Give some examples of everyday vibrating objects.1 )ihdvoms.gmpnr 9s1b.et1 t oh25n. Which exhibit SHM, at least approximat.hmpd1evnbs1m)t sn.1g9h 5oor . 2 tiely?

Is the acceleration of a sih/bf ; (wxfm z w l8 f+lek-iw,f;fn/:do:ty0wmple harmonic oscillator ever zero? If so, where?

Explain why the motion of a piston in an automobile engine is approximate,k,.bqii) c pu /h hk95q.(pq oc-xlunly simple harmoni 5.k kcqlbpuio qqcuiph,-.h/x )9,n(c.

Real springs have mass. Will the true period and frequency f* 09z ipl, wg2-xixqgbe larger or smaller than given i*,0i2w glf xxzpg9-qby the equations for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double th.6ys67ut 0zormdwfq 3:;l nkd e maximum speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scals 5ncoo e7ur.:e, and then is releasede5 7 .:cusonro. Describe the scale reading as a function of time.

If a pendulum clock is accurate at sea level, will it gain or los d izhd5r0a9hrr/0hu5e time when taken t0d zda9/5uhrh5r0r hio high altitude? Why?

A tire swing hanging ga 6 /frng3r/afrom a branch reaches nearly to the ground (Fig. 11–48). How could you estimate the height of the branchrga/ 3/agfnr 6 using only a stopwatch?

Why can you make water slosh back and forth in a pan only if you shake the panbacnxwm z4b9-f+p :mon 4jr2. at a certain frequexb mo .f-rzmnc 9aj b24pw:n4+ncy?

Give several everydayms ir,,sm b(q1gq g;c-8j3 lqf examples of resonance.

Is a rattle in a car ever a resonanca i+p95rb*ycre phenomenon? Explain.

Is the frequency of a simple pe*j,uu7ou qjv oq(m q58riodic wave equal to the frequency of its source? Why or whyou,j* (q q7uq5juv8 om not?

Explain the difference between the speed of a transverse wave traveta;e,pbuq 8z;8 lpl-m ling down a cord and the speepp8- e qbza8;,l;lmtud of a tiny piece of the cord.

Why do the strings used for the lowest-frequency notes on a pi)s1 qs- 92 nogo7ezhviano normally have wire wrapiqo9sz1-s2vo7neh )g ped around them?

What kind of waves do you think will travel down a horizontal metal rod +zibwd/ owi4z e8 (r.tji5)snif you strike i8+ds 5)/iwojbnt(ziz4wre . its end (a) vertically from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase tmh /:zm;h, zt0.rt2bim)apl in temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the zr):m,z0ta.pi2h lmt m /;bhtspeed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decreab4x txsp4:16ydfmc3 tse in amplitude as they travel away from sfy143bxxc4 tptd :m6the source.

Two linear waves have the same amplitude and speed, and otic).ubr3j i5w:mmzd mxy-, + dherwise are identical, except one has half the wavelength of the :ydb d-mw, z3xc m+5r)ju.iim other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the bo(5wz fxr.d,. za9wjya undary between two sections of cord as in Fig. 11–33, the frzr(j,y a.f5zwdwa.x9equency does not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there any places you could todfu7b7(f /yziuch it with a knife blade without disydi/(fbf u 77zturbing the motion?

When a standing wave exists on a string, the vimf v8p0 x.2gptbrations of incident and reflected waves cancel at the nodes. Does this mean that energy was destroyed? Epx08 .gt2vm fpxplain.

If we knew that energy was bein 1(t qu,n7+i/l*dsd mjr6n rerg transmitted from one place to another, how might we determine whether the energy was being carried by paru/*qr (ed,nst6l mdir17 +rjn ticles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the t l5y.-,am8q.ki s eaelu;x3gtg36 tuj otal distance it travels in one peri; l3 xatj.glqu 5 tskmu8,. -aieeg63yod?    m

  An elastic cord is 65 cm long when amdp 0 ( o0pb o-9x t.2wrfayld-czg+c( weight of 75 N hangs from it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” constantpm2(y0 (.-oflgo- wzcdxt rc+pd9a b0 k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg driver gets into the.w-s , .qely1 bwpw gd10)gjsg driver’s seat. If the car goes overew qd1,g- sj0). .gb lswgy1wp a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs from it. (a) Whatui .z xo9t7uvr/l- -os is the spring stiffnes o-7i t vxoru9-z/lus.s 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 kg is h gt3y4tlcqk (u3q;ws 1ung from it. What is its frequency if only 0.3 kw3(1yu3st;gq4cltq 8 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. 11–2 at:h* t.dcyi 1jm times t = 0: mi dj*1cthy.,t = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

