Give some examples of everyday vibra: avm *ne;jts/ting objects. Which exhibit SHM, at least approxisnejv*a:; /tmmately?

Is the acceleration of a simple harmonic osc 26;dm7gb2auln h0 m/g3kngoyillator ever zero? If so, where?

Explain why the motion of a piston in an automobile engine is approximatelyg*s(j 5( hkjt).mz;oxc: fmed simple harmonie5.d(s*jmkj h(; cmzt x): fogc.

Real springs have mass. Will the true period and frequency be larger oru+uwn ci 4hb)ld0w3i0 smaller than given by the equations for a mass oscillating on the end of aw ln)3 wh4u0b+c0id uin idealized massless spring? Explain.

How could you double the maximum speed of a s/nx8pdzawd gmk 0) u+1imple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to je7h-9wxmxu)dlx 8 m o z9hq6)the hook of a vertical spring scale, and then is release9l-o)juxqh xh 9)w6dexz mm7 8d. Describe the scale reading as a function of time.

If a pendulum clock is accurate at sea level, will it gdj+l6sw 7rrw9f8kgq 8on. tt2fsv+ 4wain or lose time when takek8n8dw 24sjortg r 7f6tlsww++vqf9.n to high altitude? Why?

A tire swing hanging from a branch reaches nearly to the grozdace)6m/n - tund (Fig. 11–48). How could you estimate the height of the branch usi -de 6/z)actmnng only a stopwatch?

Why can you make water slosh back and forth in a pjbma s3.ev1;, ht676vkf8l *cn l ube:swyt8pan only if you shake the pan at a certain fm,ky 7ve 6j;c *spll1whu3s8ne.: v6fb 8battrequency?

Give several everyday examl(fkns v1 0z7mples of resonance.

Is a rattle in a car everdx 0vxo .crok5r:-* : zfdziu0 a resonance phenomenon? Explain.

Is the frequency of a simplxk: +qacl .z.fch)au16m5gyue periodic wave equal to the frequency of its source? Wucf gx)ak+a.5q.6mz u:c1h ylhy or why not?

Explain the difference between the speed of a transverse wave traveling down a4hyf gxacb 0/avp85m ) cord and the speed of a tiny piece o5a4 v cbgh yfx0ap/)m8f the cord.

Why do the strings used for the lowest-frequensv s-p-yxhms. k.n.+ jcy notes on a piano normally have wire wraph--.m sykv.+jsxp.sn ped around them?

What kind of waves dgi 8 z0(tg+rilo you think will travel down a horizontal metal rod if you strike its end (a) vertically from above and (b) horizontally parallel to igilg 0tiz r(8+ts length?

Since the density of air decrealpxez67lwse0dq: p u *wrs az8+(n7t1ses with an increase in temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sou7tpp+zsq:8e7 (*rwseld16 0aw ul x znnd waves in air to vary with temperature?

Give two reasons why circular water waves decrease infsc9m )l ).lnmyw+(e x amplitude as they travel away from the source.+(e9smfwnl)mxl. y c)

Two linear waves have tq8 hc*bvv;5fcfo /k+9 xfi6y bhe same amplitude and speed, and otherwise are identical, except one has half the wavelengt8fvhk q 5;fo*9xbci f/+cb 6yvh of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses ts5j cj:xsyc ,-:3 7aq b*zmkr)s)i mpuhe boundary between two sections of cord as in Fig. 11–33, the frequency does not cha ciq sy:c7j-,)mu* 3xspz5: brs)j kmange (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there any places l/2d 51l-3ia k ww8grm bcts-eyou could touchgd3 /staml5lbkw i8-e r c-w21 it with a knife blade without disturbing the motion?

When a standing wave exists on a string, the vibrations of incidqw)3e peg7us5epayg(2f s- u0ent and reflected waves cancel at the 0e )u3 guep fepa7ygss2(5- qwnodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being t 8me*e3pth*t c2c:optransmitted from one place to another, how might :2temot hp8p*tce* c 3we determine whether the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitv)o ldars 2tw(em55.m ude 0.18 m, what is the total distance it travels in otlre(2a).5 ms 5md vwone period?    m

  An elastic cord is 65 cm long when 0iyd+(whbh,b a weight of 75 N hangs from it but is 85 cm l w(+b ,0idbyhhong when a weight of 180 N hangs from it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when ap mx9a(ja-/kt t.-zhits 68-kg driver gets into the driver’s seat. If t 9(.ap-axk /zjht-atmhe car goes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretci i)g2c4*+ 1jfbgpfz5lmqfl(jp3x *thes 3.6 cm when a 2.7-kg fish hangs from it. (a) What is the spring sti+ *j5tf(i12g3mf b qi lg cppz4x*lfj)ffness constant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a frequency of 3.0 Hz when a massj:5bm plsd11 k of 0.60 kg is hungdpjbl:k1 m5 s1 from it. What is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating th gs2-fon6vzw(t*jv8fi f2v v*e position x of the mass in Fig. 11–2 at times t *fi*jg of8(v2 wtv zvvn2sf- 6= 0,t = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

  A small fly of mass 0.25 g is caught in a spider’s web. The web vue -cxj--ivv( ibrates predominately with a frequency of 4.0 Hz.v-jc(ex- iuv-
(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 spr2om w8*9sz8zd rnd4 twing vibrates with a frequency of 0.88 Hz. When an additional 680-g mass i2sz d984zom dw*n8wtrs added 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 sjjefh( ;0g*7+d jp-lzxzls5wj+. bw uecond with an amplitude of 0.13 m. Dezepl jz0+.b*-sf;x ghu5 +wlj 7jwdj(termine
(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 SHO half the maximum vag8mc)mpy1 z2ua2it : xlux8:p2 mg1mut a2)iyzce?$\approx$    A

A mass attached to the end of a spring is stretched a dista2b qqi3 iz/51epw wy.mnce $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretches a vertical spring 0.315 m. If the spring is k5ps kfno;n0cc 70la9 stretched an additional 0.130 m and released,l07; a 9p0kf5nc onskc how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached topc .rgt qx;w; 4 :v jfg0/dz8lndhsyl)ny3z1. a spring with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the objecyl)jnf.. ng1:xgp8r dszw;zh t3v l/40; qyd ct 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 comq axqq/-g++w0timq , bqbo,8tpress the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will the ball leave the gun , ibag-mq8 qq+b0 x+owttqq,/?    m/s

  A mass sitting on a horizontal, l. cn e) au4dm8(dby,q 7ngt9k f5g;nofrictionless surface is attached to one end of a spring; the other end is fixed to a wal; gn ug8ltd fan9oq()7neb4cmk y.5d,l. 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 = j62k6)uob.x dw ds sp50.45cos6.4t where x is in meters and t iw ssd56d.2 o)pu6 jbxks in seconds. Determine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equilibrium is the energy of a SHO hazdaoe(:n fbj(;eox-7o/6k ltz +s+ 92f syggdlf KE and half PE? nl+sg7 9 t:2(-f ( ob+x;yfzk6esgz jo/oead d±    A

  If one vibration has 7.0 times the energy of a second, but their frequx)y1vo m5n wcnl3 1zru m0ns.5encies and masses are the same, what is the ratio of them3 5 .x)0z1ulnr5 c nnvsoy1mwir amplitudes?   

  A 2.00-kg pumpkin oscillayk4 :lo,e;;iwuj v2eu(um*k ytes from a vertically hanging light spring once every 0.65 s. j,u;w2yiu: k ly( *ukem4oe ;v
(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 vertica58v2z.xu klxil 6j-q ql springs, each with spring stiffness constant k (Fig. 11–49). What will be the frequency of vibration? jx-v q8kl 2zqxl.56ui

  A 300-g mass vibrates according to the equation x = 0.38sin6.aq(-ic. igg+ -(kylc y5t where x is in meters and t is ic .-y(gy (licg q-k+ain 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 abe-g4s/4 t m6 wv0 wo7,jdtdvdnd 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 horizontalddb;.j-7num1kp g8 jl spring (k = 124 N/m) is struck by a hammer, which gib-dguld 87 1mjpj.;knves the mass an 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 stiffness constant 305 N/m vibratesk- yskzhfkl4bpr 3h v7*bg,/: with an amplitude of 28.0 cm when 3 vr:khy-s*hpzb ,lf7/4 bkkg 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) with positive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two springs, with sp.w /pydgf+ias -h+q e;ring stiffness constants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes a 0.600-kg block attached to a fixed horizontalyq:;9+d3m a-movo lrw spring w-mlyo m;93ov wa+:rqd hose 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 reaching hi.aw afqoh0w (h d*5jpwhl 3bak5*;h7m s 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 5kh7apo (f5mwa*;jwq dh3w*0h a.hblof 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 vibratinfvy rj qj4,5*ons in exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly one swing pea(5yt03niow49vld ds r second? (That is, o(tvy 4wo3d0n s 9ia5dlne complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its periodanp6h;ehln e-w i.l/. on Mars, where the acceleration of gravity is about 0.37 that on Eartn ./l6-elipa e.w;hh nh?    s

  What is the period of a simple pendulum 80 jwzh. o/de1mhk suw52yxnq4 ,tx2h.5cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 m, the pendulum bob1w ;w 1mn4uzu8c.a1bw suje) j has a mass of 365 grams, and it is released at an angle of 4jw1 1 )sua munw8;.ewj 1cubz12.0 $^{\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 has3qihb:lv. db/ a length of 0.9930 m. If the clock loses ha.v 3dhlbq/: iblf a minute per day, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula forl3g/i3axy k/u:4*c /hxred. ww5bp x a the maximum 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 ai vr5 tx:x*wb4 frequency of 2.5 Hz. At it is released from rest sta x:*bv5r4ix twrting 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 everyao f-z 2sa+7,g+rxx qxga)u3u 3.0 s. He measures the dista z+7-urfogxaa +,uaxxsq3 2)gnce 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 travels with6mzdha ;n,y +ld;uff, a speed of 343 m/s How far apart a +n lmf6z,hdd ,yfu;;are the wave crests (compressions)?    m

  (a) AM radio signals have frequjo;s ;utx 6dz8ex/0 wzencies between 550 kHz and 1600 kHz (kilohertz) anzj; 6oxzs tduwx0/e8 ;d travel with a speed of $ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

  Calculate the speed of longitudi ivhx9rv+6sam+bv zgidm: 0pl ie4k) 91xk.,nnal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have )*h)ac z *;ronih;cxk the same elastic modulus, but one is twice as dense as the other. In which rod will the speed of longitudinal waves be greater, and by what facrci*)h)*n;oaz; xkch tor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apar/,o qrd5ylg 7gt. If the tension in the cord is 155,rl oyq /dgg70 N, how long will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected qcfo+1 a(c)gwto the top of a hill by a steel cable of length 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and sew 1a qcg)+c(fonds 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 si: jx/xigq7voym+ 9t r/8.lbyf de of his ship just below the surface of the sea. He hears the eof: t8x qy7v9m.i xjb/ylr/+ gcho of the wave reflected from the ocean floor directly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at different speeds, and this differ)r d(bx+g1mc rence helps g mcxr()r1b d+in locating the earthquake “epicenter” (where the disturbance took place).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced s pfvi.,y,nl:xh spo2*urface wave can be approximated by a sinusoidal transverse wave. Assuming a p. pf nh*xoil:sy,v ,2frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) t0 mkdj0p2 kc3i wu*-nrhe amplitudes, of an earthquake P wave passing through the Earth and detected at two points 10 km and 20 km fn cj- mp2wdurk 0*03ikrom the source?(a)    (b)   

  The intensity of an earthquake kxaw dz.rf.t:+jcc c3y5 v5.j wave passing through the Earth is measured to be +rt..zjv w.djkc yx5:ca 3c5f$ 2\times10^{6 }J/m^2$ at a distance of 48 km from the source.
(a) What was its intensity when it passed a point only 1.0 km from the source?(round to one decimal place)$\approx$    $ \times10^{9 }W/m^2$
(b) At what rate did energy pass through an area of $5m^2$ at 1.0 km?    $ \times10^{10 }W$

  Two earthquake waves of the same frequency travel through the same portbyj9 gdq132 xw1us*taz- fge4ion of the Earth, but a*z4-dw 2g9b3fye xjs1uq1gtone is carrying twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stret( bh;y.w: do c4 s nvq1m86jdnjfbus(7ched string have the same frequency, but one transports three times the power of the other. What is the ratio of the amplitudes of the two wav vys(1oh7qu 8m;wj:j cbnbd6 fd(n.s4es?   

  A bug on the surface of a pong+ ppz:v0m 6lnd is observed to move up and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm, by w60+zl:ngp mpv hat factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each3i 2;cwvqeu8ged7p -r other. (a) Sketch 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 hasqg7puri8 ecd 3we2 v;- happened to the energy at this moment?

  If a violin string vibrates at 440 amiipd 4sm 3t+7is1y3xg6k ;oHz as its fundamental frequency, what are the frequencies of the 7do s4yp+ ai3mx6 ti1s;igm3 kfirst four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 2 zni1d.:adbcj+6ksxzvxb:ak v j )2+ 294 Hz when unfingered. At what frequency will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of the string vibrates as a stann s.z d2bk+6:dc)jj1k x2aiva: zbx+v ding wave.)    Hz

  A particular string resonates in four loops at a frequency oeyp78-4 o5csl3xpqhghu-( gff 280 Hz. Name at least three other frequencies at which it 7(8 xhp-go hu c-gsef3p5l4yq will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves 2rb+slo7ec7c on a string is 92m/s If the frequency of standing waves is 475 Hz, how far apart 2ccro7es7b l +are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 rexzb)f,p 3mzb+ c6r73(j(aioszu.g Hz and 350 Hz, what is the frequency of the fundamental?73c.m3(b o ()ua zxbrfp+6 jz e,rzsgi    Hz

  A guitar string is 90 cm long and has h1e6ukodv(5v0 bf1cua 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 the fundamental a561o 0e dku( vvcbu1hfnd first two overtones?    Hz

  A particular guitar string is supposed to ws k2lo-6g3w 68 ahyxfvibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?So the three freque 36-6wg8 flksyxawo 2hncies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hz, but it is me49leu7pjog)xk n 0 *3ro cb-dtasured to vibrate at 205 Hz. By what percent should the tension in the stc)e43nl t rd9u7kbj0 x*oog-pring be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a smlcdhl73 *gy8 *ax zfi93i-gz us;i( onall-amplitude mechanical 60-Hz vibrator. The string’s mass pen(3h;i*da8xg7z9o scl fz*-y iiu 3glr 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 be1 +s a2 fetqn.tp/ib)y 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 Lqe12t /i) +.bfanpste between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at just the right frequency, to.(fdp6yer b ie*s 18n(4caqhhe water alternately rises and falls at each end, remaining relatively 6dn(4cepe(bar * 8is.yf1ohq 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 withinbpue0 cgp:2k4 hp; ): a4ekvus the Earth begk )pb:s ;ep pu4au:hk04v e2ctween two kinds of 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 vel+jk ne8o0qsjyr 3k6s -ocity changes from 2.8 m/s to 2.1 m/s If t80 yj+-oqs3s ekn kjr6he incident 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 xl.cq8;arc o: cold, dense air. If the sound wave hits;a8l.cr oq:xc 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 betwhi: 0nsv+m+6;tmqah a een two types of rock at a nati v: mh0hsa6+ +m;q38 $^{\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. Accordi smxviwb:ku: k a;6f7 0l9k:vhng to the user’s manual, the dish has to be pointed in the direction of the satellite, but an 0vkxvlm::fu; a:9k b ihw7sk6error 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 8 l3.kthk04tef. i kohslg s,8the 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 tsunamis, some of them attracted to the shore to see stranded fishes and boats.)h8 .hfgt0s tl .s k,e3ki48klo    min

  An energy-absorbing car bumper has a spring stiffness consx)mrqz+)e o) gtant of 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 (approximately 5))r +x)zoqem g mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window tvvqz6g:dl,3 i4iid:macy l( 4o a fire net 18 m below, which stretches the net 1.1 m. Assume thaz4vm( d6id3cl iyivg q ,la4::t 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 freely hanging spring. T b)c43hu;vs rzhe mass then falls 33 cm before it stops and begins to rise. What is the frequency of uv rs3h4;) bzcthe oscillation?    Hz

  A 950-kg car strikes a huge 6.* 5g 7mrq 48 rx:zo q1jvnmhki4klslspring at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiff 8k1qxn4qs.rlm :ojvh *z 5ri6m47lkgness 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 3xw 82f.iprbycup of coffee (diameter 8 cm) 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. 118xb2f.riy3w p–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 8qk18zy oc3;kbpefp kn3 ./z h10.8 cm from the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequency of theqo13fzpenk 8h bpzk 8/c.k3; y sound emitted?    Hz

  A 2.00-kg mass vibrates according to tp kcn/ ny0-.d ou))lkld,wm-the equation x=0.650cos7.40t where x is in meters au t.0k-kywm,c)ln- /olnddp )nd 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 oscroxzs sz- qnes9m.y to,:)+ 4qillates with frequency f. What is its frequency if it accelemo rzsnes9,.x-qt4oz)+q:ys rates at 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 rafte,c:t2h 9xbzi;ej ) 3pz6cr fn, it sinks 4.0 cm deeper into the water. W,c rhe;2)p6tj xz:ezf3 nbi c9hen 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 to play at 392 dew,:c; f(riiHz (G) and 440 Hz (A):, dfi(cer; wi.
(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. 11–3k7 x.5 j8mhyuql4 ut2so9ipw:3. 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 th 85p7koqmw ustui. 9yxhj 2:4le 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 thea 5+d s jo7/ )tfcr0l9px:ij2un *msro tip of each prong moves 1.8 mm to either side of center. 0op oiaj:xrjmunsf*r7tsc9+ 2/)d5 lCalculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates wivz lj/7r 0hzonm5aj 6m6+ ro:+ws.svdth 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 t+ ohrm 6 nvz/sw5zsj.vd:0j6 7mo +larhat 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 o 19ty.uyun um8w5 6s y.xxs+vto 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 withu+w.yx6.xs ovu t8myys95n1u one end fixed and the other free.

  A “seconds” pendulum has a period )8 yamemu(54m *l2qe ,qish+ moz3smwof exactly 2.000 s — each one-way swing takes 1.0004me5sh ye), az3q+(omsum wqm * m82il s.
(a) What is the length of a seconds pendulum in Austin, Texas, where $g=9.793\mathrm{m/s}^{2}$    m
(b) If the pendulum is moved to Paris, where $g=9.809\mathrm{m/s}^{2}$ by how many millimeters must we lengthen the pendulum?    mm
(c) What would be the length of a seconds pendulum on the Moon, where $g=1.62\mathrm{m/s}^{2}$    m

A mass hanging from a spring can oscillate in the verticmozp3fw7uh.1hc aq*-v qml-:al direction or can swing as a pendulum of smacmm*f.h oa-p-qz:7w 1qlu3 vh ll amplitude, but not 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 h-vr2:m81snf))lffyw zu jh 8 is stretched under a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is genernvjlf8wsh:uh8 r)-2m y1 z f)fated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spr 3qn:zre+rh2gq:n fxewwd+a,.npw, ( *zcpw4 ing with spring stiffness constant k. A penny of mass m is placed on t:z2 n3q 4.*+w+c,hpen,rn( q wwgadrpex:wz fop of the block. What is the maximum amplitude of oscillations that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1/9tl -ob7thz 1aw 7dm1 ynsr;t200-kg car at the junkyard. The steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the had; 79tt1lyrmto7wzn/b -1 scar bouncing at the end of the cable. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a p/nt hh la2o6hof2s,/nks9f8 xlate 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 hnso 2, /2fhx/k8sf6t9l hn oathis 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