Give some examples of everyday vmg9fqvgm j8/ 9ibrating objects. Which exhibit SHM, at least approximatelyqv8m9mf9 jg/g?

Is the acceleration of a simple harmonic oscillator ever zero?j3 -gw i7buyzwio 9,x8 If so, where?

Explain why the motion ,qtuzq kl7ofq2 ;n 3-lb 1:aaivjof1 -of a piston in an automobile engine is approximately simple q,j ;q v n 7qo1u-bzt-a3fkli:ao fl21harmonic.

Real springs have mass. Will the true period and frequency be larger or e*:lgx/w 1wj39x zv easmaller than given by the equations for a mass oscillating on the xelj* 1g xvz e9:w/a3wend of an idealized massless spring? Explain.

How could you double the maximum speed of a simple harmonic oscia4uihf5nwu n lwb0 7)1gl430pbxm (frllator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scale,vp2 g3scch l:7 and then is released. Describe the scale reading as a fun :hsgcp7c 32vlction of time.

If a pendulum clock is accurate at sv/lyyf )kb;x3 *:p 01;fpcjkz m phdd)ea level, will it gain or lose time when takehc:pdd f 0fxkpv1/ ;* kj y;mz3ly))bpn to high altitude? Why?

A tire swing hanging from a branch reaches nearly to the groupg nc sxpk7mb7;8f4aa:6c/ zj nd (Fig. 11–48). How bma jnx6 gp8 7zpccf4a:;s/7kcould you estimate the height of the branch using only a stopwatch?

Why can you make water slosh back and forth in*7 vuk6cw(9kpgs9o azti*/ dhkecth q /tp-34 a pan only if you shake the pan at a certain freque6i/k9qoc v*atdt/su phw(9g 7kk-h 4c3tzpe *ncy?

Give several everyday ex lv4pr.5vcx.oamples of resonance.

Is a rattle in a car ever a resonance phenomenon? Ex*jxuc j fu-s55plain.

Is the frequency of a simple periodic wave equ3 vpueixqlf:7; ;hbs: al to the frequency of its source?i;v ;el:fxbh qs:37up Why or why not?

Explain the difference between the speed of a transverse wave trx( /1k8cl(huy*xm a/nfyd 7vwrv/ mx1aveling down a cord and the speed of a tiny piece of y*(xf/ vlnxrhckd7 a(/ymxwu1m /81v the cord.

Why do the strings used for the lowest-frequency notes on a piano normally g8; mcgzstayx(j62m +have wire wrapped a8g; s6t2jc z+y mmg(xaround them?

What kind of waves do yoti /3pm0ts;gg u think will travel down a horizontal metal rod if you strike its end (a) vertically from above and (b) horizontally pag/mtt p0is g;3rallel to its length?

Since the density of air decreases with an4 ed nh+q7k4pdf5mqasy3l-gl+ e8 /zy 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 l 3/eepay4df g8q zmlq+y4hkd 75s+n-temperature?

Give two reasons why circular water waves decrease in amplitude as they travelx8i-fxavy2+e (p 60aitr7w gp +3reiy away frteai pi( a 83y xe7fyxwi20grr ++p-6vom the source.

Two linear waves have the same amplitude and speed, and otherwise are i1tl06 l - 2dbh0r)zabaad+awbdentical, except one20 albhbd1- l ta+rd0z a)6baw has half the wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary betwmlu 20f:1duf x0 lhs0aeen two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocity do change). ulf 0adum 0:hxs 0l12fExplain why.

If a string is vibrating in three segments, are there an-s0zwp :u; lsjy places you could touch lsj 0:sz;p-wu it with a knife blade without disturbing the motion?

When a standing wave exists on a string, the vibrations of incir x02bjy)3z zqdent and reflected waves cancel at thezq3)2xryz jb0 nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one 85) g+9bkjiag hq:6ykn rcw*aplace to another, how might we determine whether the j9w8r:+g a kycbig)56 ankh*qenergy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is thej*k;xwqysfb f uh0;17 total distance it travelss q; 0jfuwb ykhf7x*1; in one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it but is 85 le,i kua nis g j8gs/0-(nyx2*cm long when a weight of 180 N hangs from it. What is the “ng/8uija,s(g l-02yines kx* spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm whea0z8dcfa q42a7g4kdce3 + yrin its 68-kg driver gets into the driver’s seat. If the car goes over a bump, what will be the frequeg7qi04f24a d+ r3kecaa8zdc yncy of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs from u 6cix0-b ce9kit. (a) What is the spr 60ucckexbi9-ing 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 wi0ucpfpn uq; vl b6t651th a frequency of 3.0 Hz when a mass of 0.60 kg is hung frub;f6vp 0tl cp 1q56nuom it. What is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the posi)jr ox lax6v ()9t:zaztion x of the mass in Fig. 11–2 at times t = 0,t =va z(rzt )) jao:9l6xx $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 predomj)chyf e/xv+a-)yajfq7;/ ft w6 6xctw5)fl jinately with a frequency of 4.0 6xv f ff x)j5yfjca ly)qe//c h)7-wt6;jtwa+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 spra2t hxvo,0pm .ing vibrates with a frequency of 0.88 Hz. When an addivxop,ah. t2m0tional 680-g 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 end of a spring vibrates 3.0 times per second wu6d qurept 6vnpmqhf4i70mll(/ ++5l ith an amplitude of 0tf vp5 76p(mi+nh 6qumqll/ r0l+4edu.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 equ ud+n0i7xh r 5++on ulqisf-:zilibrium is the speed of a SHO half the maximum value?l r+uhd + +x0iqiszo:n5u-f7 n$\approx$    A

A mass attached to the end of a spring is stretched a distancev q xfvs*ci099.c2dbb $x_0$ 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 verti2hnwx;b h.znlzuo4jz 8nl0)1cal spring 0.315 m. If the spring is stretched an additional 0.130 m and released, how long does it take to reach the (new) equilibrium positl8j1u.h2 bz zlnzn4hnxw0);o ion again?    s

  An object with mass 3.0 kg is attached to a spring with spring stiffness constan 96jl7xczl z- rgy-na;t k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is mljr7 9azlygnx6- zc; -oving 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 comprrysmlc,5. v* o8 llhr3ess the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will the bm,*svy5 c.rrllo 38hlall leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attw g mzi u-l- oxr6n932u7eihf.hg8+ytached to one end of a spring; the other end is fixed to a wall. 3.0 J of work is y9u-m8 .nxog-h et izrflg 276+wiuh3 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 is in cpzq )8 8qhk7(zm9lma meters and t is in seconds. Determinec(9 8mz8 lmqap)qh z7k
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equilibrium is the energy of a SHO half-an8 3 blk1nkn KE and half PE? bl k-n8k31ann ±    A

  If one vibration has 7.0 times the energy of a se)qj7pb4i ,0caspr/ d rcond, but their frequencies and masses arrsaq/r0j7b)cd 4pi ,p e the same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light spring on6w( db (-qsyedce every 0.65 s -(e6wyd( qsbd.
(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 identi9m8frl0d2n:tev 2 495a u,p pwgpts z6i8qmhqcal parallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What8g m6rs,u2vai:pd f hwpnz80 9q95 tmet4l2pq will be the frequency of vibration?

  A 300-g mass vibrates according to the st 5ydrybdk(p512jj m 1k,s9 z/jmi+g equation x = 0.38sin6.5t where x is in meters and t is in sm +sd dj/s z1 k jrt29ij(1mygyp5k,b5econds. 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 e5o.ggi )0o qqlla,gf) xamples of SHM, 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 sl0 j(87juacsN/m) is struck by a hammer, which ga(jsuj7 cs0l 8ives 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 constant 305 N/m vibrates with+ 4;mftr yx +nf53efxj an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium py+3;m tff+4jrx5fe xnoint (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 spv)1mxf6va bzssp)(1h rings, 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 a 0.600-kg block attached to a fixed horizontalatn 97,i+bhw a(gi*za spring whose spring stiffness c+bg aiiazw nah7( t*9,onstant 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 bridge. After reac cxy5*pp2pz x*yk1:d dhing 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 m5x x:yzkpd* dy2 *c1pp 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 vibral d+iexrl5 x29acbnpz k0 y8fj :9hiza/+a78etions in exactly 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 one swing per secondvo 9jq:jvqabx2h r g )poud-3ig g74(/? (That is, one complete vibration takes exactly 2.0 s.)(2qrp uvx3gi )jo7q bg gav4h-:djo9/    m

  A pendulum has a period of 0.80 s on Earth. What is its y(lhjrp10tv an0d 8oqdh7c c)6ws3 j(period on Mars, where the accele0)tarocw8hq6lj(n d3sp1 d0y jc7vh ( ration of gravity is about 0.37 that on Earth?    s

  What is the period of a simple penduluc:qu(z g-i p4mm 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 mass of +w g7 bpcs,nw+365 grams, 7 cwns +w,+bgpand it is released at an angle of 12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’z5nag/hh)wuq34 dm y2s pendulum has a length of 0.9930 m. If the clock loses half a minute per day, how should you adjust the length of the g 5ndqh/hyu 3m)w42zapendulum? shortened by    mm.

Derive a formula for the maximum sp,n/lv nqxmrju 4l.l5,eed $v_{max}$ 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 frequenc+v,e8v 6zdfo wv+ci8fy of 2.5 Hz. At it is released from rest starting at an angle of wfvf,v c6 ideovz+ +8815 $^{\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 hisur f nz2c4t7,c anchored boat every 3.0 s. He measures the distance between two crests to be 6.5 c4ft,n27c rzu m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with a speed ohxm (7sjc7,k ff 343 m/s How far apart are the wave crests ( sm7fxck7j(h,compressions)?    m

  (a) AM radio signals have frequencieskky9 9dfgv5f,3f- xgn:vs -cz between 550 kHz and 1600 kHz (kilohertz) and travel withvfcs:9fk,vgk -xyg fn9-z 53d 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 long8v-s8cr kc1 s ,ssjs+pv 8ey9nitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic moduluujr/.4p/(t kaq0c g1a)wcz jw s, but one is twice as dense as the other. In which rod will the speed of longitudinal waves be greater, and by what factorjwaa0u/ / c(4pgc. qztwk)r1j?   

  A cord of mass 0.65 kg is stretch 98stz,piza 9u,m/;qhk f-h vzed between two supports 28 m apart. If the tension in the cord is 150 N, how long will it t;-zpt z/vm8hq k9ufa 9h,s zi,ake a pulse to travel from one support to the other?    s

  A ski gondola is connected to the top of a hill by a steel cable of length 620 m wdhjnwbp 6.d/u:gv7 3a8th9l and diameter 1.5 cm. As the gondola comes to 7h wl:8g vdnwat3bpj /9h.du6the 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 surface of the sea. He hea*dyx:*8gn h oers the echo of the wave reflected fro 8dg y:*en*oxhm 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 differerk(m7cc qmlm2q 1q /h/nt speeds, and this difference helps in locating the earthquake “epicenter” (where t7qlm1/cm /rq2m(qkhche 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 apprqlep / k5itco-f e-2:qoximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequenc lkip5-oeqf2 -t: ce/qies), 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 intey n i7r0lz uc1 l(nvm8z.b,qb1nsities, and (b) the amplitudes, of an earthquake P wave passing through the 7ln ir8m1vb.yu1lzb ,(0z qcn Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthkqe6h fm 2 5nic7gy,w1quake wave passing through the Earth is measured to be ym65i e1,2cq nfhgw k7$ 2\times10^{6 }J/m^2$ at a distance of 48 km from the source.
(a) What was its intensity when it passed a point only 1.0 km from the source?(round to one decimal place)$\approx$    $ \times10^{9 }W/m^2$
(b) At what rate did energy pass through an area of $5m^2$ at 1.0 km?    $ \times10^{10 }W$

  Two earthquake waves of the same frequency travel through the same portiazd*x cm e:/u(on of the Earth, but one is carrying twice the energy. What is them*z:u x/a( ecd ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretchedcy gcf 6os(pt8an s875 string have the same frequency, but one transports three times the power of the ot6 7fs 5psog y88an(ccther. 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 tota.vdl 6* y dzk4 yge3s8pe ,r+5m6obfdpl vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the rippl,fl8e 4* kd6y.6e53+v y odbrmpdpz gses 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 eac)vc )ovho d2jcfdo1)2h other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight. What hoh2o)df) 1o cvvcd j2)as happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundamental freqfnk:bl9 d5of;*z 2ihcuency, what are the frequencies of the :2fck5n o;*9zib dfhlfirst 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 willbfec t1: g;h/n it vibrate if itb;nt/fehg 1:c is fingered one-third of the way down from the end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string raid 16kgx)m si+vb: p;esonates in four loops at a frequency of 280 Hz. Name at leaskadxm1)bgi6:p+ s; ivt three other frequencies at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is ayh-rm8orb +892m/s If the frequency of standing waves is 478rym 8a+-orbh 5 Hz, how far apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 350 Hz, whambffs+t9)bu5 ,t0kq ut is the frequenc5umq9b+) sf 0tbu,f kty of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The disqwfg s8 tm:/q)tance from the bridge to the support post/fg:m 8tw)qqs is L = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 20t:wbc p ; ,c*2+wn(rxijag as-0 Hz, but it is measured to vibrate ataw-+b; ,pr gas*tn(2wicj c:x 205 Hz. By what percent should 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 vibrate at 200 Hz, buxylg6zs7 cwz579(fg))gp mw ut it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequencypcgm9)sy(6z5 g7zg luw x)7fw? decreased by    %

  One end of a horizontal string is attached to 0pa3hwksi ykaybk; 89x akaj03m21m; a small-amplitude mechanical 60-Hz vibrator. The string’s masj8;920 ;ak3pa30 yimmak ahx wkb1ksy s 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 mp9r++vdwy:nla3r h .*:longday 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 achielly rvdnn d+ *g9.r::ohp w+a3ved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tur;* eo9ir war05p o,atb 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 standr0 ar5r i,wa op;9t*eoing 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 strikeuu yu, wi c1fc)b3q .yd1dj:y3s a boundary within the Earth between two kinds of material. If it approaches the boundary at an incident an3y b1,:ccfjw3quyud1 ) y.uidgle 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 change2 y tpm(:zwgl1s from 2.8 m/s to 2.1 m/s If the incident wave cr1t zpwg:2yl(mests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in.fw e6ehja7,0tis 6d0os3),ox bp2 /bsbjm wj warm air when it hits a layer of cold, dense air. If the sound wave hits the cold ai0, o.w6tedjbwjbs3 ,s 7 i )fba0xep26ohsmj/r 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 earthquake2gq)z0zno ,ictm p*o1 wave strikes a boundary between two types of rock at a1*zqo)p0g ,miotzn 2c 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;smd3yfa u/13f2mj uq . According to the user’s manual, the d2mmqf;u 3/s3uja d1f yish 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 travelsnng2zk kl(r)4 rk sr.5 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 the shore to see stran2z4 n5 .krkrksrl) g(nded fishes and boats.)    min

  An energy-absorbing car bumper has a spring sc-x*mkw1 chz ghe11g5.+nv xjtiffness constant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg,xcm z.vg5*e1c-h wxhg1j+ n 1k 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 from a window to a fize6g 5xvavh uk 0.oy8*re net 18 m below, which stretches the net 1.1 m. Assume that the net behaves like a simple sprin5e *zx.vy08oga hku 6vg, 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 s5 f0 t6 rke)eo6m2euk voi3.uqpring. The mass then falls 33 cm befue i uom.023 ektrq6k5 o)ev6fore 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/7h dvb1v zxt0- kg.qv5s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffz-q xvdkt v0.51 hvbg7ness 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 jus.,pp yzy 7e qwx*8mp)kt the right pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the to*8m p,yq)yp7.xz wepkp (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10. d4p al5z9jpb:c3yy)v8 cm from the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequencp5 4jy)c:3azp v lbdy9y of the sound emitted?    Hz

  A 2.00-kg mass vibrates accordi3,qi iy7kv8 ot ewarhc1. ,)ning to the equation x=0.650cos7.40t where x is in metyohkri1nwi t,8a, 7i3 .)evq cers and t in seconds. Determine
(a) the amplitude,    m
(b) the frequency,(round to two decimal place)$\approx$    Hz
(c) the total energy,(round to one decimal place)$\approx$    J
(d) the kinetic energy and potential energy when x=0.260 m.(round to one decimal place) PE$\approx$    J KE =    J

  A simple pendulum oscillates with frequency f. What is its frequency if henk t/ *vuds ju2a6bv2x*6z4it accelerates at 0.50g (a) upwautv6 ekxju*6 /4vn 2ahbz d2s*rd,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg (njewlj.o7jux )2k7 lman stands on the raft, it sinks 4.0 cm deeper into the wate)enx jku j.(72low lj7r. 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 instrument are tuned to play at 392 1byrj,lwt d5ae0tj ) 9Hz (G) and 440 Hz (A)y dtr,0le)jt5j 1a w9b.
(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-pxxo j5,gz (9joart 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 ,xgjz59 oox(j 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 vibrates6dlhj.f3z d3yb7+ecq at a frequency of 264 Hz, and the tip of each prong moves 1.8 mm tc3bl3 dfde.67+jy z hqo either side 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 simpleih edkqo3,2,arqc. 9x harmonic motion of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the3a ei9,rqxh,c.q d k2o board during the oscillation?

A string can have a “free” end if that end is attached to a ring that can o qqt ;)u8bll 9hgj7*eslide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the restl q)j l8o *;h9bu7egqonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exacg : tswg.,n vqf/ hyn dj:rog(u:-0.motly 2.000 s — each one-way swing takes 1.f gg(r:.uqt.vgyo-,/wnd: o:j0h m n s000 s.
(a) What is the length of a seconds pendulum in Austin, Texas, where $g=9.793\mathrm{m/s}^{2}$    m
(b) If the pendulum is moved to Paris, where $g=9.809\mathrm{m/s}^{2}$ by how many millimeters must we lengthen the pendulum?    mm
(c) What would be the length of a seconds pendulum on the Moon, where $g=1.62\mathrm{m/s}^{2}$    m

A mass hanging from a ,c w9 8htfad*1 ouqd24n4dcvuspring can oscillate in the vertical direction or can swing as a pendulum of small2t4uh8*9dq,aonc4cu f 1d vdw 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 unde5-sn h9 oi(l9c*vv3x siq821sfynv lhr a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulsxyiv nv-h*3 9i2(f8 1h5sonslvlc9qse is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is sus8dlkyd, k4r lg +t 3;u og75qu3jw7uzbpended from a ceiling by a spring with spring stiffness constant k. A pezo+rlwbkg 7g d4 u d3ku7jyt3,5l;u8qnny 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 jx owszp;n3u9.m5.jm 6f x+hj junkyard. 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 Tabl jxj f6psuow.nxj+ ;9.3 z5mhme 9–1.]    s

  A block of jello rests on a plate as shown in Fiuuy2q)o- zf uf m*n)g;g. 11–58 (which also gives the dimensions of the block). You pf;*muzo- q2fuuy gn) )ush 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