  A small fly of mass 0.25 g is caught in a spider’s web. The web vibrates predoxm6q skzp. i 1-d-;kkdminately with a f sx1q.zm;pdd-kk - 6ikrequency of 4.0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a spring vibrates with a frequency of 0.88 nh4;hbvh-kc/ Hz. When an additional 680-g mass is added to m, the frequency is 0.60 Hz. What i-h c/ hnvh4;bks the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per second x co5w; xa4x)q-chob(with an amplitude of -oq5xc b()xwoc;xa h40.13 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 maximum v4 wjqgby9:jix:v 1q r2alue?qj2v w gybrjq49::1x i$\approx$    A

A mass attached to the end of a springj1gkxxpg k 8(9.n;hzt is stretched a distance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretches a vertical spring 0.315 m. If the spring is str3 0m2gf4-q evcu:.qve 40 fis- gj)fgl7dmwddetched an additional 0.130 m and released, how long does it take to reach the (new) equilibm0cis)4ejf4.-m0v-dq gf fv 2d:u73gqglde wrium position again?    s

  An object with mass 3.0 ihy3ru jm1u-pzt,b ;/kg is attached to a spring with spring stiffness constant k = 280 N/m and b3yrt-i, 1 u phmj/u;zis 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/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 comprotmob o(g j+81x- t/i0wy(rmbess the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will the b+jmr10bbo(mo o t-8/tw (ygi xall leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to one end y5hb ,)x4euxp 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 h xu4,b5py)xe 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 = 0.45iox14a ( 77asrox 7ftrcos6.4t where x is in meters and t is in secondxt sf1r ( x7ir7a4o7oas. 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 enen+dm)o/ ) cxw0.:ptstv3 osxwrgy of a SHO half KE and half PE? ±3t/:mw. )w tcs0noxodvps)x+    A

  If one vibration has 7.0 times the energy of a second, but their mfj r16a+u *oifrequencies and masses are the same, wha6 uafi+jrm 1o*t is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light sprinxbnw3by63 hid rl9+ 9fg once every 0.65 s.i ydwlf+3bb 9n6xh9r3
(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 twh h 6acf/a wj;-eleo,v+nv7d1 o identical parallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What will be the frequency of vibratinv1 adoae 6/wec v-fjh,+lh; 7on?

  A 300-g mass vibrates according to the8*cn gjozbxv w7y) /o: 1yij6n equation x = 0.38sin6.5t where x is in meters and t is in seconds. Determine jzy1*67yowi8ncn:/g vxjb )o
(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,48 dpz jml4l1xm v0,ig labeled A and B. For each, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on the end of a horizontal spring (k = 124 N/m) idy:jxs z 6o9wks9;kv-s struck by a hamm6:wzkojs yk;xv 9d-9s er, which gives 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 stiffness cons,;11tnsfr cnmdtla u/:9s( wftant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The wsft;1/,sc:rna9t dn1lm u f(mass passes through the equilibrium point (x=0) with positive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two springs, with spring stiffness dq/ i+q 85 (ryyl1dmtzt5 oyo1).iclkconstants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes a 0.600-kg block attached to a eumn8*ii/lp;oi m 7x2fixed horizontal spring whose spring stiffness i *xi lenu 78/i;omm2pconstant 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 jugycs:jr mcf( e /hk315mps from a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate the (ysc :kmce1h f5j3g/rspring stiffness constant and the unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrations in exactly 60 s. What is its q 8;r8/*5qf ak vosnsa(q3ily
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make +4n* h s+9+hjv wotl4d9dxuqcexactly one swing per second? (That is, one cvh+oc x j9wd++s4 tudnl hq49*omplete vibration takes exactly 2.0 s.)    m

  A pendulum has a per4ayosl 2 h tn4)x-yzm-iod of 0.80 s on Earth. What is its period on Mars, where the acceleration of gravity is about 0.37 that on Earth? )-yolt4- mna 2syzh 4x   s

  What is the period of a simple pendulum 80 cm long)k.4 uo: adx/g8bgmsb
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.q::t q (2esgh rgdyy-lq)5(al 760 m, the pendulum bob has a mass of 365 grams, and it is released at an angle of 12.5:y(gqay(r- hl t lqd2eq)sg: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 clo 8luy:1 qery4bck’s pendulum has a length of 0.9930 m. If the clock loses halfy 1blq8ye4:ru a minute per day, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximum speed vbeo,fd+o6s) $v_{max}$ 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 frequ --ab ykcwd:e( 8ir+lyency of 2.5 Hz. At it is released from rest starting at aed( y k:clyria-w8-+ bn 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 t d.e3yh3)zcbehe bow of his anchored boat every 3.0 s. He measures the distance betw3db3e) yzhec .een 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 travels with f*+sb b*wn0fv( tyom-a speed of 343 m/s How f+ syf *o -(nb*bmwvt0far apart are the wave crests (compressions)?    m

