Give some examples of everyday vibrating objects. Whichiz0ls5 pxq 1i0e/0gpw exhibit SHM, at least approximax qzs piw1p00/5l 0egitely?

Is the acceleration of a simple harmonic osg)/1 oep9+ +g ap :mhoaxz/hapcillator ever zero? If so, where?

Explain why the motion of a kg1x aw2-g3j rpiston in an automobile engine is approximately simple harmonk3xgarw2j1 -gic.

Real springs have mass. Will the true period and frequency be larger or 0l *a/i.lxz3*)v1iu vnq vbymsmaller than given by the equations for a mass oscillating on the nl1y l / v.x**bvziq0)3imvauend of an idealized massless spring? Explain.

How could you double the maximum s2u ;;:m ywmjzk1.xosypeed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hoo;a27gaarle hac y:/ -gk of a vertical spring scale, and then is released. Describe th cgaay :raae-lhg;7/ 2e scale reading as a function of time.

If a pendulum clock is accurate at sea level, will mr )9zsyo)x4rv.bvqo dr) 8i4 it gain or lose time when taken to hib)8 mv .oi4vrxz4))dsqo r9yrgh altitude? Why?

A tire swing hanging from a branch reaches nearly to the ground (Fig. 11 cy-fikw7unr8 sg .a6ipx; o(1–48). How could you epkr;su aywci f-x(go.1 8i7 n6stimate the height of the branch using only a stopwatch?

Why can you make water slosh back and forth in a pan only if you shake tizo(35 f1i* 5k mdlyrzhe pan at a certain fi(r3zzky5*i5m 1 lodfrequency?

Give several everyday examplev28u:*yz 7hx)ic bcch s of resonance.

Is a rattle in a car ever a resonance phenomenon? Explai1o7tsu6b1m 7k7zvudk xaf h(-n.

Is the frequency of a simple periodic wave equal to the frequency of it.. 0bchp uven/s source? Whyebhnp .uc.0 /v or why not?

Explain the difference between the speed of a transverse:f;tj6orv;sn8j f 2zh wave traveling down a cord and the spnojfj; t82sr;v 6zhf:eed of a tiny piece of the cord.

Why do the strings used for the lowest-frequency notes ond1,fd1k7 go lcs gi *h m+p)s+z0pgrfj3t;;n p a piano normally have t )s3f1 1jlk70p h pgo;rzpi*s;g+ ,fdd+n cgmwire wrapped around them?

What kind of waves do,y6(26uauug jae6qs0pu1 g lm you think will travel down a horizontal metal rod if you strike its end (a) vertically from above and (b) horizontally parall(ug2myasq06 6 6u1, eug paujlel to its length?

Since the density of air decreases with an increasgk7.g*bw-(:n kg7la:1j b mze q*xw ejea8, cue 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 wl( e:-z*7aqc wek .nj87 g* ,jagmwe:kbg1buxith temperature?

Give two reasons why circular water waves decrease in amplitude as they t1v s)6z4jsu /jsyw/ brravel away from the sous/ /ss) y61b4uzv rwjjrce.

Two linear waves have the same ampeya+ fmxzx:)p yo ed5 ,)hp1s,litude and speed, and otherwise are identical, except one has half the wavelength of the other. Which transmits more energy? By what f ,1y,e5:eha py mo)+xf)zdxsp actor?

When a sinusoidal wave crosses thb3yay64k:wh4( 7pz1ec bb cw ye boundary between two sections of cord as in Fig. 11–33, the frequency does not change (although the wave 1 b3 7epwb c(yz6b4:yakwhcy4length and velocity do change). Explain why.

If a string is vibrating in three segments, are there any plaes13 :lvwjbj: bem03mces you could touch it with a kni0m wejbmbl1jve:3:3 sfe blade without disturbing the motion?

When a standing wave exists on a d.85f 1gyqdwp)n0pfsa f.w ;j string, the vibrations of incident and reflected waves cancel at the nodes. Does this mean that energy was destroyed? Explap)j0g ;d8 w y1dqs.n.fap 5fwfin.

