Give some examples of everyday vib,b6-s(vaztyh rating objects. Which exhibit SHM, at least ap,yz b( avtsh-6proximately?

Is the acceleration of a simple harmonic oscillator ever zero? If so, wherelvi8p3uly*kwf3 ;y 8n ?

Explain why the motion of a piston in an automobile engine is appro pves2u 6fz09z0bc6cx,a.lbzximately simple harme2 uvp6.6 zbszfzbl0c a9,xc0onic.

Real springs have mass. Will the true peri :lsta bt3j+ ;p82al;z+p sarzod and frequency be larger or smaller than given by the equations for a mass oscillating on the end of an idealized massless spritp;:z;382r sltj +a bpzaasl+ ng? Explain.

How could you double the maximum speed of a6f7n:gw(i* zkv+ig ye simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical ) ldz)q n7krlvl+v.38 )g1yx bz:mvl,lug r3dspring scale, and then is released. Describe the scale readinul,)3lgq: )rm 1lxd8vblzvdv3 7n). yzgk+lr g as a function of time.

If a pendulum clock is accurate at sea ,1thuz*gvp6onu j 9o3c)*mpqf s: 0xolevel, will it gain or lose time when taken to high altitude? W:fqpmo uocu63z,hvo1* gnt*j x p9)0shy?

A tire swing hanging from a branch reaches nearly to the ground (Figlzm, s5a /uk*lp48g+ jzqm/so 9kq8vj . 11–48). How could you estimate the height of the bkvu9+ gqlam/z pkjl/5 s8sq* 8zm 4oj,ranch using only a stopwatch?

Why can you make watg3lw.tv+8m h3j- zf ller slosh back and forth in a pan only if you shake the pan a g mh3tf3vl.zj+wl8l- t a certain frequency?

Give several everyday examples of resona+6 dce tkmm,z5nce.

Is a rattle in a car ever a resonance phenoq61wr nydu7x 8(sf; nymenon? Explain.

Is the frequency of a simple periodic wave(balt5rfv: sh6 w.jni230p fl equal to the frequency of its source? Why or why noa(l3h5 :prv2b.60fn tl fiwsjt?

Explain the difference between the speed of a transverse wave traveling down au2z5d w+ty;kziwbbf 0 pib9:s3 cqdmuy/ .3n6 cord and the speed of a tiny piez;3bsdpif mbwb6z3:.wy+ y9nct2k d iq 0u5/ uce of the cord.

Why do the strings used for the b v(b-rp0e+ku lowest-frequency notes on a piano normally have wire wr(+0 revb- kpbuapped around them?

What kind of waves do0 b5 gz9/rpaaw g.2sfu you think will travel down a horizontal metal rod if you strike its end2f p.a50ugbwasz g/r 9 (a) vertically from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase inlshegh)c-x2 b ;x2 (ej temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the spee)xgse; h h2j- lex2(bcd of sound waves in air to vary with temperature?

Give two reasons why circular rtryl/s6la(.kt. 5 di water waves decrease in amplitude as they travel away ll6rayi.t(tk ./d 5sr from the source.

Two linear waves have the same xa1qdd. ax v-xw3rygq5tww+t 1,2u.xamplitude and speed, and otherwise are identical, except one has half the wavelength of the other. Which transmits more e-qx+xy2trx 1q 1udgtv 5w3ad..,wx wanergy? By what factor?

When a sinusoidal wave crosses the,d 149m klx ziqgg) rvn1o6gf5 boundary between two sections of cord as in Fig. 11–33, the frequ1ivq4mgog, ng6rzf)d5l19 xk ency does not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there any pp0pqj j5wa: -nlaces you could touch it with a knife bladenj :pwap jq0-5 without disturbing the motion?

When a standing wave exists on a string, the vibrations of incident and reflecttm3 ttvo/zk8d5+ d(b s)ds y)led waves cancel at the nodes. Does this mean tha tsd zy)dk3vl (/5btdt+ 8s)mot energy was destroyed? Explain.

If we knew that energy was beixc3s .* lrq6bwng transmitted from one place to another, how might we determine whether the energs.qbcw*6l3 x ry was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with bj +4 ruri)d*kamplitude 0.18 m, what is the total distance it tra krdbu *4irj)+vels in one period?    m

  An elastic cord is 65 cm long when * mo0k,egq hzd z. ybd9m35(nn-sjdgp)mg* j8 a weight of 75 N hangs from it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” consoz5djs,nem-ykh8dgp m* nbq.jg 0z *d )93(gmtant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg driver g5g 2 z* xh5tlvdhcq:*nets into the driver’s seat. If the car goes over a bump, what will be the frequency of vibratihntqh5xv2 l z c:d5**gons?$\approx$    Hz

  A fisherman’s scale stretches 3pmae6 4*yg/u2) g* y5uqfsv 4svx s0qa.6 cm when a 2.7-kg fish hangs from it. (a) What is the spring stiffness cons4p )f**ygmg5624svqua/vaqxs ye0 su tant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a frequency of 3.0 Hz when a mass of rks/3c) gqo6z q92i hahlm5k;0.60 kg is hung from it. What is its frequencrs3h5 ;2k hgmzco i9kl 6aq)/qy if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the k;-zfoem j q;3mass in Fig. 11–2 at times t = 0,t je;;z 3ko-fmq = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 gbkon20 mbs:;w is caught in a spider’s web. The web vibrates predominately with a freqm2b:bsw 0;kn ouency 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. 8d yopw brm-6w8aqt.- When an additional 680-g mass is addmwt.b- q6 o88wyp-arded 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 with an a* g(,rfdtjt 0dmplitude of 0.jdd,f*gt0t r(13 m. Determine
(a) the velocity when it passes the equilibrium point,$\approx$    m/s(round to one decimal place)
(b) the velocity when it is 0.10 m from equilibrium, $\approx$ ±    m/s(round to one decimal place)
(c) the total energy of the system,$\approx$    J(round to one decimal place)
(d) the equation describing the motion of the mass, assuming that x was a maximum at x = (0.13π)cos(  πt)

  At what displacement from equilibrium is the speed of a SHO half the maximupe)sx xyoa62y/+zs 5mm value?am )52+ pzssey6/xoxy $\approx$    A

A mass attached to the end of a shnf4h)p/6g, o-txdgc z*p1y ipring is stretched a distance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretches a vertical spring 0.315 m. If the -w y h ll8 cg65idh:hu-be7lr(spring is stretched an additional 0.130 m and released, holh yh-hbi6d crewl (:l7g8-5u w long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is atta/ abflp/dzmw8sm e)3jv)7 o 4cched to a spring with spring stiffness constant k = 280 N/m and is executing simple harmonic motion.m)oms7w a)/f/43d8 cj p zbvel When the object is 0.020 m from its equilibrium position, it is moving with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compress the spring of a toy popgun 0.20hshsm/+hy rkf ewbv690v 4 v/(0 m to “load” a 0rb+vvmhh( /kh9wv6s0ys/f e4 .180-kg ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached rsrc cm:*70fmb) s: rcto one end of a spring; the other end is fixed to a wall. 3.0 J of work is required to7br)c0ms mf*:r csr c: 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 accordid- qp+ps 5q mkktd;0)xng to the equation x = 0.45cos6.4t where x is in met k;dmk- q+tppd)sqx50ers and t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from t05 mr5hfqv0jl /az t8equilibrium is the energy of a SHO half KE and half PE? 0rtv almjq50z8th5f/ ±    A

  If one vibration has 7.0 times the energy of a seclqer7p l fm,e4 d2jnr4n-31cs m1ykn(ond, but their frequencies and masses are the same, what is the ratio of their amp7dp4lny fr123 (n 1c4 rkmej-nlsmqe ,litudes?   

  A 2.00-kg pumpkin oscillates from a verticallye,:yaew5iu6 (xc pddpfz3p2r u3o x*, hanging light spring once every 0.65 s. w,:,* p2yu 5d33xppzcex f oeu(i6 adr
(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 identi i5*i 5uy:8sk eattggp2b01pical parallel vertical springs, each with spring stifkg*:p u1 i giat0p st5ebyi852fness constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t fey* x 0t+ a c4)px /)fssfws91chh-fjwhere x is in meters and t is in seconds. Determin y ha*f0 s4 hcst c1pfs9+w/)f-f)jxexe
(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 ixxa20giyi kc ln81/ :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 a horizontal spring (k = 124 N/kh pa(ki rb(y ;7,dc/nm) is struck by a hammer, which gives the mass an initi( 7;kbcdh ,y/(k airpnal 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 *d; fm75t uug9r mqimt1drm:1N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point (x1mu;g qu dt*:f1d7mi9rmrm 5t =0) with positive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two springs, wijt83l2 )vs9e iyuwzyw7jhdko;7 x 7(ath 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 bloc+ym/ ur.ojs/yduy 0z :wybk2rg /y3f2k attached to a fixed horizontal spring whose spribg /oyjuy+r/02f /ysk.w y:2 yzmurd3ng stiffness constant is $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with mass 65.0 kg jumps from +synqjzz p syq2 h: *x/3l:up7a 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 bexq :*lnyp/q +h327zszsujy:plow 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 vibrations qq2 qad*z9. w,.x: k cdcv.omfin exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if:sduq) q eac*8 it is to make exactly one swing per second? (That is, one complete vibratie)8q*a :q dcsuon takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on Mars, wherj0pfv,* g8hs)w 7ng wae)-ykfb 25sehe the acceleration of gravepgfb-7 wsgvk)awh 0)*h8 ,2 n5jsyfeity is about 0.37 that on Earth?    s

  What is the period of a simple pendulu8/zr8p7 /l.hc u )2 zlm0:(bwpivlbdd znopv7m 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 365./nf:fka s i*t4x rc*s grams, and it is released af*sfa x*nt/4.r:skc it 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 lenrf vbdq- nqbpl/)oc ),pw(x 58gth of 0.9930 m. If the clock loses half a minute per day, how should you adjust the length of the pendulum? shortened by d8(qq/c )p-f x)rb5olbvnw p,   mm.

Derive a formula for the 7 r6ycix tkv;io2i5ax:8bfq-maximum speed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at a freqt09r/ /6r 4t) rganwr bcs8yfbuency of 2.5 Hz. At it is released from rest starting at an angle9y)b s4c r08r//atfw brr 6tgn 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 his anchored boat every 3okltse5d j9)z3l. ib*.0 s. He measures the distance between two crests to be 6.5 m. How fast are the waves traveeb.i t*j)llsok95z 3 dling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with a speed ovz 7e6a1mudm1 i.ky:/osm z.sf 343 m/s How f ye/:i.udmm.zo1avkz761 ms s ar apart are the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550v8dzma zk : 6gh4*hc2c kHz and 1600 kHz (kilohertz) and travel wi:6zgk8 z*acm cv h4dh2th 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 longitudinalfte.1ze tzyrqsice4 c82c09 1 waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modja,m)c,jk5 jm 4zqoy;++ csmoulus, but one is twice as dense as the other. In which rod will the speed of m ;cjjm,4+acy mzso+,5)oqkjlongitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m advv27 nfk6vzuh,ui 1)part. If the tension in the cord is 150 N, how long will it take a pun hf7izvuk62v1v,d u)lse to travel from one support to the other?    s

  A ski gondola is connected to the top; px k(nrh;:vw2/ rzms 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 pulxw ;vmkn h/;(rr:z 2psse 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 shixj qa,-8dr. qjji -7bip just below the surface of the sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is the ocean at this p7qd- j-i,q aj rxbij.8oint?    m

  P and S waves from an earthquake travel at different speeds, and this diiw5.n lk80(sewj 4vyufference helps in locating th8vj .wnyw 0l (ke5ius4e 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 ap3 8pefu*p ycxhrf) apdos+l8h860 za6proximated 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 contact with the gl*8hac h6 6ypux p0p3 drs)f8+8z oefaround? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) tflx p.*kql9m5he intensities, and (b) the amplitudes, of an earthquake P wave passing through the Earth and detected at two points 10 km and 2l5 lq9 fkm*xp.0 km from the source?(a)    (b)   

  The intensity of an earthquak6*ibiq w(ok/eyv4 /jd e wave passing through the Earth is measured to be k/ q id(evbjwy/oi4*6 $ 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 sam2ykol fagoih0sd89 ;4 1jbim9e portion of the Earth, but one is carrying twice the energy. What is the ratio of the amplitudes of the two wam;s 9i0jf8lok24o9 ahg yi1db ves?   

  Two waves traveling along a stretched string have the same frequency, s)s*, xkcpim w w2:jhhgyk5+0but one transports three times the power of the other. What is the rat:*kjs hhk5p2i sgw0c +) ,wxmyio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed l zrl+4o a7xu-to 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 does the baxu -olz+4l 7rug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving towaro0i5mt6 nrx*rd each 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. x 0n 5*6tmriro(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 frequ6ze: dosj lmnn*sa0; uuv+h--ency, what are the oj+snlhz- sen;0vu - daum *6:frequencies of the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what frequd7j ;lq45vlyv ency will it vibrate if it is fingered one-third of the way down from the end? (That is, onl q5lyj dv4vl;7y two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequency of 280 Hz vx6g ek* yapl;7m0+ i(8oeyfi. Name at least three other frequencies at which it p 6 vfly e7axy*o;+g(8 0kmeiiwill 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 isix qf.pade as0k p df1k;c+an7p+(/ /t 475 Hz, ho7x+a c+ipatpqf0s /; n apd1.ekk(df/w far apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 350 Hz, what ((s c)www0w e-d-ygoj is the frequency of the fundamentswec-0(w)-ogwy(jw dal?    Hz

  A guitar string is 90 cm long 0hgl t;-8 e3rc(xlbh3fze ea-and has a mass of 3.6 g. The distance from the bridge to the support post is L = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundamental and fire3 chah3 geezfll x8;(b-0r -tst two overtones?    Hz

  A particular guitar string is supposed to vihi6x8wr)d k*yh.*xcc t0ps;w brate at 200 Hz, but it is measured to vibrate at xwydirkh c x ht*60.w*c)p8; s205 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 vibrat ri4r3 0wit pna0,ftx40bp g;;c8jl jbe at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent shoi;p pj0 ;r3itfn rba4wjc0 l,t0g4bx8uld the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-a0xr hij07l* kvmplitude mechanical 60-Hz vibrator. The string’s masl* j70ikhvrx0 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 may be adjut(jhftn k29p3o(ub5 ysted by moving the pulley. If the hangn923otp k(j5(yfu b thing 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 forvrv g*z 7/.vecth in a tub at just the right frequency, the water alternately rises and falls at each endz*gvcv/r v7 .e, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundary within the Earu;snk ;0r3w szth between two kindz;;s 3snkru0w s of material. If it approaches the boundary at an incident angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “shelf” where the veloci bxs m)-u*fzr3chr p.mr1(ex) ty changes from 2.8 m/s to 2.1 m/s If the inc 3m*zu(cmrhpef 1.- b)r)sx xrident 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 it hits a layeru dajn+qk9b+yaw6)j/6ag db+ of cold, dense air. If the soundn6dug+ q96d+waj /kba y+a j)b 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 boundary between two types o ey 2fp2ntd -9cwj4v-o7c 4kswf rock at a 38 ks 2dwo4 n cjp2fct-y94ew-7v$^{\circ} $ angle. As the wave crosses the boundary, the specific gravity of the rock changes from 3.6 to 2.8. Assuming that the elastic modulus is the same for both types of rock, determine the angle of refraction.    $^{\circ} $

  A satellite dish is about 0.5 m in diameter. According to the user’s 8q: liq-nwzm .manual, the dish has to be pointed in the direction of tq-.mn w8lqiz: he 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 kd qxa(5qcw vzi05mlt 64k02l vm/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an uc5520 lqixvdt alm k6w4q(0zvnusual 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 fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffneshzni) itd2 wkr 1kf2)*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 coni22zrf)*k )itwh n 1kdservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m below, 7 bko2 ps74m gjuhm83x0kcq f+which stretches the net 13hxsmc4jf pm kgqou 8b07k+27 .1 m. Assume that 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 on the end of a freely hanging sp7iy29ee*bf. l h4.*nz4ua zqa0in xvnring. The mass then falls 33 *zax an vn *ih9.l7z q4f4uyie.2b0ne 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 of 22 m/s (Fig. o4v ,smwewg : :htq7;e wsl/e.11–54), compressing the spriehsw;7 4 /oeq t:ws.e,wlm:gvng 5.0 m. (a) What is the spring 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 cuc n7a9or y5gv.p of 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 to spill over the 7yg.o59c nvartop (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the centwqd )0-o 4,few-ygdr ter of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be towdg -),y-rw t d0eqf4he frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.6505y;ljelax6 --i j(rxkcos7.40t where x is in meters and t in seconds. r-y-6ax5x(ll eikjj ; 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 it p4cb/ hjl.twcgl10a7+ 20.doewsde f it accelerates at 0.50tos1.l g00c je.w et2wdphacd7+b l/ 4g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floatn;qmwrxk 3- o5 -uj y:mjlw95ds on a lake. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. Who -5 5 jmrdy-xjm: lw3;uk9wnqen 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 * i**lr5)0jkhxnww8 m7tgav c(G) and 440 Hz (A). 8wj)vx5 mrn*hg*k 7t0lc*aiw
(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)ybzc2y pj3r6r7v-o g the stretched two-part 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 t6br g)rjcy32p7 -oyzv he ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates atj51ytj :4-jte vtit:y a frequency of 264 Hz, and the tip of each prong moves 1.8 mm to either side of center.ty5- j:itj:4e1 vtytj 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 har90 +/xvtnsfa -k+qiflr6 qx8 eln- 0fqmonic motion of frequency 1.5 cycles per s6qtx9 af-ksvelq x rlq++/n-f8f 0in 0econd. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that end is attached 0wifc5f1xz rb 1zjn5 9ufm9q/p3wq6u to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths 19 r 0quzxfj5nm936wiupf/ bcz w1fq5of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s —ao0, oli rmduaq+r 4(jj2z2(g each one-way swing takes 1.000 s. o, 4(j+ agqudjo2 z(2armi0lr
(a) What is the length of a seconds pendulum in Austin, Texas, where $g=9.793\mathrm{m/s}^{2}$    m
(b) If the pendulum is moved to Paris, where $g=9.809\mathrm{m/s}^{2}$ by how many millimeters must we lengthen the pendulum?    mm
(c) What would be the length of a seconds pendulum on the Moon, where $g=1.62\mathrm{m/s}^{2}$    m

A mass hanging from a spring can oscillate in the vertical direction or cnifrzbr0: 3wu ;bha+ :an 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?0:3+ niauhrw r:bfz;b [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 ox*8qwy t2niq8 mej4k1ziof 18f mass 123 g is stretched under a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at the opposite end. Where will the two pulse o1ei1f2 yxqqt8k8*iwnz mj48s first meet?    m

A block of mass M is suspe1wfacli/dpxukogx(mqo 81k69 f ) 3m4nded from a ceiling by a spring 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 t /x6dmm(fk1wqap ) c9io84 l1uoxkf3ghe block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the juni c dcb0ro/9)r)zq/iikyard. The steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car b/) c9)/b icrzr qio0diouncing 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 xa-7djomu:gykcg wq.,xw .0.j5s bog3 4 0wb malso gives the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this vibration, given that the shear modulus (Section 9–5) of jello is 5 q,4wjg.0xc0sa m xoj7w-mb dgbo:.uy3wk. 5 g20 $N/m^2$ and its density is 1300 $kg/m^3$    Hz