  (a) AM radio signals have frequ 9m)r7x;-okxy k ovf 32xk-og28orraiencies between 550 kHz and 1600 kHz (kilohertz) and trav rkkvi -y oo2)mx2k-9xrgo aox3r7f8;el 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 lomdz fm c*0b/x)ngitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elasticp *x8 .dd6b81 qei9z/ tzldjfd modulus, but one is twice as dense as the other. In which rod will the speed of longitudinal waves be greater, and by whadfj/iq d e d.96tldx8z*8zbp 1t factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apart. If the ten klf 9t(z/7smasion in the cord is 150 N, how long will it take a pulse to travel from one supporl(7a tk/s9mf zt to the other?    s

  A ski gondola is connected to th *.as4r b*ogo ndn*r,ee top of a hill by a steel cable 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*e*nnog 4b rds ar,o.* 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 surfap/ (c *8rnrodoop7l)b kb2yu7ce of the sea. He hears the ech2d7p 8)bolo*y kc( orbun/rp7 o of the wave reflected 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 travel at difz,x4o a /o/i) vdca*fjferent speeds, and this difference helps in locating the earthquake “epicenter” (where the disturbance tooocd,/*a oax v4j/i)zfk place).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced surface wave can be approximated by af0gc+h2o geet7m67 *gehfr zo)+z ; cs 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 obf+ hcom)f 0;cegohg7esz t27+ 6rze*gjects 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, yw3 o ui/in48;vr( jhrof an earthquake P wave passing throu 4r;uiw h r/8i3(joynvgh the Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Eartbh,z owmvcle 4 .itpiq13t*t -o. bn8.h is measured to be ,wzeit4bpn o-13t8. .. *cb otlqmvhi $ 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 skz7xvuw2,w* d ame frequency travel through the same portion of the Earth, but one is carrying twice the energy. What is the ratio of the xw2d, *w7vzkuamplitudes of the two waves?   

  Two waves traveling along a stretched string have the same frequencybmodl ;gip 0/:, but one transports three times the power of the other. What is t g:0mlo/p;d ibhe ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move up ando9)0d*6g2yuz xw d7a uvw yes- down a total vertical distance of 6.0 cm, from 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 c sx9 gdy-w0) *wevdo ayu26u7zhange?   

The two pulses shown in Fig. 11–52 are moving toward each other. (a n:ed 5 sq3kh07dzco4recu+chn dc72xkyp;46) 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. Whatsqc44ked+7 5nu20nek 3cp dorh h:z7 x6yc; cd has happened to the energy at this moment?

  If a violin string vibrates,ak- fv 2noz(w at 440 Hz as its fundamental frequency, what are the frko2(va-, wnf zequencies 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 unfingered. At what frequency will if +8e ls7wy y:e,e (bkao-vbb+t vibrate if it is fingered one,+abo7yk ef:esblw bev 8-(+y -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 28xjxwa*9 v*oq2*yu0c1 cpc z :m0 Hz. Name at least three ot2yc10x *q9 *ajvc oz up:mxcw*her frequencies at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves onhi 1r8p) 67q a)sen*gt:r4c/ 9inz7 gxcaiixt a string is 92m/s If the frequency of standing waves is 475 Hz, how far apart are two adja74a)ep xqrzac:n1 87xggihsi)ric* 6n tt i/9cent nodes?   m

  If two successive overtone(a us. ,x0zniss of a vibrating string are 280 Hz and 350 Hz, what is the fre0sx .(, azusniquency of the fundamental?    Hz

  A guitar string is 90 h6orhc rf+g yn8 e,o 7-)qono2cm long and has a 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 frequencies of the fundamental and firs) ooec-gn6 rr oy8q7+o2h hf,nt two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, but it is measured6 sdy8 o5a*mqfu5wp0w;a a e7y to vibrate at 205 Hz. By what percent sho67*wp q5sfmyaa;y5 u8aeod 0w uld the tension in the string be changed to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibra .a v+a5uj7tkx r.n4adj)my89sqw)qs te at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string bexv a )n y.sa57w)qs ju4dt 8.9aj+krmq changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached t8t;7jav mt)rma8jylia6p z +7o a small-amplitude mechanical 60-Hz vibrator. The string’s mass per un z mm 6tatpi)av 87rlj87aj+;yit 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 lengt 9 qwizztj,xq651n+uah of the string may be adjusted by moving the pulley. If tqxw jti6,1 5z+ nuaz9qhe hanging 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 for ok;r.mb n5/kwth in a tub at just the right frequency, the water alternately rises and falls at each enm/k5k rbw; o.nd, 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 the Esm ,qt35zqlgt:fle(3f ;cz : sarth b:3(gf3cqs5t t m :lql;szzfe,etween two kinds of material. If it approaches the boundary at an incident angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “shelf” where the velocity changes from 2.8 0ew4byu(j -; vz)brmsc il)a:m/s to 2.1 m/s If the incidei:bel0;ju (b-ra)zmc )yswv 4nt wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveleqcez i /7ja42ing in warm air when it hits a layer of cold, dense air. If the sound wave hits the coq/a2ic zje4 7eld 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 bounaahn*ivgbn,v a;,xqo):ab 46 dary between two types of rock at av: qhn g ,,vnbio)*xa 64ba;aa 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. riczh81h3i .a /1 nlbuAccording to the user’s manual, the dish has to be pointed in the direction ofciznh8r/l h11. 3bu ia the satellite, but an error of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 250 km and velocity 750 km/h travels acro-bd 3;jrcn3tqh o2dkc -ii5 :nss the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. bjk-2qhic;:n nr5d t d i-3c3oApproximately 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 stiffc/tq,4j+4 cxeua lb. uness 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 conservatileq+b c4u c.4at/x ,juon of energy.]    m