If we knew that enerl ( (f/xqrp/dhgy was being transmitted from one place to another, how might we determine whether the energy was being carried by r lphfx/( d(/qparticles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the total distance m:rjt 9ryfmes 62:.rvvg8 8ag it try:v6va m9r.r28fsemg8 tr jg:avels in one period?    m

  An elastic cord is 65 cc y)nk;y zhc)vg ee-f5zt;-9pm long when a weight of 75 N hangs from it but is 85 cm loz-zc5hty;- kn);vcpee) g9 fy ng when a weight of 180 N hangs from it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-v4m)qx g1 c0u-m cdnr7u.eoljmr/8 ;rkg car compress 5.0 mm when its 68-kg driver gets into the driver’s seat. If the car goes o4/.m 8m cr7vueumq;o0nrc)j-l1 rd gxver 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. p1qp -bec-)e3ejyotg6 msqc 3pm 2x(;(a) What is the spring stiffness cons-m-pp1cq)ygcejq ebxe2p 3so mt 3(;6tant $\approx$    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+8.k4oegxpz /pinm 1f a frequency of 3.0 Hz when a mass of 0.60 kg is hung from it.4+gizpm8epkf.1 n/xo What is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mxt-tm , dm-;qvass in Fig. 11–2 at times t = 0d v, -qt-xm;mt,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 ajiqh(i)db/ p v)2l6re spider’s web. The web vibrates predominately with a frequency of 4.0 Hz.ev/))p q(hr i2jl6bdi
(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 0x4y.o y;jwgg;-m )f-tffy,n h.88 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 Hzj 4,ft g;mn xyw-;.fygh)f -oy. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times pero0gvb- cct p) 3qg+c;a second with an amplitud+qvp3tca;0b ) cogg-ce of 0.13 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 spel,p d)+)7igt8 ;iv rtk*iec wled of a SHO half the maximum valuer+t l;livi)ti c )dew*p ,8gk7?$\approx$    A

A mass attached to the end of a spring is stret+9szs0.l sk sgched 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 streotroi+13 ieij /se8 a0tched an additional 0.130 m and released, how long does it take to reach the (new) equilibrium por +8oi13 jieoit0ae s/sition again?    s

  An object with mass 3.0 kg is attached to a spring with spring stiffness cons(eydwhqt:+b y f rk4*cp6 qr/(tant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it i4k fdq+w*/yhq6(rb:cr p t(yes 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 compreshgzh y6p*xyo *mlg)i+8 tps10 s the spring of a toy popgun 0.200 m to “load”h)hx lt6gp8 i1z*y gm* po0ys+ a 0.180-kg ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attachei w / qa79v5xg3qosy6ed to one end of a spring; the other end is fixed to a wall. 3.0 J of work is rwiva37exyg o5q96 q s/equired 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 = 0.45cosfuv p,r5lm-ut*+m5s n0u 6+klo m ah3o6.4t where x is in meters and t is in v,k+ortnalmp + u 65l3 -5mu*f ohmus0seconds. 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 8 c4iu u. s;3,gdsipogenergy of a SHO half KE and half PE? ,4p;8g icgs uu osdi.3±    A

  If one vibration has 7.0 times the energy of a second, but their fdhcfs98n5 0 fjkj-.yzrequencies and masses are the same, what is9hsk j 5-z 8f.yndjf0c the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light sprind99 zlol2+kbfg once every 0.65 s. zok9l+2f9dl b
(a) Write down the equation giving the pumpkin’s position y (+ upward) as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. y = (   m)cos($\frac{2\pi t}{0.65s}$)
(b) How long will it take to get to the equilibrium position for the first time?    s
(c) What will be the pumpkin’s maximum speed?    m/s
(d) What will be its maximum acceleration, and where will that first be attained?   $m/s^2 $

A block of mass m is supported by two identical parallel v-zn7tj:yjj*sh z. h 7d 4j*gmfertical springs, each with spring stiffness constant k (Fig. 11–49). What will bd4 :7m.*h zfys*tnzj-jgjh7j e the frequency of vibration?

  A 300-g mass vibrates according)b gqbcg4spi7 2fx;v(q s mk k1i+i):u to the equation x = 0.38sin6.5t where x is in meters and t ixb g;si p+ q1:fi)ugi7mc)b2kkqv ( 4ss in seconds. Determine
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows two examples of SHM, labelew ,so k8y5;holg**ih 8wrswo 17)losbd 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 onqu6 ; .qqey0nw the end of a horizontal spring (k = 124 N/m) is struck by a hammer, which ge0nqq;6. wy quives 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 an am j.x5-b,6c7 lqoee/ cxcnu-ylplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) with positive velocity a cce7x.o,lb/5eu- ncy- 6 ljxqt
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two springs, with spring stiffness constants z)4 w1hkua, yw0/cdzo$k_1$ 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 h)w2b usb-j4ciu3 )qt to a fixed horizontal spring whose spriw)4-c tsbquhb2)u i3j ng stiffness constant is $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with mass 6/:ze8 cm+*eo yto( d8fjd uv1u5.0 kg jumps 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 spring stiffness constant and the unstret d+u z(8uc:f*j81oedemy v/otched 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 l4*lc*pj+kbpe50waerf (km :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 swi gy2qajdi h4z 3tok26;ng per second? (That is, one complete vibration tyok 2q2i3t daz;h 6gj4akes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on Marsgje,6n(ztf(x; haa1;i 3mpa 0uqd)y s, where the acceleration of gravity is aj0a z;)tufh3,dinp m1aa(ye6x;q( g sbout 0.37 that on Earth?    s

  What is the period of a jguz 8t/x s5*d svgs,,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 m, the pendul9c73v3zfijnw um bob has a mass of 365 grams,n3c97 v jifzw3 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 up sjvw-r+(0og x; i0z)(nm zathe clock loses half a minute per day, how should you adjust the length of the pendulum? shopwi+ n)0z;0s v-g(xuj oarm(zrtened by    mm.

Derive a formula for the maximx6 e tl4zeef c8c1n-p:um speed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscilla(ni,2 w-,drx iww5dxbtes at a frequency of 2.5 Hz. At it is released from rest starting at an ,niwx,2wdxw ri-5b( d angle of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests pass the bow of hisk2gmuyf -:k4r anchored boat every 3.0 s. He measures the distance between two crests to be 6.5 m. How fast arrk y2: mu4-gkfe the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels withw8 *ppvhpx8jdv 1ye-z(h5fh 2vd3(rrhx32vv a speed of 343 m/s How far apart are thejh83 5vfd*dy1 rp(vhv3h2xxz vr8 pw(hpv2-e wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (kilohert 43 xairg;qi.az) and t4gxirqi.a3;a ravel 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 longitudinalidr *dk ;s /4uk3jdyq, waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, /jg+hbf::qp.iizh-j (bz 5nj but one is twice as dense as the other. In which rod will the speed of longitudinal+zfin-5gbjzjq (j:i/p b h.: h waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apart. If the tebyzu26d+0s; 1v. zkhd johb, snsiozvh0 hu oyb2sdsj.1k+bz6;d ,n in the cord is 150 N, how long will it take a pulse to travel from one support to the other?    s

  A ski gondola is conn2vvqt . fp7i5lected to the 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 that it took 16 s for the pulse to return. v5iq2.fp7 vl t
(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 beu8.i ie.3r)zrrdgd:ts 6o6gllow the surface of the sea. He hears the echo of the wave refi6rto.d .rzr g8i dg:3l6es )ulected 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 different speeds lyc.wamo;r ,ap +0zmt1 )epo2, and this difference helps in locating the earthquake “epicenter” (where the disturbance took pl+l ;.w1apoyct,2 arm)ome z 0pace).
(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 apuz4)nfwgg3+ /ct8fuf n 4*rr;kl o-sv proximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contactnwf t+3 )klu f-;rzn*44g/vfs8grcu o with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amu: (s ijwi sg/ tj5l,2a12ubmuplitudes, of an earthquake P wave passing through the Earth and detect5s w2u,12ugjbi(sj:ta u/i lmed at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an ea8i y6t.0uyjdbdczx2 55 ptwu4rthquake wave passing through the Earth is measured to be pcdjxd yzw25.4608u5i tbuty $ 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 trach4;kq6b j ,lgvel through the same portion of the Ear4b,gk;hql j 6cth, but one is carrying twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have iztlw b) z-gim y3m1(c2r,rg -the same frequency, but one transports three times the power of the other. What is the ratio of the amplitudes of the twrzt2 )l gz3bimr( -g1m,-c yiwo waves?   

  A bug on the surface of a pond is observed t9y,3 m.nlmuvi41tic4 is r b*bo move up and 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 d iir4,9vs1 m3ctu b.4biyl*nm oes the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each pvba9 avg/o(rnb 3:j,other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sb gva /j:,9 a(vrobnp3ketch 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 vibrt b iebmjj(o -v2w7co2 y;e3t6ates at 440 Hz as its fundamental frequency, what are the frequencies of thejviote7w3m( bjt-y;e6b2 2oc first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hztu63d 2f3bjn e when unfingered. At what frequency will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of the string ve 3dt6n u2fj3bibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequency of 280 Hz. Name arkk t9our,hjjh *t4u qo 0d1,4- lbo.vt least three other frequencies at which ito9lh1 4r 0tok d.uj,,4t- q*vkbohjur will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a sfp/w5 :p/1puolw+b tdtring is 92m/s If the frequency of standing waves is 475 Hz, how far apart are two adjacent n l ot+//bwf dpp5u:wp1odes?   m

  If two successive overtoneskmfs5wxw.71xv mu,1 1c(fdxy of a vibrating string are 280 Hz and 350 Hz, what is the frequency of the fundamental?f x1f ww1m.kx(7vmy1 s ,5dcux    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distance from u ,7iorxcm(2d, iqu gel 8up9-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 first two overtones? rc 2 xgiimou(79u,dulq -e p8,   Hz

  A particular guitar string:lu,u fv7;i/vmj e(ch t,l2de is supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in : ;lfju,(v 7l2 ievhdme,u/ ctthe 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,+0t 7yu qug qaqzio(lo0)*am: but it is measured to vibrate at 205 Hz. By what percent should tho:7qo aa g+q0)myt ui(zql0u*e tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-amplitude mechanica(b 1lchxprw7,)u7 g zfl 60-Hz vibratorp,(7ch wx)rl f 17zubg. The string’s mass per unit length is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of the string may bekt fw;ne45 d9w4va7lz adjusted by moving the pulley. If the hanging9 an4evf l4;5wtzdw7k 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 forth in a tub at just the right frequencvs/b/t(u5q7j n6 :qwuauc l 9qp3( ojny, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frj s: nuw9u(p/l7q/jvba q63qouct5( nequency 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 Earth 6 evv2jfm+st8 lpz8 5lj)+bht lxam:9 fqa 2p)between two kinds of matemvm+ : t 2axp l+ql2flfb6jp a)h9 5setzj8v)8rial. 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 cha/wc5ae2bdb jz)mi0q )nges from 2.8 m/s to 2.1 m/s If the incident wave crests make a cbi/0w2q)z)mb 5a ed j34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm airqe4xu,f u++ ,wx7svpr6dq )gq6gxwt( when it hits a layer of cold, dense air. If the sofr+w+guwvu,s7tq4 (6 xe) xpdq6gx,q und wave hits the cold air interface at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave strikes a b92drs,o4e zih(+vm m youndary between two types of rock at aeihm 49srz+y,(vd o 2m 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.xqb1k)zl :xb8sb;(he 0z q t+h According to the user’s manual, the dish has to be pointed in the dz80bb lt sxzh bqeq+1;k)(x h:irection 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 tr3e7 *g/hrlqsp 9+ /cbu x6+h ;hxjrtand velocity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximatehh/3 +l/ st7 je6pr*g9xctrqbhxu + ;rly 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 09m, g gtcmew7stiffness 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 conmm, c t0g7w9geservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m below, wh6dz opshgish5w qwxp e++. 88 ) 8hve7xbcz(v,ich stretches the net 1.1 m. Assume th g7 8w 8he6pv,v5zw ixdehzsqsb 8.)(pocx++hat the 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 a1xr 2(lgw xu7on the end of a freely hanging spring. The mass then fa l1xw2 (xr7agulls 33 cm before it stops and begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed ofu( zt:t5 *emcp 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the emt(t5 :czp* uspring stiffness constant of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of coffee (diameter 8 cm) at just the right pajkib8 wrhi575. wi45mmf sxsl 7,oy g3ce of about 5m.4i wmg7of5slri7, 8i5y sjx3b khw1 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 waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the center of a 33-rpm phonograph sn6 v:gtanej3hi /d 6;record have a wavelenge d6g6;tav3 :/ni njshth 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=0.650cos7.40t where x is in wph r/3r,+ nagc25 2qia(opbkmeters and t in swkcp3/ri p r2a,h a +gbo5qn2(econds. 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 frequencsw6 cl2rj4k 8h7n7 ma8fpi*7/dl nho)jn ,bpky if it accelerates at 0.50g (a) upw c6)pn wjdpj 4l, i ml/7a h28*h8soknk7nbr7fard,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. Wnpw. rv;jde4a oof,z(/2nmr) hen a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the w rjo/4 m,df .e;)vonwpa(r2nz ater. 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 a:e z078mm8m6 gqc(oktu g6r car5iz u5re tuned to play at 392 Hz (G) and 440 Hz (A). icgz:u 0zmmr(aqtugoe8ck6675rm5 8
(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-partckt+)s* ubub; 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 b+;csk*b )tuuboth sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequy wbnv5xwd-3 :xj y15cency of 264 Hz, and the tip of each prong moves 1.8 bwcyynw-5 1x35 xj:d vmm 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 si:xpg0gdol,fp :wjq+l,c(h k 7 mple harmonic motion of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the bok+pjlfoqp7xg:c, l h( 0w ,:gdard can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that end is attacheueh xyy u(q1:zr479/n:l/qvi 9qvksx d to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavee/l49( yuu kr/ q qvy:vx71i:h9qxznslengths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has nc.d63j r6lvw7ap cq1ypv25* oscr5b a period of exactly 2.000 s — each one-way swing takes 1.y cr5vrp1vc3.6obd2spwn 6 *5ajq7l c000 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 spring can oscillate in the vertical dib7**0xa.n-hpwc g)seny1haqx 0 m)pm rection or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontal swings, and by what amount? [Hint: asyenhm c*07)bw)1 xq 0 n*mg-xp.ahpLet $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

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

  A 10.0-m-long wire of mass 123 g is stretched under a tension of 255 N.xs6c3: *bl on8ec s11)xyb5vnmvo7w o A pulse is generated at one end, and 20.0 ms later a second pulse is generated at the opposite end. W1x7 cn)bo5 vob6 s lo*vns183:wxey cmhere will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a sprinlauw,.jq 6tbw :/2ekcbuv)w 7g with spring stiffness 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 stay on top of thekva/ulj6cwqbb,) e .2wut: w7 block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel crane cable is 22 etz9ejl.- lr 7m long and has a diameter of 6.4 mm. A breeze starts the car bounl9e-rzej 7t.lcing at the end of the cable. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (which also gives the djwz:7xvs j9 1yimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrat9vywjs1z x7 j:e. 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