Give some examples of everyday vibrating o cb//a*sjqno2 bjects. Which exhibit SHM, at least approxima/q n2a *o/jcsbtely?

Is the acceleration of a simple harmonic oscillator pzckr6o/4sy/ever zero? If so, where?

Explain why the motion of a piston in an aut:e/b6ts gu wp+omobile engine is approximately simple harutesgw:/b+6p monic.

Real springs have mass. Will the true period and fr qpllwz4y u .4jkh8t,s(+3rr91fzrncv) cg 2hequency be larger or smaller than given by the equations for a mass oscillating on the end of an idealizedhrl )kzh. z8rvrjl43g+cqy92u( t 1wnc4,fsp massless spring? Explain.

How could you double the maximum speed of a simple harmonic oscillator (ji rwthx a 1at6.f1:k5SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scale, and then mjzu/ ro)e- yj*/uq7- x+f etvis released. Describe the scaxujte-/my-)or+7uf*qe vz j/ le reading as a function of time.

If a pendulum clock is accurate at sea level, will/ k-eyyggx:; hi6lql)c9jxn2 it gain or lose time when taken to high altitue6nk/gl qxx) jy;:- lcghiy92de? Why?

A tire swing hanging from a branch reaches nearly to the grt+4; -(i //cl/obfucrdg fla mound (Fig. 11–48). How coul-ff oc(r/gl i+b /utl;4cda m/d you estimate the height of the branch using only a stopwatch?

Why can you make water slosh back and forth in a pan ov)(jxzm8tx 2 mnly if you shake the pan a)xtj8z2 xmm v(t a certain frequency?

Give several everyday exampdp:dbjy c1+ 1w ixon j0m,p 8y7;pfk(iles of resonance.

Is a rattle in a car ever a resonance puh,k38-kp/ myvz o1,4hm e2plghj-duhenomenon? Explain.

Is the frequency of a simple(xvmi 3ohys4:7vk(w v periodic wave equal to the frequency of its source? W v(o: 3kiyw47x (msvhvhy or why not?

Explain the difference between the speed of a transverse wave travelvi7aj ts,i z0 hf4m8l-ing down a cord and the speed of a tiny piece of the v7h8s m4izj al,ift-0cord.

Why do the strings used for the lowest-frequency notes on a piano normally ha -0sy/us/ k tlxviqiu;xz/ ;0ave wire wrapped around thq-;s/kivu0uxxa0li;t/ zy /sem?

What kind of waves do you think will travel down a horizontal metal rod if yh99nvg *m3-dl; aomdn ou strike its end (a) vertically from above and (b) horizontally parallel ; madd *9m3n g-volhn9to its length?

Since the density of a0ec /c*qe + onfwz)vns-k) g)iir decreases with an increase in temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves in air to vary with tevo c)znk )e-einc *s) 0/gw+fqmperature?

Give two reasons why circular wate,tr uw3h( 1hdpr waves decrease in amplitude as they travel away from the sourc1u(hwp3 ,hdrte.

Two linear waves have the same amplitude and speed, andu 3cuu os x9r(a)pjy:9 otherwise are identical, except one has half the wavelength of the other. Which transmits more energy? By whusu p9oxy9r: a3j()u cat factor?

When a sinusoidal wave crosses the b v9)p2 iuq(kvjr3ve -1nrsz4honx 5-zoundary between two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and venho-uekr2)x13q- (4jvpv 59irz vnzslocity do change). Explain why.

If a string is vibrating in three segments, are there anp: )e i7jxv/plz yyn2,y places you could touch it with :/)j y 2p,yzpevx 7nlia knife blade without disturbing the motion?

When a standing wave exists on a string, the vibrations of incident anuk)okwd -/*l(cbz j k7ie z21nd reflected waicl7 ku*jb kden()/ zk1ozw2- ves cancel at the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy wa6h- r,qe sf/x50ae;sfwmk( cj s being transmitted from one place to another, how might we dff5;kwee,cq(-m jxa/ s r0 h6setermine whether the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the total dimi 2 q-qd0ju7estance it travels inq72-qi de0 muj one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from.q;2x - jdi/wu,a/k9h qjixh: p9oang it but is 85 cm long when a weight of 180 N hangs from it. What is the “sprin2owih- :kjx 9g//;au9q.in hxa,pqdjg” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg drjy bbt6tfsh 2-b(h 43e argq77iver gets into the d fq2 a7byt-47j6 ehtbr3s( bhgriver’s seat. If the car goes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fis s6zhtwqeg1 tvs:j(0( h hangs from it. (a) What is the sprin ez10jtqhsgv((w s6 :tg stiffness constant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a frequency of 3.0 Hz when a mass of 0.60 kg0isw p+e s6ws4 is hung from it. What is its frequency if only 0.38 kg w6 sssw4 e+i0phangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. 11–2 at times rd jem dl)/ (lu7j.ge.t = 0,tjl(.rme.jd/ eg7uld) = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 vibratescu 4h6npq 4m..+meet4jqh0r0lpmh q6 predominately with a fh p. 0u. ec4mnh+q4mr4pl jqqme6th 06requency of 4.0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a spring vibrates with aqd60p:xkgmbq2b8z1lli 6 6s x frequency of 0.88 Hz. When an additional 680-l0 kxql68 d x6s z2p1gi:b6mqbg mass is added to m, the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the endq6k rm.rls*14 kx m7zc:d(yrq of a spring vibrates 3.0 times per second with an amplitude of 0.13 m. Determinek q6d 1z7y: 4*cmrmx(srrklq .
(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 e2:u(cw/u7j7d bd 1h 5 ynlkqjof a SHO half the maximum valulh/ 1 75 u: ndjbjewydckq(u72e?$\approx$    A

A mass attached to the end of a spring is strexwo 4 y3b+zg0x9c2z+wk *iyd xtched 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 eg66tw6wfbv m jp(.c 5m. If the spring is stretched an additional 0.130 m and released,.pfe6 6jmv bt5gc6w (w how 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 ar96.srx 8y+v ikc :ywstiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 8 ia:9wy r.srvkc+x6y0.020 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 Nlup r:g iq0w3 -q1s2yc to compress the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. Wir2wcqip -qg3 us1yl:0th what speed will the ball leave the gun?    m/s

  A mass sitting on a horizo3z 4js 2 fdgcxb n0*r7z)cygj,ntal, frictionless surface is attached to one end of a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, the mass experiences a maximum accejy,c zn )0g2cr3bfs47x dzgj* leration 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 = 0.45cos6.5 n7l5exr.rtu,9ut : n cqco;o4t where x is in m,utco trn5o n:75qcu9er.l ;xeters and t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equilic5eg k8 -mw8iwbrium is the energy of a SHO half KE and half PEc5m-w eki8w8g? ±    A

  If one vibration has 7.0 times the energy of a 5m u68fqcv 3jesecond, but their frequencies and masses are the same, mv uq6 8ejc5f3what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light seti 9m) wz.if .y06x;b yn3yuapring once every 0.65i.y tuim;y)ya6enb x f9.z03w 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 parallel ver*o9xo y5eihec/ p4a v(tical springs, each with spring stiffness constant k (Fig. 11–49). What(aio9oe4vh e / 5ypx*c will be the frequency of vibration?

  A 300-g mass vibrates according to the equatiobl.g elsuf)0 2n x = 0.38sin6.5t where x is in mef0llgu )b2 .seters and t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows two examples of SHM, labeled A and B. For each, ww;v koe*j1x( lhat is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on the end of a horizontal sprdd-(3,w 3xcygb8n whcing (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.96m/s D3xcwc-w 3b(ydnd 8h,getermine
(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 w -0id/f6)a1)) mooqn ovm bvwsith an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) with pof/ )dvo1) s0mwimoqo n)-v b6asitive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two springs, with spring stiffness constants siljdsgo(o*w/d ,w3o1+2 s pt $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes a 0.600-kg block attach6i(bscp1(d ua0tij)e+ r f o6s3pey1q b(suz: ed to a fixed horizontal spring whose spr6 qyt)3c(obsfua (bis 6i z 01+r:(d1speuejping stiffness 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 jumpsr2q0k ni 5/ykj from a high bridge. After reaching his lowest point, he oscillates up a0kk/n 52iy rjqnd 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 vib6k8+80orglgipa be / 8tlbrqw,k. vq,rations in exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if0dc q p6vh51k (fr1knk it is to make exactly one swing per second? (That is, one complete vibration takes exact 01k6vhdp5( rn1fkckqly 2.0 s.)    m

  A pendulum has a period z;ie,c4dog 1l of 0.80 s on Earth. What is its period on Mars, where the acceleration of gravity is about 0.37 that onl1;iz 4g,oced Earth?    s

  What is the period of a simpf5f:ri r4u8uj le pendulum 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 pendulum bob has a mv ;*q+.y:njw1jsyw aj ass of 365 grams, and it is rel1yjsnq +;.yj*: vjaw weased 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 pt uh*;vv4cx8m j 1l)wrendulum has a length of 0.9930 m. If the clock loses half1v wl)rc8vj; *4thxum a minute per day, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for t)1x sbo*9c z+jluw4 hqhe maximum 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 8z j7lyhxta+4a frequency of 2.5 Hz. At it is released from resthxzj87 4a +ylt 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 hiswj wxm i+g9: lm4pt9:h anchored boat every 3.0 s. He measures the x9: +w:im9hpj 4lmtgwdistance between two crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travb8i d3jz0 blu(els with a speed of 343 m/s How far apart are the wave crests (compressions)dlz( ib83u0jb ?    m

  (a) AM radio signals n+rp f3pteezoit7 :n9n 1 -2k7tx4zt ihave frequencies between 550 kHz and 1600 kHz (kilohertz) anxtp e37ki7i-+o4ft pe9t z2 tn :nr1znd 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 w0s;/g; jcv no) lx;a3r9pfu ru5-rbapaves in
(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 a x oat:-ct*njz /a,m7ys the other. In which rod will the speed of longitudinalx ttn,a:-cz*a 7oyj/ m waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between twa gr3oat1jxi) q0 3dt-o supports 28 m apart. If the tension in the cord is 150 N, how long will it take a pulse to travel from one support d) x ar3- tg01ja3itqoto the other?    s

  A ski gondola is connected to thec(cqu qguf9mp qd. -ee9 ::1puyoj d-1 top of a hill by a steel cable of length 620 m and diameter 1.5 cm. As the gondola comedej. y-:1ucm( fegqu9oqu- :1dpqc9ps 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 below the surfac 6u+pecgkw4 i 2ni w*wf(:9xfte of the sea. He hears the echo of the wave refxw*+pifnwe gik9 u cw:6( t24flected 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 travy66ovz87 ao49jxsx 0fb)g axnel at different speeds, and this difference )7ynx6a s o9xog0 xfavjzb864 helps in locating 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 approxima* jfuabf* .x0rted by a sinusoidal transverse wave. Assuming a frequency of 0.br0.fxa **ju f50 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]    m

  What is the ratio of (a) the intensities, and (b) the amplitudes, of an ezv1f; kh qn;8cyy,.xparthquake P wave passing through the Earth and detected at two points 10 km and 20 km from the source?(avh8q x.p1fcn,y zk;y; )    (b)   

  The intensity of an earthquake wave passing through the Earth is measured tosplyyc)e i ,mu9fkt2;.r 7 fh; be sy;rm7fyh9e).cl 2ftu;k ip ,$ 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 k/nym; 8,.s m knwgfg0pv+w g.the same frequency travel through the same portion of the Earth, but one is carrying twice the energy. What is the ratio of the amplitudes m;/0 gk n f+..wknywmvgg, p8sof the two waves?   

  Two waves traveling along a stretched string have the same frequ0 ,n3myfby)xu3 qw)bnency, but one transports three times the power of the other. What is the)y 3y3 ,bbxqfmnw0 nu) ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is obsfjr3k)+g1qu sv6 -jf merved to move up and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passesfkj6vqg-ufr m1) s+j3. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 1r)r+2lco ghk ,1–52 are moving toward each other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the str+h2c)l r grk,oing 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 fundamf ;dkb05r0bi gn(+r+ t x(waizj7q :dfental frequency, what are the frequencies of thef b0f( kd 0i(; bgr7j+nd+5azt r:xiwq 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 it vi l0ixel;i 1ikmff i:9)brate if it is fingered one-third of the way down from the end? (That is, only two-th:0i;le 9)x lfimki1fiirds of the string vibrates as a standing wave.)    Hz

  A particular string reso;cv ;t4ppph82gumv) l7 6dobvnates in four loops at a frequency of 280 Hz. Name at least three other frequenvp)ho 7lc dp;8tbvmp;6gu 4 v2cies at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the frequency of standing wavete29is4/r7 pqa+qs y xs is 49isq7/y2 qsre4at+ x p75 Hz, how far apart are two adjacent nodes?   m

  If two successive overtones of a vibratingw t1co3y*imvv q1i(l) string are 280 Hz and 350 Hz, what is the frequency of the fun vi(qc1i)ty1wvlom 3 *damental?    Hz

  A guitar string is 90 cm long and has cirj o riy2 0tdq34(,1o*llo qr4 ypyz/s2.e aa mass of 3.6 g. The distance from the bridge to the support post is L = 62cm and the string is under a tension of 520 N. What are the freque0j21src*qri yo pl.2 aoo(ly3r,yzte i/q 44dncies of the fundamental and first two overtones?    Hz

  A particular guitar string is sy9oukjj, eg 86upposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed 9ojkeg, yu8j6 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, bu;x8 kp) /x)go ecym8jtt it is measured to vibrate at 205 Hz. By k/ )xyx)cp 8m eg8o;jtwhat percent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is r5 *zeq)z3 hprattached to a small-amplitude mechanical 60-Hzz*z5hpe r )3rq vibrator. The string’s mass per unit length is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of the string kby*5n hw0p ve i6 /avqijwl h2h4+a22ha 04samay be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying L between 1y5wha4kvw*s a020ahi n4 pqvb a22+ l 6j/hihe0 cm and 1.5 m?   

  When you slosh the wa (-8p aiy9l+ihlbqp (pter 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 topipyba8 q( li(p-+ hl9 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 witwv 7n46y,h g*odb 2 2r lrj,o.zg-re6km u+ibihin the Earth between two kinds of material. If it approa. n*evkow6lo4 r,u -bmig zbr7d+hir2 6jy2, gches 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 “sheldkb vhl.k5 8v)r .my0dm ibno5vv5m 1,f” where the velocity changes from 2.8 m/s to 2.1 m/yrvm5k1v bd)i.,5dmvh 8mn0ko b5 .lvs If the incident wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is trave wgfzw oi4flnu*.:dll*q2, i, ling in warm air when it hits a layer of cold, dense air. If the sound wave : 2ui,d no4flqlwf *,.il*wgz hits the cold air interface at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave strikes a boundary between two types of rock at aw3yf0. x6cc hqqrj 45w jyw 03chx.r65qwqc4 f38 $^{\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 manua-rm(4d0jgls/ezm js 7l, the dish has to be pointed in the direction of the satellitmrs4dj/ z-m(l ge 0s7je, 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 *a kdu el-2)gyq8ztihy9 3 nu+km and velocity 750 km/h travels 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 tsunamis, some of them attracted to thn ia *)u28+u9tlzg-3ykd qeyh e shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring sne.6u7hfgfojuop 7 lkk w;ht*2 5ds44tiffness 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 enerhtf2uu4;sn6 kg wd4fo77lh. kpeoj5 *gy.]    m

  A 65-kg person jumps from a6np)9 b8i. gzrf .qhd n:xj9mq window to a fire net 18 m below, which stretches the net 1.1 m. Assume that the net behaves like a simple spq.9xhqjd .g b9)mzpf6rni8n:ring, 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 hangj 79ihrb7 -+rolk8tcv ing spring. The mass then falls 33 cm before it stops and begins to rise. What is the frequency of the oscillation?thk-7brvrc9iol +j78    Hz

  A 950-kg car strikes a huge spring at a speev ukf9/1m/kq:w, l *okuw1:iwb zk3akd of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the sprinko w kkz:11w9v:/kuuiw*m blq k,3/afg 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 (di + 97xwg ronwr.2upmn ++fyk;vameter 8 cm) at just the right pace of about 1 step per second, tum +pr2+k ;gf+w 7wxyrn9.nv ohe coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the center of a 33-rpm phonovnoax x7r54p1 :dk m7dgraph record have a wavelength of 1.70 mm. What will be the frequency of the souno77x1: x mp r5kdvn4dad emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t where x j 1/ r*zt,4ym,d-x4uftl osmhis in meters and t in seconds. Determinejfotz*4,lh-dmx,my1 r u/ s 4t
(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 it acceh rkqv8 )q;vn0s+,7 qqwusgr-lerates at 0.50g (a) upward, vrnq)gssk8h v;, q 0q7ruqw-+   f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a /qa)nxep :5fk75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the qfenxa: 5)k/p 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 inuburh)+. 5 ioviu8)wfstrument are tuned to play at 392 Hz (G) and 440 Hz (A)i 5)+uu 8oifvr h)bwu..
(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 coc q-cx,i)oh e6rd 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 freque ehci6qo)c- x,ncy is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the tip of each pron( wu u-i7xg-sng moves 1.8 mm to either suwxs u-i7( gn-ide of center. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simple harmonic moti;tb ,zrxv))f von of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of tv tv))fzx;br, he board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that end is attached to a rin ; re9duo;*(h 4t+ uwplqdj0aag that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the ur0ahd9;+(eoqj* tlu 4p awd;resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 spl-sv sqq01.t — each one-way swing takes 1.000 s- t1 qv.pqs0ls.
(a) What is the length of a seconds pendulum in Austin, Texas, where $g=9.793\mathrm{m/s}^{2}$    m
(b) If the pendulum is moved to Paris, where $g=9.809\mathrm{m/s}^{2}$ by how many millimeters must we lengthen the pendulum?    mm
(c) What would be the length of a seconds pendulum on the Moon, where $g=1.62\mathrm{m/s}^{2}$    m

A mass hanging from a spring can oscillate in the vertical direction or can4zig9h.jwa 5b swing as a pendulum of small amplitude, but not both at the same time. Which one is lon iw9a .5jgzhb4ger, 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 stretzfq z.a+jn/cm55jb a1ched under a tension of 255 N. A pulse is generated at one endz/5qzb.jaj5nf+ c 1am, 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 withnnyt9okwhp*d8/ lfjc:;x c 0d8 vm9+k spring stiffness cokj:yn 9cmpc/ *dl8+ f90w;k8 oxdvhn tnstant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillations that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-f qnd;.4 kjp,hkg car at the junkyard. The steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts thj;k,.npq f 4dhe 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 sho 4ajx f*gxlx.k34h.gr cc bc--wn in Fig. 11–58 (which also gives the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of lk xx4.rfchxgg-*.b4 j- 3acc 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