  A 65-kg person jumps from a window0)kgk* +b)mw78qb lji)oh-bd0zm sfc to a fire net 18 m below, which stretches the net 1.1 m. Assume that +qos l jiz8mbm k *-wkhcbg0)d )f7)b0the 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 the end of a freely hanging spring. The maf-j 37 eu ommi5 (npbt:ykb9b:ss then falls 33 cm before it stops and begins to rise. What is the frequ75mmifj9 (k-bn y :etuob3:bp ency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 11–54), comprli/04zfy;h:cr pwp(r9 dn ao7( b*dtkessing the spring 5.0 m. (a) What is the spring stiffness ldnzk c0bdp7 9haro;(4*f (w it/ :rpyconstant 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 r3yk np .ue1b e(z.f7ymv,v:z vk3brx9ight 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 speed of wavy ek(ynr. 7 3zv1 pez9ub,x.3k mvfb:ves in the coffee.    cm/s

  The ripples in a certain grow( - :xfewzz,nove 10.8 cm from the center of a 33-rpm phonograph record have a wavxe(:zfwzw-n ,elength of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.n7pwe6ib)o j oxt- .o.40t where x is in meters and t in seconds.n j x7bw.6io-e) opt.o 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 itsh r+0v8sg1 leb frequency if it accelerat 1 re8hgs0lvb+es at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on the9 ga-cys2bkf6 raft, it sinks 4.0 cm deeper into the water. When he steps off, the raft vibrates for a kc9yg6s fa2-bwhile.
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a musical instrument are tuned to play at 392 Hz (G) and qn) nvuu;9gee u3s/p4440 Hz (A)3 nu )e/q upgv;4se9nu.
(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-0eisduw b5 evw7y-2nyymf1gt;.r5 2xpart cord of Fig. 11–33. Determif.igy e7 eyrd2ws;0mxvtu1w-bn 52 y5ne 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 the lighter?

  A tuning fork vibrates owz ;dg;uo53o 6v)2;hsr zs4n)bl8 of bu0tmeat a frequency of 264 Hz, and the tip of each prong moves 1.8 mm to either s); 5onf tmo82b s0zhdoogu usr;v)e4 w3blz6;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 motion of frequency 1.5 cyclevg gwqlp ;fni580+u 6 lcb+:xes per second85w cnql;+ 6p0blegv:+i fgxu. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” e1plo:/q;uhxe p2yz rfhwl(6-nd if that end is attached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a stri/;u(e rpw2 hfy:-h1xlp 6lq ozng with one end fixed and the other free.

  A “seconds” pendulum has a perd::8x9cg8 tumt u itl-iod of exactly 2.000 s — each one-way swing takes 1.000 s.-: u8 m:t8uxtg9c dlti
(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 sp sx8k ec7(du6+ afx0xwring can oscillate in the vertical direction or can swing as a pendulum of small amplitude, but not both at the same time. Which one s(k x6c xxe7+dfua08wis 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 stre(p; ar,: pen+7quzc kdtched under a tension of 255 N. A pulse is generated at one end, and 20.0 mecz p+;dapnrk(7 :,qus 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 sprjagpsg f+.2 c :zd3ced+ai7: ;uv+ nxhing stiffness constant ksigv+2a+eh ufj 3 +dcx.pgca:z: dn7;. 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-kg car at the jt1 f m1 o7uchh*p44cb+gayr 7zunkyard. The steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. What is the period of the bouncing? [Hint: Refer to Tabc7t17cyg+1hb uza4*pf4h m orle 9–1.]    s

  A block of jello rests on a plate as sh34 r/ e jg/cu6iobsra7own in Fig. 11–58 (which also gives the dimensions of the block). You 7ue4rj/s3icb /ora6 g push it sideways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this vibration, given that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz