Give some examples of everyday vibrata)v . ,gorkqpctb:ls*z5 b h*)ing objects. Which exhibit SHM, at least approximately*p*h ckrsq5, ):tlbvg.)azo b ?

Is the acceleration of a simple harmonic oscillator ever zero? If so, wherek n itcxktk7- 0qa:8.y?

Explain why the motion of a pistonuawqiz *xfe/- v3bb6- in an automobile engine is approximately simpleb v3q*zwf/--be xi6ua harmonic.

Real springs have mass. Will the true period and s3jrl) ufzus /rh9p8pzk 7//afrequency be larger or smaller than given by tuas p//rl7s) zpjk rfh/z893uhe equations for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple harmonic oscillator .m8x yff i(jxv0 i/-ei(SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scale, and then0 68g3u d.yqkv(jcyql is releaseq.(d3yjkv0gl8 6cuq yd. Describe the scale reading as a function of time.

If a pendulum clock is acc) l4xz ,jnz bqhu30vh.urate at sea level, will it gain or lose time when taken to high altivqh3 z0u xl 4b)jh,.nztude? Why?

A tire swing hanging from a branch reaches n1nu ws 9 wv6ldt;e5ic+early to the ground (Fig. 11–48). How could you estimate the height of the branch using only a sto5l uwt619sw;nie d+cv pwatch?

Why can you make water slosh back and forth in a e*qvmj g. ovdg/xew)s4, r*;0f/ao,pgrpv 1dpan only if you shake the pan at a certain frequence.;0vq4ra,go,eop sfd vdw/ xg)p**v1 grmj/y?

Give several everyday examples q2gaoyh15ac1f xd 6v5of resonance.

Is a rattle in a car ever a resonance phenfa8+/jmpv :w9il uos+ omenon? Explain.

Is the frequency of a simple periodic wave equal to the frequency of itsblse; g 1k /z*4/pnymg source? Why or why mn1l/4gzk;s/y p*b genot?

Explain the difference between the speed of a transverse wavcmy(s a-d9 iw;e-p3karpw ;2 qe traveling down a cord and the speed of a a-ck;2dq -ia pwe;wsrym 9 p(3tiny piece of the cord.

Why do the strings used for the lowest-frequency not+24oqzo j1g s9iu v+rfes on a piano normally have wire wrapped ao+rji+19zvq fo2 us 4ground them?

What kind of waves do you think will travel down a horizontal metalmuuml ,fg1 t:; rod if you strike its end (a) vertically from above and (,lfu mtm:g 1u;b) horizontally parallel to its length?

Since the density of air decreases with an incku38; jzg nlb-b 52lbsrease in temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves in air to vary with temperat-z28b;3 llb knsu 5bgjure?

Give two reasons why yqed/j 2)(o)8 jnqywtcircular water waves decrease in amplitude as they travel away from to (yj)/ enqt2dw8)qjyhe source.

Two linear waves have the same amplitude and speed, and otherwi: /,vps260ao epxkmxnse are identical, except one has half the wavelength of the other. Which transmits more energy? By whax p2mxk:eav6/sno,p0 t factor?

When a sinusoidal wave crosses the boundsu e.oq6ij6sh0 ;t qc(ary between two sections of cord as in Fig. 11–33, the frequency does not change (although th(6j; uh.qsseoqci t60 e wavelength and velocity do change). Explain why.

If a string is vibrating in threevj0yw-2oh t b7 segments, are there any places you could touch it with a knife blade without disturbing the motith -20b7 oyvwjon?

When a standing wave exists on a string, the vibrationkl38h4e +yigyje.w)x jo6g9gm2 f 3 hzs of incident and reflected 32+z lg)jijk oyg6w4gh3eyxf8h .m9 ewaves cancel at the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from onev,sl .cp.p9n t place to another, how might we determine whether the energy was being carried by particles (material bodies9lpn tc,vs..p) or by waves?

