Give some examples of everyday vibrating objecqp 0x0kq(qrfulw c3h+z*- v238 xzb ycts. Which exhibit SHM, at least appro 3+qb 30r8fxxpkqv2lwh-z u0( cqcz*yximately?

Is the acceleration of a simple harmonic oscillator ever zero? If so, wher 7pr d:lsz p+eg0wy4-we?

Explain why the motion of a pisti6.j3rmdjk g -on in an automobile engine is approximately simple hgi-jkrj3 .6 mdarmonic.

Real springs have mass. Will th3ngc92xj 9mpta/ ).:v0 pjmljk)vfvd e true period and frequency be larger or smaller than given by the equations for a mass o0 l )9 )m vx:v2ktmva9jnj/ gjd3cpfp.scillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple harmonic (x-;m k jlrb)m h01xdaoscillator (SHO)?

A 5.0-kg trout is attached to the hook of a verticarb f*q)wss :5kl spring scale, and then is released. Descrwbqsf:r5 s*)kibe the scale reading as a function of time.

If a pendulum clock is accurate at sea level, will it e17v0j lh d8i7ba6rknw1 ;bzb gain or lose time when taken to high176ezi bla0kbnh1dr;b7 8w jv altitude? Why?

A tire swing hanging from a branch yb upa 5s-io jnfb7o9p*a/z,a) ov:k*reaches nearly to the ground (Fig. 11–48). How could you estimate the f/pojbbko: y7 ua- vps*n5i,o*za9a) height of the branch using only a stopwatch?

Why can you make water o z,m((pdlffvy+za51+p uzi2 slosh back and forth in a pan only if you shake the pan at a certain f+2u , 5fazz(1l(z fydpop+mivrequency?

Give several everyday examples 7uj(zxu4 dpsb 8,gup1gpk,l :of resonance.

Is a rattle in a car ever a resonancehzkp2 opm:o jgu),ca1l 6v, *i phenomenon? Explain.

Is the frequency of a simple,xz9 cruc,u6x(/cchf do/ rl+ periodic wave equal to the frequency of its source? Why or why n(ch+ zr cdc//uxx, ,r ou6c9lfot?

Explain the difference between the speed of a transverse wave traveling rwg 6)g.o- +zwvodb;e1 v*l epdown a cord and the speed of a tiny piece of tolr+6 z;-pdw.w*)g 1eo vvgebhe cord.

Why do the strings used forj x r;4w2p.z1:d3,fx sr yufsn the lowest-frequency notes on a piano normally have wire wrapped arojx3n, ufdsr1 .y:z s24w;fxprund them?

What kind of waves do imk ,9)o( bozeyou think will travel down a horizontal metal rod if you strike its end (a) vo,eki9zbm )o( ertically from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase in tem,hvb,2qnci- x perature, but the bulk moq,vcbh xn2, i-dulus B is nearly independent of temperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in amplit0ulym;9qt y 3yude as they travel away from the sou ;90uyyl3 qytmrce.

Two linear waves have thep 3 30o,,(-mzrpg( enwcs/ynm4yqz sx same amplitude and speed, and otherwise are identical, except one has half the wavelength of the other. Which transmits more ees/-,rm o 0ygpc znwsyx4m,3pzn((q3nergy? By what factor?

When a sinusoidal wave crosses the boundary between two sec+:8ocb;v zc vxtions of cord as in Fig. 11–33, the fre+z;vx o:vccb8 quency does not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there any pla:v f0ig zr*wn+ces you could touch *in:+0f zwvg rit with a knife blade without disturbing the motion?

When a standing wave exists on a string, the vibrations of incident and reflect)qv6gi*9 drd a(smpon*g (cy(ed waves cancel atoyg(pr d dq)*sav(6cmi (n g9* the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy wk,u f5f7 (t;t1pbulx,tu4rlfas being transmitted from one place to another, how might we determine whether the energy was being carried by partr 5p,4tu fftl1l7f,utux (;bk icles (material bodies) or by waves?

  If a particle undergoes SHM with amp :i,j wad9m*r*mu2n ,s ygql:glitude 0.18 m, what is the total distance it travels in one periogmw saqud,,:*nigm:* 2y rl9 jd?    m

  An elastic cord is 65 cm long when a wea*i vwxq5+c56mrj(xy g 6:ls hight of 75 N hangs from it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” constant k of this elastic cord?(vxay5+qi6wl:s* c x 6gh 5mjr    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kf- g vjs m677rli.rv:pg driver gets into the driver’s seat. If the car goes over a bump, wh7s7i m v6v j:gprfrl.-at will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretchw7 4nd ,5rutczes 3.6 cm when a 2.7-kg fish hangs from it. (a) What is the spring stiffness consdwz ,457 ctnurtant $\approx$    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 kg is v, 9a2hqv,3gml b.gffhung from it. What is its frequency if only 0.38 kg hangs frg2.g ml v,vfq9 bhf,a3om it?    Hz

Construct a Table indicating the position x of the mass in Fig. 11–2 at times kfyr61y(ru qxil1t 4,nz i,0kt = 00,ulr1,r y4 (i6zkk qxy1t fni,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 vjxdke mq pc b91g)jz.:6pr0i,lre,4caught in a spider’s web. The web vibrates predominately with a frequency cqmv0dj1:r) gxe 4 ,.r,ejppbzi69 kl of 4.0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a spring vibrates with a frequency of 0.88 Hzp 2z xuo.3g4uqat 8fypx z0m((. When an additional 680-g mass is ada uou 8qp(m2 (zt4.z0xyx3gpfded to m, the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per second withfd1d c 0glglk4o2d9iw/t2 wb ; an amplitude of l/f 92ddd 120 gwgkco4;bwlti 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 x4 .ip2s2ukh 8bq(thvequilibrium is the speed of a SHO half the maximum valb2usqp4i t v8h.2k x(hue?$\approx$    A

A mass attached to the end of a spring islzb r j8p s.1ye u1.n7m sw1ud,aab+8t stretched a distance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretches a vertical spring 0.j3 ux*wbicwtcs;dqrt-5qmz :3 x)1.j 315 m. If the spring is stretched an add.5xxmw-3i:z31q*wd j utscr)bc;qjtitional 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 spring stiffness consta khwka19mh 0f4nt k = 280 N/m and is executing simf wh k9h01a4kmple 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 i/7 tb.qlzlvm.s-ci /sau55 j a toy popgun 0.200 m to “load” a 0.180-kg ball. With what sp/u- taszjcql5/sim 57i .. lvbeed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attachedh(c1y v q.q/gp7(4)pqzgs uhk to one end of a spring; the other end is fixed to a wall. 3.0 J of work is required to comkc(p)p1 z7sqh(q.4/ hgvuy qgpress 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 where x is x;l0zwi)km/zreb/ 0zjvaljc7 g 08-y in meters and t is in sec/ 0vbw /mxajz7zgy )8e- ;0zik0llcrjonds. 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 SHO wr1 6p;5mk,ue4yw afzhalf KE and half PE? ± k1f a6z ymwue;w4,r5p   A

  If one vibration has 7.0 times the energy of a second, but their frequencieshb : 2n+ezdtc1 and masses are the same, what is the ratio of2bn dte +:1zch their amplitudes?   

  A 2.00-kg pumpkin oscillates from a verticallh0,t-mp4/fyz qr 68buw0 sazr y hanging light spring once every 0.65fzrhsa /8 b- 6yw,m0u4rzqp0t s.
(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 vercar4;aqs x /uo*)gqn)tical springs, each winur4/ )xa*qq) oga sc;th spring stiffness constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t where lxifo8 .sqg3vlb(e8f4 ,w)jx x is in meters and t isb ( lov,4xf)qjilgse.38xf8w in seconds. Determine
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows two examples of SHM, labeled A and B. For each, l *vqyee u1nia7(hn 3,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 o /0e 1s )fvq*gqlb9ubgn the end of a horizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass vbggl * q9)f 0usqe/b1an initial 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 stif0soco5hxe9b5, sir-b rdv *x9 fness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equili,0erdxoi*-5oxcsvrbsb9 95 h brium point (x=0) with positive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two springs, 7;gzgf(eht+ bwith 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 ax0 zr zsc*70i:9io ff. vras-w 0.600-kg block attached to a fixed horizontal spring whose spring stiffness consfr xsszav 7:i.09 rw*0oif- cztant 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 w a8jl+c*z )lhz:ezqh bi).d;65.0 kg jumps from a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the br)hz8z:dl)z +qlia*;bj. e hcwidge. Calculate the spring stiffness constant and the unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrations in exactly 60 s. What is it ,o/esc795srju vi-tp s
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly one swing per secfex jl2ku5i+uf:n-0o ond? (That is, one complete vibration takes exactly 2.0 -2u jni+x0ol fuk5:efs.)    m

  A pendulum has a period of 0.80 s on Earth. What is its periodvu f+f5r9wxvvtn7o9 ud3 xc* 7 on Mars, where the accelera99vwfufcn x 7vo3dt7v+u* 5rx tion of gravity is about 0.37 that on Earth?    s

  What is the period of a simple pendulum 80 cm long p4ilx9m krc)4
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 m, tha:03qwazt e ) irjup:1yp65zwfk) dx*e pendulum bob has a mass of 365 grams, and it i*5yetzxu)dqf01wprz3:apwk ): i j a6s released at an angle of 12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’s pendulum has a length of 0.gbj il 424 imp kc+4inpfx*+s69930 m. If the clock loses half a minute per day, how should you adjust the length of the j46pf+s i4l2igic kb4mn*p +xpendulum? shortened by    mm.

Derive a formula for the max6b63hc ljk2 ppimum 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 j u; xm0w43m gsam:+neHz. At it is released from rest starting at an angleg+4umwm;:3 mes axj n0 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 xlm/zy z6/ipc1ywna+j 14s ;rn wnb41of his anchored boat every 3.0 s. He measures the distance between two crests to be 6.5 m. How fast are the waves travelbcyp1lxs1rm 4/ n/ 16zz wj;an+nyi4 wing?    m/s

  A sound wave in air haswua22 ir9stn9 a frequency of 262 Hz and travels with a speed of 343 m/s How far apart are the wave crests (compression2ta9r2 n9swuis)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (kilohertz) akqe1,59 ntw1ivw15ta o 0/mrnskl 0yxnd travel ,5 lnq0519/nksy11ex wmt ov airk0wtwith 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 longitudfyw awg u/- 2r);wuaa8inal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one is twice as denhlpzo s5 4g.kcz iwitgfjt8:4. 8ep53se as the other. In which rod will the speed of .i cg 3.4tls5 :pjz8tgwk4 heio85pfzlongitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apart.xjn; 9umm.sz0 If the tension in the cord is 150 N, how long wilzmjun.9s 0mx;l it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to the taklg).*/ aiavj :q0cvfk 1z1i op of a hill by a steel cable of length 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bum1lj)c*:k0/1v a zafg.ik qiav ps 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 a dx:l;o0 /lk ogskl*fk 37n4fhis ship just below the surface of the sea. He hears the echo of the wave reflected from the ocean floor directly belox 4ls7no f:afk ol*;gdk /0l3kw 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthqu mx5mp404p.bb opcvh: ns f /q v-b94jnf63koqake travel at different speeds, and this difference helps in locating the earthquake “epicenter” (fnj 0b f4q.3 ms4 q5n 4oo:v-hvkpm/bx6b pc9pwhere the disturbance took place).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced surface wave can be ap5p dj2b s(mr.hproximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave conta2pj.rmh5sd b( ct with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the inte -ii4eo0nlljivldg5 )-j 3g 8qnsities, and (b) the amplitudes, of an earthquake P wave passing throughg3ii0q)5 jdv n4iolljl-e 8g- the Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is measured to be f l:ccn3tmi5* 53f*ni c:mtcl$ 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 t9rjty30vu;io ad kt 0j.0(jk uhe same portion of the Earth, but one is carrying twice the energy. Whjv00kk; iy3ato.r0u ( du jj9tat is the ratio of the amplitudes of the two waves?   

  Two waves traveling along amo( wc2hh(6 po stretched string have the same frequency, but one transpoo(cm (6hw op2hrts 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 obsevdsy5v15nlj:3g d r(p:5 mkt vrved to move up and down a total vertical distance of 6.0 cm, from the lowest to the highest point, ad j3r:l1 vpkm y5:(vg s5tdvn5s 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) Sk*ldjw* rys(t ,etch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight. What has happened to the energy dsl j**w,r(ytat this moment?

  If a violin string vibrates at 440 Hz as its fuih x :z;hxc kuv,g4)gory8fnq ds*28b1 a+8kwndamental frequency, what are the frequencies of the first four harmonics 88h duo w)xghq2;c: fkngk*b1 4ry8+ai sv,xz?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when uneh)h29c:pqj a d)pqq8 fingered. At what frequency will it vibrate if it is fingered one-third of the way down from the end? (That is, 2da)qpj 9qqh p:eh)c8 only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequew cd *.qgwv ;5ntj a5x)c3cv,sz2bdn *ncy of 280 Hz. Name at least three other frequencies at which it wiws5;zdtx *n.b 32 cg,)5v ccnwv ajqd*ll resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the frequency of standingkuyj/, a0 v.pr waves is 475 Hz, how far apart are two adjacen0jpv.u yk /,art nodes?   m

  If two successive overtones of a vibrating string l+f)p;dm(ge t g4ylh4 are 280 Hz and 350 Hz, what is the frequency of the fundamegf+;lytl(4epm4 h g )dntal?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The dicg 7j3 pp 6/kbzir4yh-stance from the bridge to the support post is L = 62cm and the string is under a tension of 520 Ny/4g7r3- p bhki6pczj. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, x.d, 3o(esu3;ppp pl gbut it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to u p3 ;3.,odlpppxg es(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, ihugl,. * +h(n)kyzjxbut it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to +i.hykxh, ju) z*gnl(correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-amplitude m usz6x5ab*)s fd ,ae9pechanical 60-Hz vibrator. The string’s mass per un)pb dxsfs5aa u*,6z9 eit 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 l6 jiacy 0 sjyieq;)w0-er2 -gf+tur3rength of the string may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how macuj e e-0tsr jg62 +r fra;y0qy3i-)iwny 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 at just the right frequency, th b kml6snv*psui: (v/06ig(xpv.ayi,e water al p ,yn 0gk/:i( .sxivpmlu(*i6va6bvsternately 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 svg5:r, 3uvbdc a-waagp v5v :ooj1);a boundary within the Earth between two kinds 55s vvowo cp;-aa ,3:j g )ru1vgdav:bof material. If it approaches the boundary at an incident angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “shelf” where the velocity change2jkh u)t98mmj7 xx7wzs from 2.8 m/s to 2.1 m/s If the incix7x) z8m9twh k2mjuj7dent wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air when it hits a layer of cold /-spp* ;ft 8 qogvg+rf6rcb1e, dense air. If sr* c;vfr/t8 epb- 6pfqg+1ogthe sound wave hits the cold air interface at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave strikes a boundary betwcv :n a)w n6.:5lvw ch0z8wieyeen two types of rock at a i :wyn hzac. l)50cvnv8we:6w38 $^{\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 96 ic + t:*zc9u oo vhh,vnk..+crltgjmanual, the dish ha j*g ,rl +tkiht: .coczho6v.+vc9u9ns to be pointed in the direction of the satellite, but an error of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 250 km and velocity 750 km/h travels across the Pacifw/ *wizsu-jn5ic Oceanjiz *5s/wwun -. 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 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 ysb+(w qqkx*b08 gd+ hof 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approximatelybwqb*gd+q+hx0 8k s(y 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fihft:/w:b;e--d rmpal -x h8q mre net 18 m below, which stretches the net 1.1 m. Assume that the net behaves like a simple ;h:pb h mm-ed -:wf-la/q8rxtspring, 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 hans31 m1rm +ztp+jj(id oging spring. The mass then falls 33 cm before it stops and begins to rise. What is the fre+(d msjzt 1 1pj3ro+imquency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 11–54oyo3 celrug 5h/i /6b-), compressing the spring 5.0 m. (a)ubhr3o6y le/ -cg/ io5 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 (diameter 8 hy zu7;(hfsz h e.*ae7 akq2m0cm) 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. 11–55). Estimate the speed 0eeaz7q.uhm7h y a(k2hzsf ;*of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm fro id3 :zjl./,cpe7)tyjw +jtctkl 1zx 8m the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What z7zjtlkl3+c8)ctyj pi ,xj ew :/.1dtwill be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t where x is in njpk.yrg) 1g+:+lq zi meters and t in segi)yl+q n 1r+:kj z.gpconds. 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 1s;65ga0h wl-2,c xylp yinenfrequency f. What is its frequency if it accelerates at 0.50g (a) upwaxnal-w,iysl yp12 e06 ;hc5gnrd,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man 68p-lt,txzo y stands on the raft, it sinks 4.0 cm deeper into the watt, 68lzyx- poter. 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 instrument are tuned xwx/z1zt1 ts2l6 ic+vto play at 392 Hz (G) and 440 Hz (A). /zt1sxc 6+2i1 xlvzwt
(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 down64nviuqw8x 0k the stretched two-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of thw nv4ikqu8 x06e 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 vibrates at a frequency of 264 Hz, and the tip of each pron jxctte23); c*u04lmgj);chf t7 dijjg moves 1.8 mm to either side of cetx;2ce c3jjlcj);mf 4i)u gt7jt d0h *nter. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with3ywweloxkh;2 c,ss* 8 simple harmonic motion of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the s3 lyo8 *kswecxw2;,h board during the oscillation?

A string can have a “free” end if that end is attached to a ring that can slidd4au/,yrie udlsg mx3k (ixl d39j:06 e without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a,3l9dxd x3gr y0u i u(4emaik/ :jds6l string with one end fixed and the other free.

  A “seconds” pendulum has a period of exact1o (fh264rybo d2r3v( zpekon 3 zo4hhlc;h4v ly 2.000 s — each one-way swing takes 1.000 shyv4oho vp4o 2fk1 h3h c r4nol(d 3zb(re2;z6.
(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 direct3cf bg0qiyud,0z48g pion or can swing as a pendulum of small amplitude, but not0, zg84qc0pbuyf gd3i both at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontal swings, and by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

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

  A 10.0-m-long wire of mass 123 g is stretched under a tension of 25npfplid6)gp m .( 1m3r5 N. A pulse is generated at one end, and 20.0 ms later a second rg 3d6npf im1 p(lm.)ppulse is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is sum6* .pvqm(2 avlemh/hspended from a ceiling by a spring with spring stiffness constant k. A penny of mass m is placed on top of the blocm6v.m l/h*em(a h pv2qk. What is the maximum amplitude of oscillations that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. u2yw,va k j0ww5e3h9aThe 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 pe9e5,wwu 3 yajh2avk0wriod of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate avfbl1wp1qyg)2 ,)do n s 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 an)),nqwp l boyd v12f1galogy 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