Give some examples of everyday vibrating objects. Which exhibit SHM, at leastnn rz3t-e mao,e 8+,bq approximatelyon me q ,,+z-8nebr3ta?

Is the acceleration of a simple harmon3cb. j4,hgrmoic oscillator ever zero? If so, where?

Explain why the motion of a pi ys : 51siv3c7wcqf0x8 g:lxxqston in an automobile engine is approximately simple his35xqqcv0ws 1 g7yx f::xlc8armonic.

Real springs have mass. Will the true period vk uwf2sdfu/ 2k61x.vand frequency be larger or smaller /uvsxf2f16dw v u2.kkthan given by the equations for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of16od qp8uue8*k zaa ,i a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertica3crup djw2,3n l spring scale, and then is released. Describe the wpd,rc u3 n32jscale reading as a function of time.

If a pendulum clock is accurate at sea level, will it gain or lose time:ytic m/ ;q0g r06ydtf when taken to high alt f:q/ry g6myd0t0tic ;itude? Why?

A tire swing hanging from a branch reachesr4;kb/.su,(bnwr qsf nearly to the ground (Fig. 11–48). How could you estimate the height of r (fsw,4ubrn; .qk/sbthe branch using only a stopwatch?

Why can you make water slo h*9un0vjhd-msh back and forth in a pan only if you shake the pan at a certainhj *-9umdv 0nh frequency?

Give several everyday examples of l* dfsm:7foj *resonance.

Is a rattle in a car ever a resonance phenomenon?z m/ ewqmwfw,47*bbr+ Explain.

Is the frequency of a simple periodic wave equal to the frequency of its souryrtjtoj;,)5.s .zdmwbwj*( gce? Why or why not t(gw;.tyrjs.jjbo,d wmz 5)* ?

Explain the difference between the speed of a transverse wave traveling 8 o-ngk3bv.ou down a cord and the 3k gvn.b-ou8ospeed of a tiny piece of the cord.

Why do the strings used foqyj48(c +ahln gh4n6fr the lowest-frequency notes on a piano normally have wire wrapped around them?gq 8y4nhnf4jc + lah6(

What kind of waves do you think will travel down a horizontal metal rod i3g8)um : n3 +vi;rkltd2afstvj2j 1n cf you strike its end (a) vertically from above and (b) horizontally paral;)n3cl+g2 j3i t f12 vtnamsj:rkd8vu lel to its length?

Since the density of air decreases withp6okm(z 6e -tsk0af b( cz-cn-9k 2ski an increase in temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves i-bma s 0k2(sk-(z ocz9kicfkn6-t6pen air to vary with temperature?

Give two reasons why circular water waves de l2.2(cqvm*zvy2zhd)u0 :0syi qz yiacrease in amplitude as they travel away fro2vvy zyciz:a.yi(2d0qz mq*u s) 02 hlm the source.

Two linear waves have the saoys,:q 0lz7v2zqfpu 3me amplitude and speed, and otherwise are identical, except one has half the wavelen:py 2 z0z3v qfsol,q7ugth of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sections of cor2zaoja)l j;f -jv;(and as in Fig. 11–33, the frequency does noj vo j za(n;;2f-alja)t change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, sfm yujd/nz60b: z 2bp,hi r+7are there any places you could touch it with a knife blade without disturbing the mbs d zf/2ihy ,b0u7z+p6j:mnrotion?

When a standing wave exists on a string, the vibrations of incident an(). 6nnvubr+esvaq2pk 7eyv0d reflected waves ca+.0(vuq ypr) 2vvab see7n6nk ncel at the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted f.rn42xwlx7 n from one place to another, how migh42wx f7xrl n.nt we determine whether the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoesd, x)q0do(x8ws8 jbscsy+w6i SHM with amplitude 0.18 m, what is the total distance it travels in onec8s6xq,dw 8s)bw oyi( sj+0xd period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it but is 85t*s g*7k- :sy;khp zzw cm long when a weight of 180 N hangs from it. What is the “spring” constant k of this elash7 t*zw;spsk:kzg y-*tic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg driver gc 6b- yyqvv 9roa429 c)yd4nwtets into the driver’s seat. If the car goes over a bump -6v b94awd2 4 ycqcntyvr)9oy, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm whenxv6- 9d sr;uhx3 p0gof a 2.7-kg fish hangs from it. (a) What is the spring stiffnepg fr3s69xo;x-0 du vhss constant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a frequency of 3.0 Hz when a mass aoy (aotrzd: j 96/7ntof 0.60 kg is hung from it. What is9 rd ajnz/ 7ytot6o(:a its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in : ..l7vgs gmbbp:w kc((wah;tFig. 11–2 at times t = 0,;hv:: tgb b .. w(wmk7cpagsl(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 a spider’s web. Th r/4m0 htwyxwq o o3g*s*.q.gae web vibrates predominately with a frequency of 4.0 Hz.o q03xm.t *qr.gswwg*y ha/4 o
(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 frequency8r86 mwb0 gmyo of 0.88 Hz. When an additional 680-g mass is added to m, themor60y 8 wgmb8 frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vib e9ea :p9)umygc)i.y(hyaro )rates 3.0 times per second with an amplity))9 uah( .riyy:gpoae c9e)mude 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 speed o:y15x+rxaemtq t15g 7e agr u fb(*:phf a SHO half the maximum valueqe1(5:a1 *rfxg gebxt7myp:+ 5 r uaht?$\approx$    A

A mass attached to the end of a spri e-r ayfe1zm4*ng 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 *y7xjxee +. qpq76 a rxaj)kg7 e23plsspring 0.315 m. If the spring is stretched an additional 0.130 m and released, how long does it pqxj.) e7a7j6 gxeersk*py 3q2+x7 latake to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spq;/ xq -bgivq4 fv7:dnring with spring stiffness constant k = 280 N/m and is exf4vvn-q: / g;qqb id7xecuting 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 80.0 N to compress the spring of a toy popgun 0.200 m t.qgo4c / )c;qa8fnlwhl2g mf)o “load” a/f 4cqg)q)w 8 .hl lcofng2ma; 0.180-kg ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is att6/ ;)3jgdzl qe jqgz85n w0uvzached 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 t0 zd6l85jq 3jwnzegvzu/)q ;g he 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 vibraph i(q4 jh8ba(jpt (cww+h06vtes according to the equation x = 0.45cos6.4t where x is in meters and t is in seco h+w08wv(h 6haqpi bt((jcjp 4nds. 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 energy3f9fz tjkd/s2 ql7an. of a SHO half KE and half PElf.t2 7djn s3z9kq f/a? ±    A

  If one vibration has 7.0 timkc 46 ;jv shnh- b-um(eebgh82es the energy of a second, but their frequencies and ma(;uvmen6b-8h eb hh24sk cg-jsses are the same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hangi/ejigh:n gig74g f1(f ng light spring once every 0.65 s.gigg 4 ie fhg:fn(j7/1
(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 twowj2g3jcu; ,9qldy ii) identical parallel vertical springs, each with g,dcyj;i3 2l i) w9uqjspring stiffness constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0lwlaz3b)js6vz 9 6) en.38sin6.5t where x is in meters and t is in seconds. Determinln6zsj b9)aw3e6vlz )e
(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 any6z- l,qt/oog) kgpu( d 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 = 1 djac.3 uf8sj*24 N/m) is struck by a hammer, which gives the mass an ini j*cf.s 83aujdtial 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 wi/ yetb3:xjbo/nze 0 2ith spring stiffness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The/: 0xe/oi ze3ny2btjb mass passes through the equilibrium point (x=0) with positive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two spr9ssuyzy:ve 4 *ings, with spring stiffness constants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes a 0.600-kg block attached to a96 s/jwwfp cj k0wxs4f((u+v y fixed horizontal spring whosfy64x /f(svpj+w ws9j 0kuc(we spring 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 a high bridge. After reachinx3n0vl+i 8uv2olwr(s )vmi)-1of xh bg 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 l ulw8 )vx0 his2bv 1fonvl ior-m(+x3)evel 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 exactl*mej ::gh(ko pig; y1ny 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is t )hg:i4t baazbe*0)y ko make exactly one swing per second? (That is, one complete vibration takes exactly 2.0 0)4a)eh*yabitg: zkbs.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on Mars, u+r i vu0p 9ozuwg84t(//wuc+)gv aj mwhere the acceleration of gravity is about 0.37 that on Ea)vuu w+0jo 9 uw /gz4crp(a utg8v+/imrth?    s

  What is the period ot/hcemc*f 4 3/1zjtra 8fq anue.1d5 xf a simple pendulum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simpn+2+me f07g0x i6 edab5+szirk pw z5jle pendulum is 0.760 m, the pendulum bob has a mass of 365 grams, and it is released atmwnkgef50+ja6p+i 7r5b xd0zes 2z+ i 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 0.916e+o to p wbe,)vyv5k930 m. If the clock loses half aoeoye1 w6vt+bk)v , 5p minute per day, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximju+0t6i ; xd1ao+6e2rf ea6ugwktz1fum 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 frequency of 2.5 Hz. At it 2m0y2q4q 4a.cycd svu1ax2vhis released from r hvsmxy vyuac4a24q2 c .dq021est starting 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 t/8vm7l)zwi 9q3nx ) hmeto2g anchored boat every 3.0 s. He measures the distance between twoemv)nox tzi/7)gql h mt3982 w crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with a speed of 343 m/rt p /2afz8*j)fx n.pws How far apart are the wave crests (compfpza.rnf x*8 pt)w2j/ressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (xh j76ee.ne:y sq-,aqkilohertz) an7 e6j-e:xqay en.h,sq d travel 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 longitudinal waves in j c u; mn)qs2exk7stcneq(;0(
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus,q;t8vbpyjov/r7 dcq :)4q -b w but one is twice as dense as the other. In which rod will the speed of lowb)pcqrj : v 8/-4q bt;7voqydngitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched betw bn(x9xw8msq+ ru yt74een two supports 28 m apart. If the tension in the cord is 150 N, how long will it take a pulse to travel frn (qwx+7um8y4bx t9rsom one support to the other?    s

  A ski gondola is connected to the top of a hill by a steel cable of length 6y9bsl*hw 2sq v*ruv+vwp.w,9 de6 ;zu 20 m and zbq wu2p+evrlw, v*hy96sd s .;*wvu9diameter 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.
(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 hi(m d9w7isu 3s de:)tqrs ship just below the surface of the sea. He hears the echo of the wave reflected from the ocean qt3 ( dru :is)me79dwsfloor directly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel atep9s4de8 9p 6adry-02 ,wywhcsiwpn4 different speeds, and this difference helps in locating the earthquake “epicenter” (where the disturbance took place)9 wyrsh42ins9awy0 p-cd6 dp8wpe4e ,.
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced surface wave can be approximated by a2xf5fk*2a ,fpsi 1f my sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, w, 2f2f1xpmk*i5 ffyashich actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplitudes, of an ear jhqki:4 -/ackthquake P wave passing through thik ak/h:cj4-qe Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an bvhhx7,)ub2h7xno/aor. h7-5 jlzhcearthquake wave passing through the Earth is measured to be brh7hvh/ ou7 lx)57canz x .-2 hojhb,$ 2\times10^{6 }J/m^2$ at a distance of 48 km from the source.
(a) What was its intensity when it passed a point only 1.0 km from the source?(round to one decimal place)$\approx$    $ \times10^{9 }W/m^2$
(b) At what rate did energy pass through an area of $5m^2$ at 1.0 km?    $ \times10^{10 }W$

  Two earthquake waves of the same frequency travel through the same pp.hbim/mil 5 lvku * ct0i*t9,ortion of the **mcpk mi9 5,l biv/.u0i tlhtEarth, 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 the same frequencywmrn ;nvzr)3u*t 3n bxs-og(), but one tranr3 gnb ot-wnmz)(; )x*sn ur3vsports three times the power of the other. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to mfc pqiq .3hz u/djc:g-r-6*zbove up and down a total vertical distance :cd*/3pzqjr6.ib qfc h-u-gzof 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 maximum KE change?   

The two pulses shown in Fig. 11–52 are moving 2pwbp;j *o7j itoward each other. (a) Sketch the shape of the string at the moment thepi7 jw*b 2o;pjy directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundamenea36oh(nmu026 exs7qy a :ougtal frequency, what are the frequencies of the6a hensxque0m3:u ayg6o27 (o 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 wy a)11kaoeiw 5hat 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 vibra 5e1ai1y )wkoates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequency of 280daz.iu, 9p;m: ,bs kgw Hz. Name at least three other frequencies at which it will resonauk: z md .g,ap,bisw;9te. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the frequency of stajkm(wnfa r/otc3:y1rm+a v+ yme2*3rnding waves is 475 Hz, howo3rmeywma v/ +t r* +:mykr123afjc n( far apart are two adjacent nodes?   m

  If two successive overtones of a vif14y4l7dp tbibrating string are 280 Hz and 350 Hz, what is the frequency of the fundamenta 1lt44dpi7y fbl?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. Th sw3hg4gu1 ;die distance from the bridge to the support post is L = 62cm and the string is under a tengh 1dwg3s4i ;usion of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 40dng7k4m oj q200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in tng4k4 j0q7mod he 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 Hq ;u.r(vo ey7l*+2 weoak8wt wz, but it is measured to vibrate at wov;+ew .*l8 7ua(k yoe 2wtqr205 Hz. By what percent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizon0zm()z :dt. jnqv* rrptal string is attached to a small-amplitude mechanical 60-Hz vibrator. The string’s mass per unit length is0zj .rz*rv(npt dq m): $3.9 \times10^{ -4}$ 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 the pulle/6ljsr3gfeu5/ fugd- y. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be /g/ g 6-d3uursf5j fleachieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth iwno q(1;6djhg oed,tc35ky 0rn a tub at just the right frequency, the water alternately rises an0o; 65rcejo g1 hkqn,(3tyddw d falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundary within the Earth c:ze0 qi40r-q1vr )q rfhr kol9xn5)zbetween two kinds of material. If it approaches the boundaryr l94 crkqx)i-)fe:q rzonr zq50h0 v1 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 am50kkypzr- eo6;x0 i qrf qz21xw4qc g-z:7bw n underwater “shelf” where the velocity changes from 2.8 m/s to 2.1 m/s If the incident wave : zkw p7orbqf4qx- ie0x rc- qg6wyz;zm1k205crests 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, dense (e) kpcj kb)lww/xi m -d5,8fhair. If the sound wave hits the cold air interface at an a5)k-)wl fdwm h,cxeb /ip8k(j ngle 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 be.kufa.xjv+ + jtween two types of rock at a 38.jkf+vxaj .u+ $^{\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 t;jxjg 9g;-kry.iq, b4-zy xghhe user’s manual, the dish has to be pointed in the diihjxy r;bz x 9kq;g.,yj-gg -4rection of the satellite, but an error of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 250 km and velocity 750 km/h travel,v0u3suz 2 efds across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do thsz 302udv,e fuey 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 spy2gsq u d6m /;rxgh,zsdm93i+ring stiffness constant of 550 kN/m Find the maximum compression of the bumper if the car dsdq,si6/9;2ggzr hyux +3mm, 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 firth/wge ;c 2 0*hpty+ope net 18 m below, which stretches the net 1.1 m. Assume that the net behaves like a simple spring, p 2/t*o;tp+chgy0whe and
(a) calculate how much it would stretch if the same person were lying in it.    m
(b) How much would it stretch if the person jumped from 35 m?    m

  A mass m is gently placed on the end of a freely hanging spring. The mass th)4p *okm(rbo oen falls 33 cm before it stops and begins to rise. What is the frequency of the os komo* rb()po4cillation?    Hz

  A 950-kg car strikes a huge sposog tcf.by hf*h651l sg1 +m9ring at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m.fgo5oc1.tbh h16s*m gs+ y9lf (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 cup of coffee (diameter5mutgernhb*a c2n0e ,ne2 e f(:0m0 xz 8 cm) at just the right pace of about 1 step per second, the coffee sum2b0(2c,ft nmer eh*xgne :n 5e0z0a loshes 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 gro6, g) mjcxfj /(dj*mupove 10.8 cm from the center of a 33-rpm phonograph record have a wavelength of g(6fdm/,jx ju)cj*mp 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibratw3a9tb q(zwpa.j 8*k eze7a/xv ogi/ )es according to the equation x=0.650cos7.40t where x is in metew )*a/37ejoe qwkatxi .a/8vzb(9gzprs and t in seconds. Determine
(a) the amplitude,    m
(b) the frequency,(round to two decimal place)$\approx$    Hz
(c) the total energy,(round to one decimal place)$\approx$    J
(d) the kinetic energy and potential energy when x=0.260 m.(round to one decimal place) PE$\approx$    J KE =    J

  A simple pendulum oscillates with frequency f. Whacd48/cvmszs 2y6h ,vm t is its frequency if it accelerates at zc/y vv,4 8chds mms620.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on the raft, itt0:(tanhws-q sinks 4.0 cm deeper into the water. When he st- :h0wn(asttqeps 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 instrumen b(daq )j5u2rvt are tuned to play at 392 Hz (G) and 440 Hz (da)ujv 2(5rbqA).
(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 stre()tpc8 u *pomctched 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 sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lc)(*u cpp otm8ighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the (/ d* dmt7oyjmsxm-.xs ju+ /dtip of each prong moves 1.8 mm to either side of center. Calc/dtx +m.oyd-mds /s*m 7xju (julate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simple harmonic motion of frequency 1.5 cyceml* o2)qyz i1rw ,:q6-t kfrj51 ggo/chtd-kles per second.6qqy moej-fk tzgd2hrtc1 5ol *ki,-g: w/1)r 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 to a ring that can slide sj6,k7l11 lt e5rq8lczv1trb without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a sttq l,vts el1k568b1rlz 1jcr7ring with one end fixed and the other free.

  A “seconds” pendulum has a period of exactl76zqs7dp+4o c-egfe ey 2.000 s — each one-way swing takes 1.000 s.-dg4cqose7zf7p6e+ e
(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 vqz(r g j,p5ut,rolj705b i t.aertical direction 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 pjia,l. rtr,zb 57gto5ju (0q 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 maspvp449wz nk: zs 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 wiz 4 :v4n9wppkzll the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spring with spring.pee -8to 3j6* tgwlnc stiffness constant k. A penny of mass mnj l8wcgop6et* 3t.e- 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 120sr+vip2w //:vodr*ot 0-kg car at the junkyard. The steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starto: 2ov/ rrw *dvpsit+/s the car bouncing 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 (a2tt4 i md+uxas shown in Fig. 11–58 (which also gives the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a sprin(+axt4dmi2u t g, 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