  If a particle undergoes SHM nhzqj2s.:qtdt 8 i;n9 with amplitude 0.18 m, what is the total distance it travels in one period2i j8 :q.;th n9qsztdn?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it bu j ,vjv4u-cr2sc-x7usk +juw3t is 85 cm long when a weight of 180 N hangs from it. What is the “spring” constant k of this elvw rc42jjj-7, k+uuus sx3v-c astic cord?    N/m

  The springs of a 1500-kzb hz/hxx q:vu-2.q3pg car compress 5.0 mm when its 68-kg driver gets into the driver’s seat. : pvx b-hx3zh2qz /.quIf the car goes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs w rrq,rv0c/ pal254 bcn9+qd/hy6 miw from it. (a) What is the spring stiffn c+wnr/wbq0 6hvq249/my r5,ia dpcrless 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 asq 1 +de;w95f.pd jouj frequency of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency if only 0.38 kg dpfejd 5s.;wquoj91+ hangs from it?    Hz

Construct a Table indicating the posit:s t ),go,mdw3tcg 6odion x of the mass in Fig. 11–2 at times t = 0,t = :omg)t6w c,d3tgsd,o$\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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. The web vibrates po xx16x66y mlf5b3ri dredominately with a frequency of 4 56o31xm yxfbixrd66l.0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a spring vibrates with a frequency of 0.88 ;n0 nsg q7n0nbqys/3pHz. When an additional 680-g mass is added to m, the frequency is 0.60 Hz. What is the ;bnn/gn qspn7ys0q03 value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per second witvld6((l5zpsvt*pl2r6 w fx6u h an amplitud6pwrdl5*6lt vp(( lusv 2f6 zxe 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 eq7hhf:h 3 d4ic8 akdw8ruilibrium is the speed of a SHO half the maximum value?:8k8 i fwcdr 7h4dahh3$\approx$    A

A mass attached to the end of a spring is stretched e mjo.e cx2dlt52/jw1yrpm.d0 oqg5, 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. In)) aa/c j:smpun-nu+f the spring is stretched an additional 0.130 m and released, how long da: njan+ c)n/pusum)- oes it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is att2vn;vr(q ek ,lymg2p7ached to a spring with spring stiffness constant k = 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 27q2,glme kp vv(ryn; 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 t7i sxwg0st(v 2-*wnno o compress the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will the ba -n(sns vo7xi*w02tgwll leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface iym luth4; ri9p:) scpfp20 e.08jqgris 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 experiences a maximum acceleration of 15i2smp.:uqcgy fr; 40)j9 te8pp0ir lh $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates according to hrt rc0aea.fl+i; j4 5the equation x = 0.45cos6.4t where x is in meters +4. ;r0aa5rctfle jhiand t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from ;r-sc 4 j 9j inl4gpwk0dmj3hxj/-q;xequilibrium is the energy of a SHO half KE and half PEd9j kxx; 4jjr/ -3;l wqp4cjg-n mh0si? ±    A

  If one vibration has 7.0 times the energy of a second, but their jf+-tb,/mwl 6lq6etde/ yz)* gfe57zym2 appfrequencies and masses are the samefta /m fpwe lq6mgey7l d/ 26yzj5 *eb,p-+tz), what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates fdfe4vh89 cp:zr z dhx.r6n;6( bx/gn7cx)bca rom a vertically hanging light spring once every 0.65 s. cn69g:. c 4ahhx)/ (z 6prncrbxdxzd b87ev ;f
(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 iden12qba8 r 6sy b7wbwoy*tical parallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What will be the frequency of vibratiosb78yy1w 2wqo6ar bb *n?

  A 300-g mass vibrates accoti.ka.nita:x ri nsi+9g 4:;rrding to the equation x = 0.38sin6.5t where x is in meters and t is in seconds. De;ain +r9t t .ki.x:igs: rian4termine
(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 anm; q/-b rfce2qvn p9k+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 horizontab :ph;dj9lcdea /+e0s i+w t)4cq+c ihos (d*hl spring (k = 124 N/m) is struck by a hammer, which gives the mass an inh9+c/ah:dbowe(cj*+di; )i qestp +ls4h dc0itial speed of 2.96m/s Determine
(a) the period and frequency of the motion,    s    Hz
(b) the amplitude,    m
(c) the maximum acceleration,    $m/s^2$
(d) the position as a function of time, x = (    m)sin(4.08$\pi$t)
(e) the total energy.    J

A vertical spring with spring stiffness constanlsi:bh4b9) ma *:;rljhkp4v kw q-7ee t 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) 4-erkb jlvph9b w* q;7ai eh:4)lmk: swith 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 spring stiffness constjn7; ip1,t fe 4.fdvkv ag;*zhants $k_1$ 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 horizontal sprin hse;:j 39-twi 2lrdovg wh;oi3h 2wlr:-sdv ejt9ose 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 reu;qvwx/0( u)s0ts k(hy 6xzmv aching his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He fik0 q/(z06vs v)xuuswth ym; (xnally 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 exacta r-ryzocq46fuh13d* mi s *4sly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple penss)*jl 5edhakv4 s3 g/oag. 8pdulum be if it is to make exactly one swing per second? (That is, one complete vibration takes exactly 2.) j 5k4 oa.ea*hlsgps8g3v/ds0 s.)    m

  A pendulum has a period of 0.80 s on Earthzcld jo xvo17s:* h2q2. What is its period on Mars, where the acceleratiocxq7so :o hd*jl2v2z1n of gravity is about 0.37 that on Earth?    s

  What is the period of a simple pendulumwg1h2 0x-u xqa 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendu0riy tm+q .9jnlum is 0.760 m, the pendulum bob has a mass of 365 grams, and it is releasedi+ 9jtyqmr.0 n 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 penduobatuf u3b136 lum has a length of 0.9930 m. If the clock loses half a minute per day, how should you adjust the length of to3b3u af1b u6the pendulum? shortened by    mm.

Derive a formula for the maximum )zzkv8hwg f2zz:0kv50ag; gyspeed $v_{max}$ 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 is rfvw76e- rl)nap3ho;q/xvsqz9jp)4rpf/, xf eleased from rest x/-nq3ql;z7)rfhe f r ) j9pov, xpsf6pv4w/astarting 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 boat ever3vfutc ;4a lah9eg n6pix /kfetc-:;.y 3.0 s. He measures the distance between two crests to be 6.5 m. How fast are the waves .;46aagc:kv lxeut p;ci-h3/ ef9tfntraveling?    m/s

  A sound wave in air has a fre5thm p9r9e:wmm: xg5 qquency of 262 Hz and travels with a speed of 343 m/s How far apart are the w5xem9q : mgw tr5m9:hpave crests (compressions)?    m

  (a) AM radio signals have frequencies between 55n.mrm we:w7kwt55+ag0 kHz and 1600 kHz (kilohertz) and travel with a spee5w+nw t5 k:aem w.gr7md 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 of8bvo7xfrsg (6gf l:k40n) p,nd, zdzr longitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same e16si.f nc 3z 2lbpzk:z ;6kgmrlastic modulus, but one is twice as dense as the other. In which rod will the speed of longitun izlg1zzcs 6fpb6;rm:k3.k2dinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apart. If ka 06j/vc lpm/the tension in the cord 60pck/v/ ljmais 150 N, how long will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to the top of a hill by a steel/2ohmkys1c9tpx m +t7mu/5o r cable of length 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and sends a wave pulse along the cable. It is observed that it took 16 s for the pu mysutth9 /or2opm/7+k5 c mx1lse 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 ship juik ,lgu8 :m.uhst below the surface of the sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is the ocean a8i , ug:.klhmut this point?    m

  P and S waves from an earthquake travel at diffe 1te ehbtv/0w6rent speeds, and this difference helps in locating the earthquake “epicenter” (where the distu0thtwb/ee16 vrbance 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 agh3v)l,+ tfa qpproximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mv3ah t,gql+ f)ixture 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, u);yd+n/veavtg hgpnb 67 7 v1and (b) the amplitudes, of an earthquake P wave passing through the Earth and detected at two points 10 km and 20 km from the p)t7ad vv/7gvg;n u+ny6h eb1source?(a)    (b)   

  The intensity of an eobd.,g:bjg x *arthquake wave passing through the Earth is measured to be ., :ogdbbgx *j$ 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 et)oq32 dfnsf9 y+ji,ooc 4(hsame frequency travel through the same portion of the Earth, cjh 4nofyt(,o si+)eof92d q3 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 ha vra/9 .6j6nyfsrhhve /v; yo1ve the same frequency, but one transports y rv1.6 ea6nj9fory /s/h ;vhvthree 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 move up and down a total c+ckplc2w; gz p ,8g7dvertical distance of 6.0 cm, f gdcpczk+2 8;7glwc ,prom 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 towa,3vuysl3r2 b zrd each other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of thev l,u z3s2b3ry 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 fundamental frequency, what are thew /yb6 h4 /3tdhv)cisc frequencies of the f/h3 )vtyid6hb4 cs cw/irst four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz wf+oqpk0s 2ntr83 z2p,e*r0uyc d w1oahen unfingered. At what frequency will it vibrate if it is fingered onecp 1d,s fyr tu 2*or2+03ekz8n0aqopw -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 fo3w ymf6*/hkrfc. 4of vur loops at a frequency of 280 Hz. Name at least threfof6 c.*v3rhk f/y w4me other 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.or k20f xuc0dzjv6u 3 frequency of standing waves is 475 Hz, 2 3u fc06odrkzjv0ux.how far apart are two adjacent nodes?   m

  If two successive overtones of a vibrating sok 7;kq7h,oa1c+ sobj tring are 280 Hz and 350 Hz, what is the frequency of the fundames oh1;co k+7q7,bokajntal?    Hz

  A guitar string is 90 cm long and hasta qy)v-xx22tn9v - si a mass of 3.6 g. The distance from the bridge to the support post is L = 62cm and the string is under a tension of 520 N. What are the frequencies of th vtx- n-22qy)txs9 vaie fundamental and first two overtones?    Hz

  A particular guitar *,/clq+zbk hed cjxvd62-rd-o1aly 7string is supposed to vibrate at 200 Hz, but it is measured to vibrate obhl+6*d-jdy qrev lcz/a,71d-c2kx at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hz, zjnco 7rwva*6 ce9y 7rjb5a1 ;but it is measured to vibrate at 205 Hz. By what percent se;7y9j5 cr 7*bac6r jo1vwzanhould 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-Hz/epjr :/ m.96-f) sjs :aa5tvmxvmuvq vibra5s . u/am vjvjqm6/9 marsfep:t v):-xtor. The string’s mass per unit length is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of the string may be adjusted bmaqhse :w)6 ;.xv y8nyy moving the pulley. If the hanging may)sv ;a6:n.e8 wxym qhss m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub :jzvz3 v2;zk c(kve 4so4hl3h hoojb78vre(8at just the right frequency, the water alternately 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 s8 c4z8j(kzhvoj4v kbo3eh h2s;(vv e7rlo3z :peed of the water wave?    m/s

  An earthquake P wave traveling at d , hnep;pw6;pk.0 km/s strikes a boundary within the Earth between two kinds of material. If it approaches the boundary at anp den,w6 pp;h; 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 c5bxho-,s*, (ol y kxtan underwater “shelf” where the velocity changes from 2.8 m/s to 2.1 m/s If the incident wo*-xy5b hk( c,stlx,o ave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling i-elzq+bnp x,4 b 7.wwzn warm air when it hits a layer of cold, dense air. If the sound wave hits the cold air 47 eb,bq-. zw+xn plwzinterface 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 wk .vce4y*-bofg o8an:ave strikes a boundary between two types of rock at a 38onkf- yc *o:8.4 ebvag $^{\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 diamete*non0v xin g1:r. According to the user’s manual, the dish has to be pointed in the direction of the satellite, but an i1gox*n nnv0: 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 anf.1 yr z r(l.esovd 5na5c7s*ud velocity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, 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 trvefcd7..5(u *5 nsylars 1zosunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness cons7si:8ir0 brrkyz27at kwa. u; tant of 550 kN/m Find the maxir;utr2 krb0iy ikz7:7.a w s8amum 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 fireixsin+t 245ex6 ap( br net 18 m below, which stretches the nep5s xrx6i i(na2 e4bt+t 1.1 m. Assume that the net behaves like a simple spring, and
(a) calculate how much it would stretch if the same person were lying in it.    m
(b) How much would it stretch if the person jumped from 35 m?    m

  A mass m is gently placed on the end of a fre6(nw dp 6 zn80iu/ocozely hanging spring. The mass then falls 33 cm before it stops and6zp6cu (n iwz 80/oond begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s 4s(km xc9;z tv(Fig. 11–54), compressing the spring 5.0 m. (a) What is the 9vtx;m4czks (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 (diameter 8 cl d,q//8z qzawf smp:-m) at just the right pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig.qz/ 8md-fz wl/:a qps, 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the cj z *) 2yltyw*(el(pfbenter of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequency of the sjty (*fl yle)z*p 2w(bound emitted?    Hz

  A 2.00-kg mass vibrates according to pg6y5mqqv64av- x q4y the equation x=0.650cos7.40t where x is in metgva46qp6xy 4 qyqm5-vers 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 frequency7p di0v-re-ybbt (p t; f. What is its frequency if it accelerates at 0b --iv 0 tb;dr(yp7ept.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floatxi, ei u9(/mq n,+5gl axwtd.qs on a lake. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the u 9t+awxi5eg/qxni, q , (dl.mraft vibrates for a while.
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a musical instrument are tuned to px5b8shab qm- l :c3z)zlay at 392 Hz (G) and 440 Hz (A). :b)8 zh-l q5a mczx3sb
(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 wavegmq22 p0td(sgqo) 8 w; ulc/fz traveling down the stretched two-part cord of Fig. 11–33. Determine a formula (a) fosqguq; lo 2 pwftcgz()d8/0m 2r 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 lighter?

  A tuning fork vibratea)f4 -(n ;uhpmt4rzbb1bfx c3 s at a frequency of 264 Hz, and the tip of each prong moves xbmft ch r3n-zb;()p b 414uaf1.8 mm to either side of center. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simple harmonic motion of frequencyn pyz8: fd1-c;dv7iuq 1.5 cycles per second. What is the maximum amplitude with which the ef8:1 dpin -y;u cq7vzdnd 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 “frej 2h7sunrb70t-1s ixde” end if that end is attached 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 sd-ji0xh7s721 trb uns tring with one end fixed and the other free.

  A “seconds” pendulum has a pex9kmed)o p)qe ,w)gvj- iua yd7/5f8 friod of exactly 2.000 s — each one-way swing takes 1.000 s.m9/d5-a8 dke,o eugiqyjfx7 f) )wp) v
(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 ther6kb*7n k6dmzk 7j;j j vertical 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 the perknmb 7d* z67krj6j; jkiod 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 y.5zxi z/n.:i:0cjc u s cv6lqtension of 255 N. A pulse is generated at one end, and 20.0 ms later a secon.c c n:iz5:.i6vql0x cj/zuysd pulse is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling han5o u 37a4z no(fet8n9q0qj-wnzf3by a spring with spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillations that will allow3tq0fw o95n4e( znh7jq3un8fona-z a the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel cran-, witck1kutr4nc na 0a010+ vdt0o ebe 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 bouncing? [Hint: Refer to Table 9–1.]kb4codwn0tei-r0v1ta 1,t0c n k +a0u    s

  A block of jello rests on ahdnfbx aj m/b 3nx(8-e/k3ps) plate as 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 spring, estimate the frequency of this vibration, given that the shear modulus (Section 9–5) of jelld) b3hf3 n/8n /-a(mxx jspekbo is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz