Give some examples of everyday vibrating objects. Which ey*/*iz *irneexhibit SHM, at least appro iz*ee/ *ni*ryximately?

Is the acceleration of a simple harmonic oscillator ever zhs9rn .ubn6s8 ero? If so, where?

Explain why the motion of a pis ioikda5toy2m 9mngt;x020:oton in an automobile engine is approximately simple harm o:x0ma;52t9y 0k dinimo2gtoonic.

Real springs have mass. Will the true period and fre fdcv5u / klxhr9k-q//sav+zq+r u0,o quency be larger or smaller than given by the equations for a mass oscillating on the end of an ide oru0dl+z,rqv+kvuf5/kc a //s-xh9 qalized massless spring? Explain.

How could you double the maximum speed of a simple harmonic oscillator (SHO)?vwp(p x3tuq0 ,

A 5.0-kg trout is attau;f9nwi npgj8j 94gnv.nk/x. ched to the hook of a vertical spring scale, and then is released. Describe the scale reading as a fu vwj njg8nfgnnu.9 .i/kx4p;9nction of time.

If a pendulum clock is accurate at sea level, will it ga-wx f6ttpt lndbc 41x5gj9cc sh8)9- hin or lose time when taken to 9tf)6-14c x lc-ts wjxcpht dg59 bnh8high altitude? Why?

A tire swing hanging from a branch reaches nearly to the ground h- x:-4e2-0te g5trzyt i xahe(Fig. 11–48). How could you estimat-tte eietrza 42yhx 0:g-5h-xe the height of the branch using only a stopwatch?

Why can you make water slosh back and forth in a pan onmhva(e mho,sq-3; t mnd t89(oly if you shake the pan at a cea(mv9 (nt-em,tqdhm hoo s;8 3rtain frequency?

Give several everyday ex;jd ib3snj 8q )uogy)0t6o(t zamples of resonance.

Is a rattle in a car ever a resonance phen te4(apu 5lfz9omenon? Explain.

Is the frequency of add : wef*jm zz/j-05fdc sa*r1 simple periodic wave equal to the frequency of its source? Why or whcjsdmd:wfar1e5 zz**d- 0j/fy not?

Explain the difference between the speed of a transverse wave traveling red5t;p6 xmu3e.h uweeu9d,p3 i(g 9 xdown a cord anpdux;ueeg3e,53t 9 e.( w9pdxur6mh id the speed of a tiny piece of the cord.

Why do the strings used for the 5lpwq;i:0y s*, mt wwzlowest-frequency notes on a piano normally have wire wraplsz*;:ip, w0 mwt5yqwped around them?

What kind of waves do you think wi+hpvr: ,4mc*a3w s,zwbm2 lsmll travel down a horizontal metal rod if you strike its end (a) vertically from above and (b) horizontally parallel to s m,vm:*la4mrh w2w3+ ,sb pczits length?

Since the density of air decreases with ahyi/jz eqx2 -e;jd. f7n increase in temperature, but the bulk modulj-d 2ey7jiz;e.hq/xf us B is nearly independent of temperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why smiglds 1(:su2/le; qcircular water waves decrease in amplitude as they travel away from thqmu/sgs;:1 sil d2l( ee source.

Two linear waves have the same amplitude and speed, anwlms* ; g* w5i5u5ltbj7i ev9td otherwise are identical, except one has half the wavelength of the other. Which transm 97 i*w5;w mtels gjtv5*lbi5uits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sections of sb6b5 6qvtc y shs+g-d- :ffznu u*8e4cord as in Fig. 11–33, the frequency does not cqb5 +-z df*s6 8:4hv6sftg eycbsuu n-hange (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there any placess3 0j t* zf29 dykepkab,jl-u( you could touch it with a knife jk9*ls0 za b3 ,fy(2kpjuted- blade without disturbing the motion?

When a standing wave exists on a string, the vibrations of incident and ref(y.ty7or j5zr 9lulx6lected waves cancel at the nodes. Does this mean that energy was destrj 7 yyl lro(56x.zutr9oyed? Explain.

If we knew that energyd u)nt kxt:p91 oifkjjs9/v9/ was being transmitted from one place to another, how might we determine whether the energy was being carried by part) 9f1s9uk/:xjtt9kid/o pnjv icles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the total distanc ti40g3t-pjlz e it travet3i0-z lp4jtgls in one period?    m

  An elastic cord is 65o-rkl2; wl /d*.eih q8)yslf:b3bby k cm long when a weight of 75 N hangs from it but is 85 cm long when a weight of yw- s/qblhlblr *ybde )okf:i ; .38k2180 N hangs from it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compresf,;jm btn8tg 74ny s8rs 5.0 mm when its 68-kg driver gets into the driver’s seat. If the car goes over a bump, what will be the frequency of vibra ,7yb;j4mnf rts8nt 8gtions?$\approx$    Hz

  A fisherman’s scale stretches 3.6 c1xk8mn3bqwuwd 78 9kvm when a 2.7-kg fish hangs from it. (a) What is the skduww 91b 88 qnmkxv37pring 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 o)1w75o8r zjt pw.a ljuf 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency if only 0.38 kg hangs 7upjl5 )wotw18.aj rzfrom it?    Hz

Construct a Table inya;rl b,)0cf .bfujd 3dicating the position x of the mass in Fig. 11–2 at times t ;. rlbyafdbu,03)fcj= 0,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 aes.zjlxruxwe1 9ne v llv-))h72h :d5 spider’s web. The web vibrates predominately with a frequency15dz9nhuv -)xj ws ex :l)r .lv2el7eh 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 ow5-r :7 7lrj(c)f vv;q8gsxulxpx a2xf a spring vibrates with a frequency of 0.88 Hz. When an additional 680-g mass is adp)l:qxvxx j-(awrrcg2sl xuv785f7 ;ded to m, the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at th0 k iob-u9e;use end of a spring vibrates 3.0 times per second with an amplitude of 0.13 m. Determ ku-9u0e o;ibsine
(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 equiojdg 5 i.s87silibrium is the speed of a SHO half the maximum valu 8id7s.5siog je?$\approx$    A

A mass attached to the end of a spring i8obm*gnu38df s stretched a distance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretches a vertical spring 0.315 m. If the spring is stretc0movkjq 4 a(-zhed an additional 0.130 m and released, how long does it k-0omz(q a vj4take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is at28yxt 8u ycl0 n w6d+m0w*lgbstached to a spring with spring stiffness constant k 8s blx ywl 0u2* +0c8nmywtg6d= 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is moving with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0vg2 4emefzarc7 zq+dn88+q: g N to compress the spring of a toy popgun 0.200 m to “load” a 0.180-kg baln:f2 q4+ 87ra8ez emgdzvqc +gl. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionlee0jb d hy,dr-,ss surface is attached to one end of a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, the mass experiene,yhd0 ,d -bjrces a maximum acceleration of 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates according to the equation x = 0.45cos6.4t whj g+xjt a+nz +c,iny,2ere x is in meters and t ,xij+gn+ +c jzan 2yt,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 equilibrium q(fh(d. :+ukjq+lxqp l6kc*fis the energy of a SHO half KE and half PE? ±q.cllu jkf pf x(q *6qk+:+h(d    A

  If one vibration has 7.0 times the energy of a second, but their frequencie k7bj ,,0jfqc)dv.ztzs and masses are the same, what is the ratio of theiz,,)70q dbz.jkcj tvf r amplitudes?   

  A 2.00-kg pumpkin oscillates i+ o ,u7 .ojc-:npbkpofrom a vertically hanging light spring once every 0.65 .co:oipn j,- pkb+7 uos.
(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 vertica 1).g+ co)x mp(xitg dftasp-;l springs, each with spring stifp;(.gcdx1-t)mtsa gix +)po ffness 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 where au 9 aq403(wl4klzmrsx is in meters and t is klq(r u0zlw3a44 9msa 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, labeled A and B. Fo3fe6 q9ca5 ;h5;lox ss+ u-bjibl5v edr 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 endts ( -brdqv,siy)j4l . of a horizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.96mvy4(s.,jqt )l- b sird/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 y9 ;gm,vkch(h spring stiffness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes; 9 m,(hhkcyvg through the equilibrium point (x=0) with positive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two springs, with sp k*n/h:lk:pqn1nzxn4-jc7ip q0ut /h ring 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 go+ jhgc48 ow,d)0a wwattached to a fixed horizontal spring whose spring stiffness consto )g4c ja,w8wghd0+w oant 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. Aft8t ,oy3 v*d+pzmc47ac dhoz)xer reaching his lowest point, he oscillates up and down, hitting a v7,podzao8hct3*dy)c +xz m4low 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 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. Wt(: -s7 djntipgs;e9-9cbc yqhat is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simplef41zpqhfsi -qc8d,j, pendulum be if it is to make exactly one swing per second? (That is, one complete vibration takes exa,-q,1z8j sd fhp c4fqictly 2.0 s.)    m

  A pendulum has a period of 0.80 s on qzb z9dun 6uet01- 9jyEarth. What is its period on Mars, where the acceleration of gravity is about 0.37 9qtyuznz9e61 du -0jb that on Earth?    s

  What is the period of a simple pendulum 80 cm n;d3xx, gklr ,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, therfy: u4mp;f)z pendulum bob has a mass of 365 grams, and i r:f; p4ymzfu)t 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 a3:;1g u i nx5z;mzhk88utivz o length of 0.9930 m. If the clock loses half a minute per day, how should you adjust t;k5vz3izu: zu g8x; mh81t inohe length of the pendulum? shortened by    mm.

Derive a formula for the maximum spm-fmxi g+ v2hym78s*beed $v_{max}$ 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.kvpw5 q8)w2f7vfh k a15 Hz. At it is released from rest starth2f1k w57f)q8wavpk ving at an 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 his anchored a8dgtn (h 8bu5boat every 3.0 s. He measures the distance between two crests to be 6.5 m. How fast are the waves traveling? nht u8d(g8ab5   m/s

  A sound wave in air has a frequency of 262 Hz and tr*sw /q; qxw6gnp.po/p avels with a speed of 343 m/s How far apart are the wave crestqppxsw.w6/ng q/p; o*s (compressions)?    m

  (a) AM radio signals have frequencies betw)a .ujlrlx nrg)7a4.*zsnn 5xeen 550 kHz and 1600 kHz (kilohertz) and travel witnlxrr)as*x..5)a nn zjlg47uh 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 longitudinal wavesgeoa o w+z2r7 l0c4o2z 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 as- d4cz;viwtqcl9/n.h dense as the other. In which rod will the speed of longitudinal waves be greater, and by what f- 4ql ;cwnv hidz./tc9actor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apart. If the teekew/;1 hgd4+e ws 6jension in the cord is 150 N, how long will it take a pulse to t;e6h1dek4 /ew+ g ejswravel from one support to the other?    s

  A ski gondola is connected to the 4 5yvlsft)zjus5)t+e 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 itst 4j+e)z) t f5lyusv5 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 shipnwc(+ ap)yz5t+ d6m sq just below the surface of the sea. He hears the echo of the wave reflected)+5w+c6pms dn aytzq ( 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 speedvs.escecdn 2 ce9 007ke1aov(s, and this difference helps in locating the.n17 eo009csecsd(k 2evcvae 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 approximatn8+dq /c l xq)zs.cc8fed 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 ground? [Hint: Set the accelerationlnqc)cq f s8+8c.zxd/ a>g]    m

  What is the ratio of (a) the intensities, and (b) the amp89lei2qpif+n9mkde h /i4srvp hs/.2litudes, of an earthquake P wave passing through the Earth and detected at two points 10 km and 20 km from the source?(a9e2e2pr h liq/nif vp+/ 4hikss9d m8.)    (b)   

  The intensity of an earthquake wave passing through tht qf7u,/3 ior jiq*9ape Earth is measured to be tufqrq7o3 9 iajp,i/ *$ 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 f g-,v )ng8cyptrequency travel through the same portion of the Earth, but one is carrpggv 8)y t-,ncying twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string ha ;r.oqc ukq0k(ve the same frequency, but one transports three times the power of the other. What is the ratio of the amplitudeskqkou0.qc(r; of the two waves?   

  A bug on the surface of a pond is observed to 8eete73j4kq y tn0g:kmove 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 bug’s mak8ty 3q0:kt eje7egn 4ximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each other. (a) Skf0ch.fpoga 9 6etch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the m 0g pc6fah9o.foment 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 d )d.2thqndbdzfw 7ioc4o 0;( the frequencies of the 7bdqd2 )z4 cdfhi0;(wdnt.oofirst four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what frequency witht0n; r6z434w3u0 0kp1z d11jvgwgrt gvfd fll it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of the string vibrates as a s00gn3 16jutv;pwt fg0zrw v41 rd1gtzfhdk43tanding wave.)    Hz

  A particular string resonates in four loops at a frl/ jr6t( jfq3,kv plk,zd)b4aequency of 280 Hz. Name at least three other frequencies at which it will resoqb 4jpa,k) ,lrt/3f z6jd lv(knate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s fa*nw)s 2 -hvh tvjg)8If the frequency of standing waves is 475 Hz,v jgahf2s *vw)n)-8ht how far apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 350 Hz, w7r+t7hax 2q9 msy/9eu-g w6wshw /vpvhat is the frequency of the fundamentaw/+e qs-yhs 9a2 x mvw 67/vgrhpu7w9tl?    Hz

  A guitar string is 90 cm long and has a ,k7g5(drc sb kmass 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 fr(7bkksrd5c ,gequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposmiv n, i2mye8/c1 y x*6rkbpu(ed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension mrvcny/1( ,u2ixi m6 p kb*8yein the string be changed to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar la i ); xc(0pqye.rx4jstring is supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changedle4rjqi ;xp0( y ac.x) to correct the frequency? decreased by    %

  One end of a horizontal string 8l 370dj h-sjjokmq;qis attached to a small-amplitude mechanical 60-Hz vibrator. The strin j8 -7kqsq;o3 jhld0mjg’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 be adjusted by moving tt n1(k)osu2-, kosotu he pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns m - un2 k(koouot),1tssay be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tuz/)vbu1)oaqi 8,: x mi;dt qq zo.fkz0b at just the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produczqkzq xd:,f0izom bt8ov /q;a .)1)uie 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 c w/pwob24z55 uye/3bprt(zjat k.0 km/s strikes a boundary within the Earth between two kinds of material. If it approaches the boundary at an inciden/ue5z34w /rbjpzty o25p wc( bt angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “shelf” where the velocity changes from 2rcfh djb28i+pl--te-g :e 8q o.8 m/s to 2.1 m/s If the incident wave crr-l8ef-ih:q p-tjo28bcgd e+ ests 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 layer of cold, den5m9af7eok ;vx se air. If the sound wave hits 57 9; movxekfathe 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 bounda * vr6jze3fc) ,+rr0.l pkqszgry between two types of rock at a 3.s k j*+ fq 0r3,rpcg)lrz6zev8 $^{\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 manual,.7i.ghhha yd/ 2nka:x the di yia.7:./dhxn hkg2ha sh has to be pointed in the direction of the satellite, but an error of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelengnp gt2kz g)1 )*qfph6gth 250 km and velocity 750 km/h travels across the Pacific Ocean. As it approaches Hqg) * gpgzh)k2p6 ftn1awaii, 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 fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness constant of 550 kN/m Fin:smaiwu 22.:y:ig9jkec xl/snr( rnci, e() v d the w/i2: r9(c, j2eiu lsgxek)cina n:: vsmy.(rmaximum 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 energy.]    m

  A 65-kg person jumps from a window to a fire xcpr0(o y ujtps2(z.30 rk(qsnet 18 m below, which stretches the net 1.1 m. Assume that the n(2u.k ysz0 c xr(p03 rpqoj(stet 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 b c(5tjq8e4jespring. The mass then falls 33 cm before it stops and begins to rise. What is the f5j ce(eb 4jt8qrequency of the oscillation?    Hz

  A 950-kg car strikes a huge spro+4 kg ac08 4-/fat35kgj;/idw eynpls lpxi*ing at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffness constant of the spfn opkxitw ;43s5+eag ck40dl* jaglp/i/8- yring?    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 fwkor6. p lc46a.fj3dvg5c z4the right pace of about 1 step per second, the coffee sloshes more and p4f j5f ck.c gd6o6vwarz34l.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 avcm-/u .t //2j*z)bm*v3 a zlyvdgumu 33-rpm phonograph record hav.v/j3 / dv*b m*zy) vuut/ magm-2zcule a wavelength of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates accoutx 9(.hh-gsdrding to the equation x=0.650cos7.40t where x is in meters and t in seconds. Deterh. gd- sx(u9thmine
(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 fre9t r0+rha + 2zc13lm u 62sahdt6lradvquency if it accelerates at 0.a+hra hl16tv2l+ucz2mt 3 9rra 60sdd50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg ma,mvo,/xyfnd mwbd68 ,n stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the raft vibrates for a while.mvnyx 8fmdbd /, ,w,o6
(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 instw45p8qmx v; fzrument are tuned to play at 392 Hz (G) and 440 Hz (A). qv8p;w5x4mz f
(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 stret bb:xv-e8ynf0vfne 4(i9v,pp ched 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 the ratio of the wavelengths in the two sectionspf :nvbp(, ef bi-vy v049n8ex. (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 at a frequency of 264 Hz, and the tip of eac2*0bj*n1ndkzyu o,p w c2.jq piwa, 6sh prong moves 1.8 mm to eithepiw*2b ,j26y qpjc ,.da*uwo1nk0 n szr 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 oscillatn3hfz v4 g4/*p5o1ylrl iqrcag ) 4zw0es with simple harmonic motion of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the bqi 3r zcowg yl/vgan0 hl4 zfr45)41p*oard during the oscillation?

A string can have a “free” end if that end is attach3sr sy :p86xueed to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with one ey8sp 3xsu:e6 rnd fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — ea z3ys08oz g.mu3mv +dmch one-way swing takes 1.0003osydumz m.g +zv 083m 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 of8ajnp 5iry )km:t7(a spring can oscillate in the vertical direction or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longy)m5tirf:p87 a on(kjer, the period of the vertical oscillations or the period of the horizontal swings, and by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

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

  A 10.0-m-long wire of mass 123 g is stretched under a tension of 255 N. A pulse 19m2fanal0 dw,cs/ o fxw-cq; is generated at one end, and 20.0 m1 -s,ax; c/o0f9admcwq l2nfws later a second pulse is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspendx b ai g9-1)(xk/n1o vvhvyoj51q5jhped from a ceiling by a spring with spring stiffness constanjbo(vyh i15qh v)-5van/pgjk1 ox 9x1t 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 the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kq 4f8dy(g9vrfg car at the junkyard. The steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. What is the pervgfdyf8q49 (r iod of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–5bkim a-z)gp* s44.r ma8 (which also gives the dimensions of the block). You push it sidesz.a4*iga kmrp) - mb4ways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this vibration, given that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz