Give some examples of everyday vibrati t)q art m(f /m)-mc)x axp*,mcrt9d.hng objects. Which exhibit SHM, at least approximhxmft)ta,9c (p/*r- xcm .qt)mar)m dately?

Is the acceleration of a simp1*dqyr-af *e7xs 7pv: ogb9xxle harmonic oscillator ever zero? If so, where?

Explain why the motion of a piston in an automobile e-q7 ocqirntq7sp) qaxp8-o*3 ngine is approximately simple hq-is oq3 8-r*tqcoq7 anxpp7)armonic.

Real springs have mass. Will the true period6vcvuql w (+klf,6l 8+tn qi6q and frequency be larger or smaller than given by the equations for a mass oscillating on the end of an idealized ma6l+w v,(8fk+nq ucq ql tliv66ssless spring? Explain.

How could you double the maximum speed of a 5p fx1+1mtlx hsimple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertic6pcibrxq4e zq971o 2sal spring scale, and then is released. Descri7oqp1qz69i s4e xc2rbbe the scale reading as a function of time.

If a pendulum clock is accurate at sea level, wi qbwo4aw 5fq:/+up:2 yblbo0ill it gain or lose time when taken to high altitude:+iqp5ow4qb/ blo: 2 awf 0uyb? Why?

A tire swing hanging from a branch reaches nearly to the ground (Fig. 11–(lv3; ;xndb yb48). How could you estimate the height of nly(vbx3 d;; bthe branch using only a stopwatch?

Why can you make water slosh back and forth in a psupsppa 4 hn )*.o)b6ro)cf2ian only if you shake the pan at a certain frequencp4hc )pouri26.n*f )bspo)s a y?

Give several everyday 98tt gpcic9 d0examples of resonance.

Is a rattle in a car ever a resonance phenomehc+; xhjend ;1non? Explain.

Is the frequency of a simple periodic wave equal to the frequency of its source b6nio )t6dv8+ pupf5t? Whypf) otd5u npb8+66vt i or why not?

Explain the difference between the gh i-4k3ibo6d/kzm2xk.:iu.zxsw4a speed of a transverse wave traveling down a cord and the speed of a tiny piece of the co.ia4x.xz6us2khok k:z3g-m 4w/ bidird.

Why do the strings used for the lowest-freq0ky ar96a(gne uency notes on a piano normally have wire wrapped (6ng aak0 y9eraround them?

What kind of waves do you think will travel down a horiz7w16qq*yf 4ew )7vlbscqq 7wgontal metal rod if you strike its end (a)7q7cwgvew6)wlq b fqy71s*q4 vertically from above and (b) horizontally parallel to its length?

Since the density of air decreases with 7rne jmf, 3x5san increase in temperature, but the bulk modulus B is nearly ind,r 75xm3njsfe ependent 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 amplitude as they trave a:*.c7+7te hfm 6bstsd-qwogl away from.ao6es 7 ht7*sqbmf tcw+d :-g the source.

Two linear waves have the same amplitude and speed, oy49:yk wytwmqw;5 t9 and otherwise are identical, except one h5 ymyk w;: 99tqtoyw4was half the wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sectionm v/caw b0w 4j3y*b9z kc+s 9-wozcd/os of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocity do change). Explb w/oz04wckyj 9-w m/vc b*+3dcaz9os ain why.

If a string is vibrating in three segments, are there any places you could kxl7f 8mw/m4ctouch it w8kxcw/4 f7mm lith a knife blade without disturbing the motion?

When a standing wave exists on a string, the vibratiopr vm8z*+qy 2ik)n2va ns of incident and reflected wav vrvyp *+8im2 k)znq2aes cancel at the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one place to another,i7 d+h io1g ,2kxswnv8 how might we determine whether the energy was being carried by particles (materiai2,wk8+n xvg1i o7 hsdl bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, whad p- 4m8q:qbsmt is the total distance it trav qmqbdm48:-p sels in one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it but is j rj j6.x-p(06nhrvfg.bv wk:/o xet/ 85 cm long when a weight of 180 N hangs from it. What is the “spring” constan(h:. kxx 6j btg/0jr .vvew/op 6j-rfnt k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68goj ;;y)zwe wjzs2: fo-mq q9zv4 8r0i-kg driver gets into the 0iz;)8zvyr wj2e -qz gjf9som4o :wq ;driver’s seat. If the car goes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm p1 m32rmk rqq36dz(:)jdvxi vwhen a 2.7-kg fish hangs from it. (a) What is the spring stiffness consxqv 31v (: mdpkz6dqijm23 r)rtant $\approx$    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 frequl8f-af v vosr d3l*0ijl3.d:e ency of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency if only 0.38 kg hangs fromo. 3da jfl*sevvilf0d:38r-l it?    Hz

Construct a Table indica0;c4a qlx7rwi ting the position x of the mass in Fig. 11–2 at times t = 0,t =r lcx074qa;wi $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 spiddoh)w7p (i)0h5e6z a 9ykh bh mhd:x:b.n9rewer’s web. The web vibrates predominately wi .wa5eb7zh):)(yhhmd6k:bhx 0 ho 9w 9rdepinth a frequency 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 Hz. When an ad.i5l e8-b+ bcob xe lu,5yy3tvditional 680-g mass is added to m, the frequency is 0.60 Hz. Whay5yxbe c t-b5veuoli8. +b3,lt is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per second with ae.itb04 5uni+- xgn5 xawl1 u/l.nzhxn amplitude of 0.13 m. Deth4g0exu+ .ntnz nlxa5.w i l/ib1-x5 uermine
(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 equiklat13d arn:6nh-ey 3librium is the speed of a SHO half the maximum value?ky d1 3lnhr6-e:ana3t$\approx$    A

A mass attached to the end of a spring xdi(odzo7,b0 is stretched a distance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretches a vertical spring 0.315 m. Ify,itkg 2qv:( w the spring is stretched an additional 0.130 m and re2tgw ,:v i(kyqleased, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a s2szrt7a(;c08x r mtfmpring with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is f8 ct0a 7mr;(ztx 2smr0.020 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 compre9ekmpxi gw4f-6/ m zfqyck .+6ss the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will the ball leave the gufm i9 y 6qzmc+-p4. wx6ge/fkkn?    m/s

  A mass sitting on a horizontal, frictionless surface is attachewb+skwy4d()g8lr l -msago,ro6g +f*d 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 mg,smwf+( y4boalr sw *)- lr+do86kgg. 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.akw;17o h -f ybcm(ankt/n2n:4t where x is in meters and t is in seconds. Dete-yk2n(hwab7 /ntf; mac kon1:rmine
(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 tlbu hooq, :3:bhe energy of a SHO half KE and half PE? ±h:uqol o:b3b,    A

  If one vibration has 7.0 times the energy of a second, but th.,fzga oxuf 0:eir frequencies and mo 0xf.:u gzf,aasses are the same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light spring once every 0n5 +m:3. tw xpbdmdzl 6/sm ap:-8efne.65 pxam-:+mstm65d .z w8nb3e f:e/pldn 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 supporteo ewi1-1ml.m md by two identical parallel vertical springs, each with spring stiffness constant k ( lw1 -eimmo1m.Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the s y/e i(3ov*5+hwkcu( f rf4ojequation x = 0.38sin6.5t where x is in meters anw*oeu k( /shovy cr+4(if35 jfd t is 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 pge3f7fh: 7xisfg02 nof SHM, labeled A and B. For each, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at re;gvnhurc: m)yc6)i ;jce cfib+ ) -5wnst on the end of a horizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.96m/s b):v;c 6c nrcc+yjgiwi ;mnu )h)ef-5Determine
(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 vibrates with an amplic ,sey0- n59i./n u1-x whbxsr1tu zkrtude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) wit r.w10,khz xs-iynre51xs9bu u c- /nth 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 stie(ln d:, 4b5:kv5ncvyk imbq+ffness 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 0/3pe*i)uc qv fi kl/f6.600-kg block attached to a fixed horizontal spring whose spring stiffness conk3upe6/i*ilf vfq/ c )stant 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 bridgemtuxsa2o(u7(rfv ;; .x csz8g. After reaching his lowest point, he oscillates up and down, hitting a low point e7;(ts f8 ;umgur.vx(x2zas oc ight 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 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 0g1u.+bzgvmz is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simpg1 klo3jke :4yjw 3 2bpx47muhle pendulum be if it is to make exactly one swing per second? (That is, one complete vibration takeskx o33lg p m:ew1h7 k4j4ubj2y exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on M7mdqy *scuq83 ars, where the acceleration o8 u3*7s yqmqcdf gravity is about 0.37 that on Earth?    s

