Give some examples of evet))0v,l m3 c c2dwl9v su;ygxrryday vibrating objects. Which exhibit SHM, at least approxim30st9vccr l2 ;u)d wvxgm ,)lyately?

Is the acceleration of a simple harmonic oscillatoz/xy(;j/ocq ;0mj pvtr ever zero? If so, where?

Explain why the motion of a piston in an automobile engine is approximately sir;xv17z8ea2wmmcox- pv/ iu (mple h m oa/e(7xz1r;m vc2uv8-xi wparmonic.

Real springs have mass. t:vepx e )sm ;fq6thh.o ;fn7;Will the true period and frequency be larger or smaller than given by the equations for a masse;f;veo6;t.x:n qthf7 )hmps oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed o+q rbs 2c7;xvbf a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scale, and theka649qse ipkddba+s;:h d;: cn is released. Describe the scale reading as a c9bddad4;s; p kah6 i k+esq::function of time.

If a pendulum clock is accura/l.2)m5/yvzd-b ubqijfes2o te at sea level, will it gain or lose time when take.es2 y oq//bjvdzl25 u mifb-)n to high altitude? Why?

A tire swing hanging from a branch reachg,en 3, juuxe17rm8ames nearly to the ground (Fig. 11–48). How could you estimate the height of the branch using only a stopw7r3gjm ,xa ,18unm ueeatch?

Why can you make waterl13 +) aatpaou slosh back and forth in a pan only if you shake the pan at a ca aap 1)l+t3uoertain frequency?

Give several everyday examples of resona zig a;gz1r+y**mrqdykt; (4 ance.

Is a rattle in a car ever a resonance phe c2bvkf,eq2e /nomenon? Explain.

Is the frequency of a5q4 ti.aejqg/ za8k5 u.gvzh2 simple periodic wave equal to the frequency of its source? 5j 8 hz.zkti4g/quq 2ea.5gav Why or why not?

Explain the difference between the speed of a trx96h a d ,n8lx6+ybmliansverse wave traveling down a cord and the speed of a tiny 68 x+xah9 ,b6nyldmilpiece of the cord.

Why do the strings used for the lowebve3.dac 3a5a st-frequency notes on a piano normally have a v33 .ae5adbcwire wrapped around them?

What kind of waves do you tlga+ jd/ik,/ chink will travel down a horizontal metal rod if you strike its end (a) verticallyci/ gk ajld/+, from above and (b) horizontally parallel to its length?

Since the density of air decreases witcmd)1w vnm04:tbj6o wh 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 vad:jcm wbmw1tv64) 0 onry with temperature?

Give two reasons why circular water waves decrease incnp;qwx3l;7 (nz pww p6 gu*isf8 d(2r amplitude as they travel away *p((zwnrxc 8 w d7g6 q n2swup3lpi;f;from the source.

Two linear waves have the same amplitude and speed, and otherwi. kj1((efibh ku;aaqcs+ 9l6sxf-:npse are identical, except one has half the wavelength of the other. Which transmits more energy? By wh6s apjs.c1 kfl:x -uh eq+na bif((k;9at factor?

When a sinusoidal wave crosse2gzjo/(owx p nk):ov7s the boundary between two sections of cord as in Fig. 11–33, the frequency/)vgo7j p o 2kno:(wzx does not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there any p*l* pw8 ek;.h8buvod)7kknm places you could touch it with a knif);kbm7pdnl 8 8okh.v*uk* ewp e blade without disturbing the motion?

When a standing wave exists on a string, t 8ek gqv;t-lx-he vibrations of incident and reflected waves cancel at the nodes. Does this mean that energy we8txqklv--; g as destroyed? Explain.

If we knew that energy was bwyzca9pn.9 b/eing transmitted from one place to another, how might we deter/zy.9p9c wa nbmine 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 to mxlpd;820t5-pr lhgr+ ym ec8tal distance it travels-gmtehrxpd5c ;m80yl p 8l2+r in one period?    m

  An elastic cord is 65 cm long when a weight of 75 N han30b ;mw3u -tfm6kgtgegs from it but is 85 cm long when a weight of 180 N hangs from it. What is the “spr gb;fm3w-tem 6u0k3gting” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 64l1(tl5z wme7g,jo yrp;ubboh + 0nd,8-kg driver gets into the driver’s seat. If the car goes over a bump, what will be the frequenc5ywlz1brenoto7d u(, pm g0,l+h ;j4by of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7oet0e*+raj vbk 8,ap56u shzn a3 hg8ps7o :/i-kg fish hangs from it. (a) What is ts8k8/3 anu0v6s*ap hoh, re:5pz ogiatbj+7 ehe spring 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 hf0m dst3+ 5pf3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency f d3t f5sp0h+mif only 0.38 kg hangs from it?    Hz

Construct a Table indicating toux1) aeda4s 1m0uaw4he position x of the mass in Fig. 11–2 at times t = 0,t ua1wd1umoa 4e 04xsa)= $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 inh9,os wfbmf 6/ a spider’s web. The web vibrates predominately with a f9,h/wb6 f smofrequency 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 Hz. Whfacg0 vsdg x6 +r7:g2p6 hao4r4ljic2en an additional 680-g mass is added to mlpgvha4ca2 6i+ rg02cfsj4 xd o7r6:g, 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 sesux5w59u4d0q 4aj p94mrb g encond with an amplitude of 0.13 m. D4b5a4sg9 nw9mj u qdp5reu0x4etermine
(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 hamys (jtm/oq yxa6z2id*.3 cqiao-75 ylf the maximum val5.7 d ys3jqyai*taxi(m czq /2mooy-6 ue?$\approx$    A

A mass attached to the end n+ xafab/wc11 of a spring is stretched a distance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretches a vertical spring 0.3qj8 (7s+kfbi.s2p dib15 m. If the spring is stretched an additional 0.130 m and rd(.q+j bi sfkb2i7ps8eleased, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is atta zjuz,vpzm)3u 7*kg: eched to a spring with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its upj 3 m*,: kgvu)ez7zzequilibrium position, it is moving with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compress the spring of a toy phgx yq)qyxflht-; . 03opgun 0.200 m to “load” a 0.y;h)x hq l3t-f.0 qgyx180-kg ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, fric -r gd5xdmr(a*tionless surface is attached to one end of a spring; the other end is fixed to a wall. 3.0 J of a rg-rxd*m(5d work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, the mass experiences a maximum acceleration of 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates according r r yis . t):etn+kwmeds239 z:vet)*vto the equation x = 0.45cos6.4t where x is in meters and t is in seconds. Determikmv eys2) etiv3e: :.r9wttnd*rs+ ) zne
(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 equilao2e.bz+h4 fcibrium is the energy of a SHO half KE and half PEha+b zo2 fe4c.? ±    A

  If one vibration has 7 woim0y,ob/y4 wa2 b3p.0 times the energy of a second, but their frequencies and masses are m3wy2o0bp4w oa /y i,bthe same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from )pyscofa,4 ;3h 0qq h(2 nsuraa vertically hanging light spring once every 0.65 sh0p4saca( o2qn),u ; qry hs3f.
(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 bykwp. fb/8wjq5 ,hv/e o two identical parallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What will be to, .ev wqf8kwjh/ bp5/he frequency of vibration?

  A 300-g mass vibrates according to the etp lz)x1ju. (p(-p9un j;guvrquation x = 0.38sin6.5t where x is in meters and t is in sgu (xjptnvlpz.; (j)r puu1-9econds. 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 77;g8kw/vjy rlee7ab examples 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 7ai-k p8.vv2 iig5g+8x ixaph a horizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.96m/s Determine ph8 2i-vi .i7vaa8xxpg 5ki g+
(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 with85zocu t(v x12(kmfh f an amplitude of 28.0 cm when 0.260 h8c15(vzm2(uoff tkxkg hangs from it. The mass passes through the equilibrium point (x=0) with positive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to /rzh i*xq:v4etwo springs, with spring stiffness constants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes a 0.600-kg block attached to a fixed horizontag ghs3* x 0gl)b wf2ax3g1ngs9l spring whose spring stiffness constan9 )l3 h201x3g * sgagbxgnwgfst 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 reaching u nbxg.)-my8zw m7gp 1yx(-fyhis 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 spri1xyguf7)y zby x -(8wn mgpm-.ng 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.:ggc) kaomf 8( What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulmp0/os u l8ie+um be if it is to make exactly one swing per second? (That is, one complete vibration takes exactlsl+ 8mpeu 0/oiy 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. Whaycp 50sv+ fz)at is its period on Mars, where the z0cy+ap sfv5)acceleration of gravity is about 0.37 that on Earth?    s

  What is the period of a zso n28;xtahv +*kzq+simple 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 mk:x3 ++x+ml,q )zco0 aupjkwo, the pendulum bob has a mass of 365 grams,++m 3pq +ulk)kj:o0 aco,wxzx and 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’s pendulum has a length of 0.9930 m. If the ghk-o+s(u f/zclock loses half a minute per day, how should you adjust the le(hozf -+/ skgungth of the pendulum? shortened by    mm.

Derive a formula for the maximum x8+0(f+rr q/xgt31 apr xpcmpspeed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at a frequency of 2.5 Hz. Atstp o:g h tk-4 n(/t0ub*hw;fl it is released from rest starting at ann;4pt tsou/f( hbg0-h *tw l:k 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 tx6( lb +w 8+imu:razphzd:;hw .r*rcof his anchored boat every 3.0 s. He measures uxp d8r .mr;hbzwr*++h :6:t aczlw(ithe distance 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 travels with a speed of 3krnoz4 peqx: n/,6ci/ 43 m/s How far apart are the wave crests (compressions)?pe nzk,6q: o4 i/xrnc/    m

  (a) AM radio signals have frequencies between 55t wp/w(rj9pm 20 kHz and 1600 kHz (kilohertz) and travertj(pwm 2 /w9pl 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 longitudinayf/p45gi,xvsbx g) wohr. +v6s5f9val waves 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 -v5vtkd3t bd3 as dense as the other. In which rod will the speed of longitudinal wavesd3bdvt -35tkv be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apart. If the ten3nsx eg 3b8ja*sion in the cord is 150 N, how long will it8 g3sj*xa n3eb take a pulse to travel from one support to the other?    s

  A ski gondola is connected to the top of a hill by a steel cable of liy6ar4(t 3jztength 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 t ja6zit3 ry(4the 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. w6/92z/n dyd x3 kx)a xyk lr:v-7m:hem jt)ycHe hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is the o y:/)x wc7zdn / ae 3mxy:lkvm rx69khj)2tdy-cean at this point?    m

  P and S waves from an ear8wegcl 50vf 6v yyhu672ardx,cvl ;y )8*yet kthquake travel at different speeds, and this difference hc8 6v;0*hyayl ,5fdy8k2 x rvu)e v6yg lwte7celps 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 approximated by 8vj1-diks, 4jeirpb( a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequen41rj-vs,k bepid (j8 icies), 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 ( l d0s3zhrk/wpz ,:)rqb) the amplitudes, of an earthquake P wave passing through the Earth and deteczrdw3q)zr hs 0,k/l p:ted at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through they i1eekan/ y71 Earth is measured to be 7yny1 e 1/akie$ 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 waves11ig( ae ys(lc rnj)4w of the same frequency travel through the same portion of the Earth, but one is carrying twice the energy egr(1)jl snwcay41 (i. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the sameb;otg(8hqgz0u8s coywy8, 4w frequency, but one transports three times the power of the other. What is the ratio of the amplitudes of the tbogwu,t y(8yhz0 8;48ocwgsq wo waves?   

  A bug on the surface of a pond is observed to mo6o(u q ckfvo*.4vtii+ve up and down a total vertical distance of 6.0 cm, from the lowest to to.i*( tivf4ck6vq +o uhe highest point, as a wave passes. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–5orm7:s 6d ep9*q9vumreo (/w+ee/cpg2 are moving toward each other. (a) Sketch the shape of the string at the momp( 9 w9p/ro e7+ uo*/m6sm:creqe evdgent they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundamental frequency, what are thh. qvs/hv37 tze frequencies of the first four harmoni.7vzq3/sthhv cs?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz t pmca*r s *cui(0,oo0when unfingered. At what frequency will it vibrate if it is fi,cuspim0 0 a*t( *ocrongered one-third of the way down from the end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequency of 280 Hz. Name atu5z ziby60pnl6 sykx 22(dv5q least three other freq( dqb56l0sy562xznyupiv k z2 uencies 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 waves iv-f2cuxt9-k+gt-a gc skgu29tx g--+-ftacc v 475 Hz, how far apart are two adjacent nodes?   m

  If two successive overtones of a vibratin ./h3wnftft g.g string are 280 Hz and 350 Hz, what is the fntf.gt3wh. f /requency of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The di1*u)qpx( bk m2ubmyw5stance from the bridge to the support post is L = 62cm and the string is under a tension of 520 N. Whpumkyx wb12 bm(q*5u )at are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string-82g-z k5aonwi)k rfi is supposed to vibrate at 200 Hz, but it is measured to vibraifar8)wzg - nk ok2-i5te at 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 suppose ovib n6s2l23md 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 to correct the 2b6i2l 3svomn frequency? decreased by    %

  One end of a horizontal string is attached to a small-amplitude mecha810jdoguh76qat 0);j (ubvtbn 6s jp pnical 60-Hz vibrator. The string’s ma pgv;6u 0uh0nj(tp6otba1j dqb sj) 87ss 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 may be adjx.+ 9* 1kf aadkbw9-5ez b ,frldon6wxusted 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 10 cm x1abod+ 9aw xf-bzrn5l,e.*96 fkwd kand 1.5 m?   

  When you slosh the water back and forth in a tub at jusz*gsi7/ e)6c 8svv j8erul;pt t the right frequency, the 8vpes8;ls/ j ri)*7e 6 uzvgtcwater alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strik hoks 1:r 1:h:pcsj*x 0mgc:gkes a boundary within the Earth between two kinds of material. If it approaches the o1r*s: x::ghk:pcsm j gc01k hboundary 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 ly)cxaqt;weug;p a0,6ey 6 r+underwater “shelf” where the velocity changes from 2.8 m/s to 2.1 m/s uw0)qat 6e +;lp y6xe,;g acryIf the incident wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air when ehrgp/q 2nak g;gs.e2tq. : k*it hits a layer of cold, dense air. If the sound wave hits the cold air interface at an anglk2.;sqh*t :agkp.e2 er/gq ng e 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 b exp7yt1 c(as. xa+yc ;)drd)boundary between two types of rock at a 3.axyx s1( d+cty ec;7b rd))ap8 $^{\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. Accordin yq -:jabp2yx6-x1y9jtuxln/,tr, osg to the user’s manual, the dish has to be pointed in the direction of the satellite, but an errpxjtat6q-nol ,ry9 bj2yys x ,-:/1ux or 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 acro03ye)cjh wkd* rx9kn 1js-f,s ss 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 stranded fiss9h1*0 kr3ynjxd jkf-wes)c , hes and boats.)    min

  An energy-absorbing car bumper has a spring stiffnesyg l:2 i.vb:-igtvq4y s 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 -i4blg2vqy ytgv::i. energy.]    m

  A 65-kg person jumps from a window to a fire net ) x)lx2spua 8iz kh2 (6;swlaw18 m below, which stretches the net 1.1 m. Assume that the xkpilwaw) s2 l6s)uhx(8;2a z 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 m- hho:qid53)shce 6kya fm; 3pass then falls 33 cm before it stops and begins to rise. What is t3opsc5 ;hyqi6h:khe) af3d- mhe frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of hf.rq5(a6domg .q nir28g qx-22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffnqqa.52gx .dqrrgnhmi- 8of6( ess 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 ow ex545bg,,qf ii8sm ff coffee (diameter 8 cm) at just the right pace of about 1 step per second, the coffee sloshes more and more until eventually it starts tf8me5b iif qxw 5g4s,,o 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 cenkjt/bqb5-zs ( o6 hlbm wn(x+)ter of a 33-rpm phonograph record have a wavelengthk l()bzb/n-t6 (sb m qhx+ojw5 of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equatxgm bf ;2gm1cpd+xs ot9 ok01;ion x=0.650cos7.40t where x is in meters and t in seconds. Determigo;b0mfd+ptm ;xsgx 2 cok191ne
(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 )s7tmueoeen*g00)f9x0jxo n frequency f. What is its frequency if it accelerates at fe )9ujn 70snxmet0e)g*ox0o 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kp9 0xsira 0sb*xqh3g 6g man stands on the raft, it sinks 4.0 cm deeper into the water. Wqa9spxs g*r 0hx i6b03hen 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 Hz (G) and 440 Hxq9 ipvw9,oj7z (A).j, i7qxp9wvo9
(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-par3, ,mumtw/aydo7p e(y)m;l kct cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength gr )cw (mema;k m7,/lt,yoy du3peater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the tip of 9.kkwhu s o pcc34 oc4g3x-*moeach prong moves 1.8 mm u3oxkm 39ok sgo wc4ph4c* .c-to 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 simple harmonic motiz()gzgctu+ hk ss9h;. on of frequency 1.5 cycles per second. What is the maximum amplitude with which the hzk9h (gzuc ts.;)sg+end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that e j989:gjzve 5huuiq 8b9dqo7ynd is attached to a ring that can slide without z8u7yjib:h9ov5g jqe 9 9qu8dfriction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum hasna : v )i(jc;;mkmobs7e *m,iu a period of exactly 2.000 s — each one-way swing takes 1.000 si,;uos a*n:c m;mmkie7b( j) v.
(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 osc /u2o qz8l4 ieviief05illate in the vertical direction or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period of th zeo5e0ivu2i4l f/i8q e vertical oscillations or the period of the horizontal swings, and by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

  A block with mass $M=5.0\mathrm{kg}$ rests on a frictionless table and is attached by a horizontal spring $\begin{pmatrix}k=130\mathrm{N/m}\end{pmatrix}$ to a wall. A second block, of mass $m=1.25\mathrm{kg}$ rests on top of M. The coefficient of static friction between the two blocks is 0.30. What is the maximum possible amplitude of oscillation such that m will not slip off M?    m

  A 10.0-m-long wire of mass 123 g is stretched under a tension of3pj)c k( f+mru* : ez:iqwzr3g 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is gen3pgi + mkc::zz( * uejqrr3f)werated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spring with spring stifa0k7m 3dpnw,p fness constant 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 sa03pwkd np7 m,tay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junky up2ezo 7vc;fpne4l,.ard. 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 bouncin7ou e.vf lc4,2 ;pzpneg? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 9e*0 eww e)fj7hejd+ iov3n jh0b* ul5(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 fre9jiv** o j0h j)e df0lbe7+ehnewu5 3wquency 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