Hz (Ag )4dtfwqw ,w97 b 8lj;,qpmclojqy/().
(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- 8t(u5os gd+y ey5rnn/ys1zd.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 heavier section of cord or t(try8u5ez g.+ 1nd ns5/ yodsyhe lighter?

  A tuning fork vibrat7n c *grq-uk*qes at a frequency of 264 Hz, and the tip of each prong moves 1.8 mm to either side of center. Calkqqrug -7n *c*culate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simpedfgzks):ud1y ori/(z9j 26ile harmonic motion of frequency 1.5 cycles per second. What is th)o (kye2ird1:/ 6zf9jsiu zgd e 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 edbz10f3 emx.qo /f ;sdnd is attached to a ring that can slide without fr3z1d bdq/ xo 0es;.fmfiction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each one-way swing py*s.yang 6-m6sh:ygs/m,xd takes 1.000 ssmxd*6ahp/6yn yy: s,g.-s mg.
(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 vert5e 9n-18/ ,zftvv omkok1yk8n8ynly yical direction or can swing as a pendulu/ n18zkk8k5fo1vynynyoemy t9v-l ,8m 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 g is stretched under a tension of 255 N. A pu/lf8da fh;g2 ylse i ;galfy/fd82h s generated 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 from a ceiling by a spring with spring stifs ; t x5qo8dh11(hvgrzfness constant k. A penny of mass m is placed on top of the block. Wht sdhxvo(5z;1 qr81g hat is the maximum amplitude of oscillations that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200 f5hrwz 7*s (,c:mw2 mph0ouun-kg car at the junkyard. The steel crane cable is 22 m long an n 7:*u,mh(mw ruf hcwpzs250od has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (which alsou dxj35 ; hyty.o,rm-b 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 springm dux- .o5y,;3tyrhjb , 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