  What is the period of a simple pendulump avl,e-wi;fv4 ppsu :z;7gycy:n *7a 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 mk yiu +12g4av +t lc*pn bt1,ja*dj1ff, the pendulum bob has a mass of 365 grams, and it is releasclv* ytjuanfpaj* dg k4 b,1 +21+if1ted 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 0.9930 m. If the bx y :v .z,,z91crdesnclock loses half a minute per day, how should youbcz : xn9ver,.s,1ydz adjust the length of the pendulum? shortened by    mm.

Derive a formula for t1w uchri1y m2 ekb,6 *g/+qehmvyp1ig/ 0nt-xhe 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 oscilmrb rj.)0zzfx42ng d 4lates at a frequency of 2.5 Hz. At it is released from rest starting at an angle of 15 xg.n20zrjzbmrf 4 )4d$^{\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 ;plu fxln* )) 1d61*n r) kwki4ejodvcboat every 3.0 s. He measures the distance between two crests to be 6.5 m. How fast are the waves travklfok eu6)ni; lx*1 j)4cdr)* 1vnw dpeling?    m/s

  A sound wave in air has a frequency of 262 Hz and traveiuhas38 7)9da n vibm5ls with a speed of 343 m/s How far apart are the wave crests (compressions3 d8su5m9 ai7n)abi hv)?    m

  (a) AM radio signals have frequencies betweend (c+bfik(e h4.zu 5mt 550 kHz and 1600 kHz (kilohertz) and tr+htf5b e4um (.dc z(ikavel with a speed of $ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

  Calculate the speed of longitudinal waves in bzt3 -(apt,fd
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, b:i(gt2jpb2 t:;cw vvo ut one is twice as dense as the other. In which rod will the speed of longitudic2( : 2ibgtvwpvj :to;nal waves be greater, and by what factor?   

  A cord of mass 0.65 k b8 4ipt8;4fof 8oa e/wb2jnl-krw;fkg is stretched between two supports 28 m apart. If the tension in the cord is 150 N, how long will it blfaob44jo2w p in ;k 8tfewfkr-/;88 take a pulse to travel from one support to the other?    s

  A ski gondola is connecte2)0m wr*bxywyc)3 npd-vvxlbcb0,5cbs 3y 9md to 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 smxb0 n vby59, w2y-r) pxvd*b3bym)c3 lcc w0terminal 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 his ship justxd9ii,f )m w61ti: xou6 l1fj z;ovf0s below the surface of the sea. He hears the ecifm1xltof;j0 )9,6dxv1f i zsiuo6w:ho 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 differea hl f),t5jp8x x5-opqnce helps in locating the qpp hj )o5l-x,ta5x 8fearthquake “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 surface wave can be approximated by a sinusoinycgb 6 zd*0 o7/e7fwpdal transverse wave. Assuming a frequecyf npzd 76 0*ob7wg/ency 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 intensivkdk )u57/ vlo nkj):qties, and (b) the amplitudes, of an earthquake P wave passing through the Earth and detected at two points 10 km and 20 km from th n)q kvkk5): u7/dovlje source?(a)    (b)   

  The intensity of an earthquake wa4da*,,igv gf dl5k p0fr+qr* 9o 6qpjwve passing through the Earth is measured to be ,p*5rq6gldr wj90qv *d4+oifp,ga kf $ 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 frbd6 *: fwbo1jyequency travel through the same portion of the Earth, but one is carrying twice the energy. What is o:d6wjyf* 1bbthe ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string ha *scra *th;45p vti0qjve the same frequency, but one transports three times the power of the other. What is the ratio o h*5pjr4ttsq ;v*0caif the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move up and down a tota: kdk9unbm ob p47wf+8s+3dhel vertical distance of 6.0 cm, from the lowest 4 wdk:hpk ef ob3d+9n8mb+7us 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 arehqr.z cw.lm-8 geji*( moving toward each 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 has happened to the ( lz *hwecq gi.m-.8jrenergy at this moment?

  If a violin string vibrates at 440 Hz as its funda5c vy9z)bhtz-mental frequency, what are the frequencies of the firc5zv9 hb- )zytst four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what frequency will i ,2m ua8xkdurafuc4ei285aofw 4d )b6t vibrate if f ,u8kaow m5u 24xd2)raad48cefbui6it is fingered one-third of the way down from the end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loopsmzx6aw*( 3ebvr a6p v 5:nzg,k at a frequency of 280 Hz. Name at least three other frequencies at which it wi(5a63kvepwbx* g,rmzv:6 a znll 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 frequbvp zj/dce+4qj/ d/ctmf5v0o +1 r co5ency of standing waves is 47 +j+e/d51 ocm d5v /zcpbfvq04c/jort 5 Hz, how far apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 350 Hz, what is 3 d-ubkcc j36*vz(g mqpmj80s the frequency of the fun0 pmj8( jc*6bmd k-3cgv zqs3udamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. * uw(f dt+pr).lhnuw.nm4 1rwThe distance from the bridge to the support p( 1p.dw*tu nwl.nu)rfrw +4 hmost is L = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibratef h6*m.m 6beyo at 200 Hz, but it is measured to vibrate at 205 Hz.f.oe 66hmy* mb 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 suppose. cvnsu o3e:i)d to vibrate at 200 Hz, but it is measured to vibrate at 20e.3io ):cn vsu5 Hz. By what percent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is x--humo f8e-ebckpw zzn8rdi7t9;1 8attached to a small-amplitude mechanical 60-Hz vib-wr zu7 ;pk88zeh18mbf- doi xe-nt 9crator. 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 bi6uh5 ssmi4sq1z) wuu m+r--by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying L betweeb z)14+- hrmui5m qsuuss6 -win 10 cm and 1.5 m?   

  When you slosh the water ba5tzp7 4.ngx mfck and forth in a tub at just the right frequency, the water alternately rises and f tz.x5fn 47mpgalls 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/y8xf:*cku/kpr8 ru x:s strikes a boundary within the Earth between two kinds of material. If it approaches the boundary at an i fucrx :xu*ky krp8:/8ncident 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 veaj4b5*0 n+52budlfbti9nnoxlocity changes from 2.8 m/s to 2.1 m/s If +f bx*ln dbt0b492ju5n5oainthe 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 laywa9-m)hvgniahevb. 6f 3ph( :er of cold, dense air. If the sound wave hits the cold air interface at an aib3v: pe -a)( hf96vhwg.amnh ngle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave stric +pwxdf*5a( ikp7qp8c n*-fwkes a boundary between two types of rock at a 37w f(nad fp5icp8qxk-* pc*w +8 $^{\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 5*xkr-( g qnzi0.5 m in diameter. According to the user’s manual, the dish has to be pointed in t5(nxq-kg*z ir he 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 (vgrlhxi8*o-rf 5d6 x the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of ldg f-rx(ivh8*o5 rx6sea 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 caraulzcp94 42b r bumper has a spring stiffness constant 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 mi/h). [Hzracp 24l4b9uint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m below, whichyx;hq y2reso)wb/l7 0 stretches the net 1.1 m. Assume that the net behavew oh/b ;)07xlqes y2rys 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 springt)ry zgj0pu- co(; vj p7hc+l,. The mass then falls 33 cm before it stops and bov;zgu(7rp clj hy c)t0,j+-pegins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spri 3 +t:;mcuaa.41isr zkpkoy0 cng at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the ckr ac34opu0;. a+ksyt:z m1ispring 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 cm) at just the right44 9bzwjd3-ju 2mrjsj pace of about 1-j43j mru dbjsjzw9 42 step per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the center of a 33-rpm phonograph ri a80ge8 a;nzeecord have a wavelength of 1.70 mm. What will be the frequency of the sounea88ea n 0;gzid emitted?    Hz

  A 2.00-kg mass vibrat-y hyz;p;o wv, 43obbfes according to the equation x=0.650cos7.40t where x is in meters and t i y-oow4vfbp;3z h;by,n seconds. Determine
(a) the amplitude,    m
(b) the frequency,(round to two decimal place)$\approx$    Hz
(c) the total energy,(round to one decimal place)$\approx$    J
(d) the kinetic energy and potential energy when x=0.260 m.(round to one decimal place) PE$\approx$    J KE =    J

  A simple pendulum oscillates with frequency f. What is its v1d2z3ka:hs1i, pnrx w0o nr4 frequency if it accelerates at 0.50 v01k z2i orxn,1spah3rdnw 4:g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats o tlx)obsa6 m vrn-o52)n a lake. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into th)b ar2l o6)m5 xtnos-ve water. 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 is7li+s p 6uy9kfbo9 x -ebgj+-*pi7psnstrument are tuned to play at 392 Hz (G) and 440 Hz (A) 6p9xs9 ppbssu7+y-flbgikij*e +7o - .
(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. 1f,ky3usr3e 2ub06xnx bwxk i+j ;a6k4f jc 2n71–33. Determine a formula (a) for the ratio of the speeds of the f;xc2xfujkkn+ 3xsn 76baj2 4ry60kwi3 , eubwave 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 7 /dook h(qff:x;hhn1of each prong moves 1.8 mm to either side of center. Calculateh/kqfh x :d7of( 1hno;
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simple harmonic motion of frequency 1.5y*vbi8d7,ono d u:)bt 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 boarv ,nd d7)tbib8 *y:ooud during the oscillation?

A string can have a “free” enatz ; 3w8c0fcndfgz .7d 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 strin tfdf30cazwg. n78;czg with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each one-way swgev vz54p4z 6uc3xk0zy k:qmi-.kr a2ing takes 1.000 s.4grv qm vzkxkk4 2p5auc0z-.6ey z:i3
(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 8mg xna*n a8q: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 period n8:nxg8a*a qmof 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 t3eo,i mk;vqj pcaq.t9 w(7 mtfkq7i 21ension of 255 N. A pulse is generated at one end, and 20.0 ms later a se(. am c1keq723q; tiwiq7tf kjvo pm9,cond pulse is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M isogttv9ag0m c 0 2f6 getz-l2aowt: :3k suspended from a ceiling by a spring with spring stiffness constant k. A2g o kv6og0t :2zctf9am -:g e3wt0atl penny of mass m is placed on top of the block. What is the maximum amplitude of oscillations that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a xvf z:t90 hnl*q, 5jfxb z::qm1200-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 car bouncing at the end of the cable. What is the period of the fj:0:*xv 5,:qntlqbm zzhxf9 bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as rtwo*op ,m1f; gl6* ra 0oxw5eshown in Fig. 11–58 (which also gives the dimensions of the block). You push it sideways as shrom,a0oe1 ;or5p6f txg*w * lwown, 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 jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz