Give some examples of everyday vibrating objects. Which exhibi+qt9thi9yj1 1gr bd7b t SHM, at least approximatetb9y+jbq7 d1 i 1htr9gly?

Is the acceleration of a simple harmonic oscillator ever zero? If bl bcw6jl1 6d9so, where?

Explain why the motion of a piston in ,9h,; ipvn y)yzy1vkl06- hxwahoq1zan automobile engine is approximately simp 96h hxow,y1hnklayz 0iqv)1pvy-;z,le harmonic.

Real springs have mass. Will n9( / fwd2 j-fr1fpg.badrdq:;fq/m6f f:yb nthe true period and frequency be larger or smaller than givm2pf: / g b6/f1b.rfjq: q(fa yd9fddn;-wrnfen by the equations for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum spenj5 e xlghm4zf+.oe5l- kx0z0ed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a .b+lf 80ocljn9 sejb3 ui c(y8wxx5h+ vertical spring scale, and then is released. Describxc i9(0jo8 .ex+5w83luc fj sbbln+ hye the scale reading as a function of time.

If a pendulum clock is accurate at sea level, will it gain or los2ihq4;6daem on i8d5x e time when taken to oe 4i 6a;d8hinm d52xqhigh altitude? Why?

A tire swing hanging from a branch reaches nearly jusq9r;3qhh6 izze .g (c :xn)to the ground (Fig. 11–48). How could you estimate the height of the branch using only a stopwahc;u6i39n )rqqgzh: xe. z(jstch?

Why can you make water slosh back and forth in a pan only if you shake the ctgs(c0/rx27yp ua v7 pan at a certain frequens 7rcpv (acyt72/ux 0gcy?

Give several everyday examples of chu6fh9u7l6 mq1v 2wr resonance.

Is a rattle in a car ever a resonance phenomenon?+ex,e.e e-l pu Explain.

Is the frequency of a simple periodic wave equal to the frequency of its sot qy13zx6s 6dwurce?wxs6d1y3 qzt 6 Why or why not?

Explain the difference between the cs --+h0 8xzhuqut2osspeed of a transverse wave traveling down a cord and th-o0z8h+s-x u qht2uc se speed of a tiny piece of the cord.

Why do the strings used for the lowest-frequency notes d l p612r3kx sg/fv2;qn ilt7qon a piano normally have w2rqn26 ltv3kifd gsxqp/7l 1;ire wrapped around them?

What kind of waves do you think 9lvpt e l-yco-4r,,z mwill travel down a horizontal metal rod if you strike its end (a) vertically from zlv -opc-y 9mr,t 4le,above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase in temperature, but the buyep*w3f h(z+p lk modulus B is nearly independent of temperature, how would you expect the speh+ y*pf3p(zwe ed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in ampli.1en tp)jjah6 tude as they travel away from the je)nj ap61 h.tsource.

Two linear waves have the same amplitude and spe2/ x3vvp5p6 *7 vnvsuz7bjyjped, and otherwise are identical, except one has half the wavelength of the p 7vv23jx 7p bzuv5j s6n/p*vyother. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the be3 c8ft1 s6parn3ic:w7 8 vagkoundary between two sections of cord as in Fig. 11–33, the frequency13g 6 t8saepnvar i83kwcfc7: does not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there any places you cou4eo q+hp fr*jh(bp ,1gld touch it with a knife blade without disturbing the motio1qhh*4r(+ p p bfjge,on?

When a standing wave exists o4ijaz,ts fo wq-40o z4n a string, the vibrations of incident and reflected waves cancel at the nodes. Does th4so4f0ai z j-4qz tow,is mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one place to anotheruhq) v2z bc8w-, how might we determine whether the energy wa 2h)uqwz8b -vcs being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is;y0ycu .2 u/xwoudk+h the total distance it travels in one y 2k; dy uw.hcx/+uuo0period?    m

  An elastic cord is 65 cm long when a weight of 7gbbpm06tqw-(8to44uom / td y5 N hangs from it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” constant -w4/ptm(4o8ydoq6mtbbt 0 ug k of this elastic cord?    N/m

  The springs of a 1500-kg car compreiv( xn8 q-:tbtss 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 o vbtx(8 qnit:-f vibrations?$\approx$    Hz

  A fisherman’s scale stretches dw3 dw6xa-u6kue*on *i44pon 3.6 cm when a 2.7-kg fish hangs from it. (a) What is the spring stiffness constann4k u -6 d e*wpd3nui*4o6xawot $\approx$    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 0.60 az*pkb(*sd;d4.nj/bv ksp5kkg is hung from it. What is its frequency if only 0.3;j.vn *dszkp( 4/a5bd*kpbk s8 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass yh) , a(b1eq35lhd-+drwkgj33hptlo in Fig. 11–2 at times t = 0 , dlo ghb3qh-3lp(h 3ader1ky+5)jwt,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 inarp+b:5vma2 a a spider’s web. The web vibrates predominately with a freqa v mb+:arap52uency 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 freqsc f2dztv6en :.d6: oiuency of 0.88 Hz. When an additional 680-g mass is added to mi.ecfdzs:o vnd6 t26 :, 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 9+8vl*-e;r7ljz : w xwnn qv9:baljm i3.0 times per second with an amplitude of 0.13 m-iwn vx vr nlm z: e+q8:jjb*la;9wl97. 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 y6j qy bl-zp 4/i(y:nnSHO half the maximum valjb6 iln q:y- 4pn(yz/yue?$\approx$    A

A mass attached to the end of a spring is stretche;r/)fgym3v ox) b-v jed 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 str3 9 cldl) jowmqx5dsc 2/m ipv9;;ss1yetches a vertical spring 0.315 m. If the spring is stretched an additiojsl9;sl ymoip3cd91v)q /md ;xs52cwnal 0.130 m and released, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with sprittbqa2 h 6:,p p/,0uvou3tzjzng stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it i v:,3,/ju2auh0qp b6t zptto zs 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 popgunev r/j 4g+n1wg 0.200 m to “load” a 0.180-kg ball. With what speed geg w/4n+j rv1will the ball leave the gun?    m/s

  A mass sitting on a horizontal, f/sf jt)*s+jh ifzsps)isbmtn0)-52e rictionless surface is attached to one end of a spring; th ss* spf0i+t -)t 2hbf)mzj/i)s5ejsne 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 experiences a maximum acceleration of 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates according to the equation x = 0.45cos6.4t nnsuqfp:8uygbn 2;o-o0am*7 where x is in meters and t is 0-o:mnoqs; 7ugy *nnaub 8 pf2in 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 is the energy of a S:cw* vi c:mts0+am/jvHO half KE and half PE?w :m:smi ctv /+avj*0c ±    A

  If one vibration has 7.0 times the energy of a seco8tclqp d6/i+8i/c+kr ed*2jw lghh 2ond, but their frequencies and masse q 6dw 82*lt r/82jo+dhpih/lkce+ic gs are the same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin osci x(:xnyol3; /jqsa6s yllates from a vertically hanging light spring once every 0.65 3aos6xy nxj /l;:y(sqs.
(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 vertical springs, each 4evojrx+ *r 9j vft6(pwith spring stiff vx6j* pvr (re+tj9o4fness constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to 7/va m j:o1ett/l v)drthe equation x = 0.38sin6.5t where x is in meters and t is in seconds. Deterotlv tr:m )/a1v/ jde7mine
(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 exh2e8-i7/2 pw y* jzyr.inb swsamples 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 rqj4clfa h.u34 ndm/)mest on the end of a horizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial speednmlm/f da .4 4)chqu3j 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 spr9o 9a .hp65( -n(xavjnhvs)d ;qjjc5p iinak )ing stiffness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) withnx) via(6oqjih (;n5adj.p-s j)a9h c5nk9p v 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 oti f0 qlmugo1+8wh9 x94jgws,6 el5vsprings, with spring stiffness constants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes a 0.600-kg block attached to a fixed horizontalkh 4gwt0)kd 1p/arq 3k spring whosgd1 wk3r4h 0kap)qtk/ e 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 reac7 ,n9:auerjkc hing his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the unstretched length c7e,aur :nj9 kof 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. u4zd tpkl9q)4pb i7.aWhat is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pen3cz, y efn*o-udulum be if it is to make exactly one swing per second? (That is, one compley *u,-oz c3nfete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is it3czd)cr 2-h:ra7 cg+rzxv ll2s period on Mars, where the accelera+r3 hc 7rvc: drc-g2xl) azl2ztion of gravity is about 0.37 that on Earth?    s

  What is the period of a simple pendulum 80 cm lo pqd/39k2hapv ng
(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-t )3eg3lh)i-n 0*gwfvg2wo z(w)ayingvn v: a mass of 365 grams, and it is released h3)znvv i-wf23)nt gw e)v -(:0ngo*igyaglw 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 penrq9nzkwv4f nt 5 (j 1o)fkhv8e-ro5y.dulum has a length of 0.9930 m. If the clock loses half a minute per day, how should you adjust the length of the pendulum? shortened (kkv95vt18nf rn-) qf e .wyhoozr5j4by    mm.

Derive a formula for the maximuccq8f)b/-c,h36g d fmngbte,t(gaj 5m 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 oscillateseo+t))do.axsc .. dz.:ij tuh at a frequency of 2.5 Hz. At it is released from rest starting at an angle of x e d:. .ot.hu)jtis. c)daz+o15 $^{\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 t 138gixd-huj kh1b. p.s lyc7ghe bow of his anchored boat every 3.0 s. cph 8dgij1hxb.1 sy lk-. 7u3gHe measures the distance between two crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and:lb ycx:30 px.zu n/md travels with a speed of 343 m/s Homld xxn / yc0::.zubp3w far apart are the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (kilohs1j:a,l7ads zertz) and tra,7za jsa1l:sdvel 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 i/r a4:,p mv-hzyt*t 9kl hq5jsn
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic mod,9z;m nq cmrr-)db np)oeu -9l7jev c9ulus, but one is twice as dense as the other. In which rod wenp m cl)7zm qrdnru o9jbe99,;cv -)-ill the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apart. If thewrwdg8,suqnz 2: ,3ce tension in the cord is 150 N, how e,qurw:,dz 8ng2 c3s wlong will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to th z,a 1z*)kev7elm m,aee 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 it,k zaevema,7mel)1z* s 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 65 09rkdppknv1xey 9u his ship 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 kye90v np9d 6px1rk5u is the ocean at this point?    m

  P and S waves from an earthquake fayn8c.0eqs,k8ec s6qa 0 e e:travel at different speeds, and this difference helps in locating the earthquake “epicenter” (where the6eqq ea0ke:y f.8ce,s8casn 0 disturbance took place).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced surface wave can be approximated by a sk x 36jlwbb/it-gqr1k9*qo-lrk,w a+inusoidal 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 grou3li j /g krw+-xo6blr9-abq tqk 1*,wknd? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplitudes, of an earth3yf;2+llw9;(r et ioy/ oqa mmquake P wave passing through the Earth and detected at two points 10 km and 20 km+rm eqwm ;;li29 ay3ol/( yfot from the source?(a)    (b)   

  The intensity of an earthquake /rhyi6/m5ptpm2j m1xz5 tla4wave passing through the Earth is measured to be itt1m5/hp ja/rl4my x2zp m56$ 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 oe kk vrp(+x77of the same frequency travel through the same portion of the Earth, but one is carrying twice the energy. What is the ratio of the ample7ovkx+ k7 (rpitudes of the two waves?   

  Two waves traveling along a stretched string have the same frey rq/5 bja)wv9quency, but one transports three times the power of the other. What is the ratio of the amplitudes of the two wavv) wq/ja r5yb9es?   

  A bug on the surface of a pond is observed to move3*z2uxvklygg .m7p1e 0 3hb rm up and down a total vertical distance of 6 lyz7rk3umg0px. hv1e 2*3gmb.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 toward each other. (a) Sketchqt+ 6meeevtu, +7+e wt the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) Ie,eeq+tet+6 uv7 +wtmn 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 ve p*keax;f pbj)tz4:9 ibrates at 440 Hz as its fundamental frequency, what are the frequencies of the first fo4:p a;)bexpkz9*t ejf ur 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 will is66h v/nhke3yt vibrate if it is fingeys n3k6h/hv6ered one-third of the way down from the end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequency of 280 Hz. Name h* pj3s).jh(bj4847jx xy h7h *)boo m sjxupgat least three otherm3bxhpg( h 8s*j.jo)u7x4jo 7bpysh*jxj h)4 frequencies at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the frequenx2 ni 6bhlwi +rz1p;fuz86t b9cy of standing waves is 475 Hz, how far apart are two adjacent nodes?b 8nwhbf9 i2trzxp1u l66iz;+   m

  If two successive overtones of a vibrating string are 280 H*+y52r4gsmjy li. ifb lbys -33renv /z and 350 Hz, what is the frequency of the fundamyli.iyj25 3 43fv* g/r n+rsbe bsmly-ental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 got;2hw h*mu( n. 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 freo nmwuhh2t(; *quencies of the fundamental and first two overtones?    Hz

  A particular guitar string is (w3t w5jon lgas p9 4mro57l:ssupposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. jos l:4ns5 g9wl7mro3( tw 5paBy 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 st8jngzop +f+ln*0i z, hring is supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By whh0,zg+8*+npjn of i zlat percent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-amplitude mechanical 60- fywvo.ja vs fij3.181y v.p8eHz vibrator. The string’s mass sav e y. vjfwfp.oyv1 88.j31iper 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 bez2sol2z( nlf ))kykwh60fr3w adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying L be2z63n0w2wk fof)hy(krl )zsltween 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at just t+;+ld -6gkbgytvrc w ;he right frequency, the water alted;6c;+b wg ytgkr+v l-rnately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundary within t1vfl3-cet y .che Earth between two kinds of material. If it ap l.v13t-eycfcproaches the boundary at an incident angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “shelf” where the velocity cna ce1x26gk:q h4emj- hanges from 2.8 m/s to 2.1 m/s If the inegnj4c- qx6:khaem1 2cident wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is travelingl4i):l yfc :m3j4byux n8de* h in warm air when it hits a layer of cold, dense air. If the sound wave hits the cold ai 48)i4*:3 fx ylenyjmc:d hlbur 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 b 0(dfjigi1,mh8; xad koundary between two types of rock at a 38 xfidki8,a jm;d0 (gh1 $^{\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, ny/0ih x/w5zfg:o ;msnbr )c (the dish has to be pointed in the direction of the satellite, but an error of abou)i myc;gzrn5x/nswf o0/(hb :t 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 velociuxbo9 k0v;q4aty 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an uvxaq0; ub4o9knusual 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 u7kvds70xf:8 1f hvdz550 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 conser h :1kx 7vv7z8fddu0sfvation of energy.]    m

  A 65-kg person jumps from p)+:i50vmc)w kvfr:zw g lxh8 a window to a fire net 18 m below, which stretches the net 1.1 m. Assume that the net behaves like a s+ xr f5hv :v:lip8gmckw)0)zwimple spring, and
(a) calculate how much it would stretch if the same person were lying in it.    m
(b) How much would it stretch if the person jumped from 35 m?    m

  A mass m is gently placed on the end of a freely hanging spring. The m2 yg o3-ugs9a7wf3pufass then falls 33 cm before it stops and 3 3 s ffa2ugg9ypwuo-7begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a spee.zcehey )tz)0 7 0f wfjiaa;)kd of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffness cons;z)ctj)i 70.0 fkwzh )yefaea tant of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of coffee (diameter 8 cm) at just the right pag 1 gsdg+xgw;)ce of about 1 step per second, the coffee sloshes more and more until eventualldxs;w1+g ggg)y 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 cea t6ht1nf7;ps)l il/nnter of a 33-rpm phonograph record have a wavelength of 1.70 mm. What wil;6 alnhp1 itt/ )fl7snl be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t svqej 8-i(h3k where x is in meters asi3hk( - qjve8nd 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. What is its )lt tt a81ilj(frequency if it accelerates at)tlj(8t 1 ltai 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on the raft, 5ne7fl , 3hrxoxiz1s*byn5ec/ ,+efa it sinks 4.0 cm deeper into the water3z1n5heol+c,n/xbyfe 5ia f*e x s7 r,. When he steps off, the raft vibrates for a while.
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a musical instg n 8l+vxe(6crrument are tuned to play at 392 Hz (G) and 440 Hz (A). c+x( lne 6vgr8
(a) What are the frequencies of the first two overtones for each string? G : $f_2$=    Hz $f_3$=    Hz A : $f_2$=    Hz $f_3$=    Hz
(b) If the two strings have the same length and are under the same tension, what is the ratio of their masses ($m_{\mathrm{G}}/m_{\mathrm{A}}$)   
(c) If the strings instead have the same mass per unit length and are under the same tension, what is the ratio of their lengths($L_{\mathrm{G}}/L_{\mathrm{A}}$)   
(d) If their masses and lengths are the same, what must be the ratio of the tensions in the two strings?   

Consider a sine wave traveling down the stretched two-part cord of Fig. zjxmha/ vhz22,xmss-3ng (*wgp)l9m(y4hs h11–33. 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 23j h*ssgg9,(xl yhpmmh/)n x(2wz svma4- zh heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the tip of 1im78s;yu+k xs hpq6peach prong moves 1.8 mm to either side of center. Calculax+ hpim16u7sq8p syk; te
(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 harmon a.u7u+7 ztj.+dth drjic motion of frequency 1.5 cycles per second. What is the maximad7t++.rudhjj.z 7tu um 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 g+z u7ess)usy-/*( rzn/bjcl 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 end fixed and thze+grzs)b(7j/l / y*-nusc su e other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each ol3/olmm *rnx :wx44x o0w 7hnsne-way swing takes 1.000 s7xwn lmml/ n3 4ws0o:x*hrox4.
(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 5xk.-esvtv+/vwgmg :can swing as a pendulum of small amplitude, but not both at the same time. Which one is lon+ .etk: vgvms/ -g5wxvger, 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. 9mtu bg)v8rs 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 u ms).8rvgb 9tgenerated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by wgk 6rz1kt6m , (b1qsma 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 wsk(r,gq bm6t 1mz6k1stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg ca;j3:2bg v qpk4wql un1r 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 period of the bounci qn2:lw u3gk4jq;1pvbng? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (which a s2y1pzv/p- tflso gives the dimensions of the block). You push it sideways as shown, and then you let go. The-tyz2 pfp s/v1 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