Give some examples of everyday vibrating objects. Which exhibit Swc4y2; z3)gegcznxw5r yrj 5:HM, at least approximacx5gjzrzw2w4:yg; ycr) n5 e3tely?

Is the acceleration of a simple harmonic oscillator ever zero?e,;1d. na8iwdsm3 wmjer; z8y If so, where?

Explain why the motion of a piston in an automobile e2s v- nh.m-a/or o5gqhngine is approximately simple harmonic- o/h5avnq -2m.sorhg.

Real springs have mass. Will the true period and fv s1r-.)nih +hic+u ivrequency be larger or smaller than given by the equations for a mass oscillating on the end hs+i+iv1-nh.iv )u rcof an idealized massless spring? Explain.

How could you double the maximum speed ofw -; 9 (krw)rknehjst2 a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical st23*p mt kv9 sbvx3p7tpring scale, and then is released. Describe the scale read k2 vtv*t7m9pt3ps x3bing as a function of time.

If a pendulum clock is accurate at sea level, will it gain od3p*ym y2o4zj r lose time when taken tom 24p3yjzy d*o high altitude? Why?

A tire swing hanging from a branch re -f akqvc/l*l8 ;crt.jaches nearly to the ground (Fig. 11–48). How could you estimate the height of the bvc l8-q/.l*cak j t;frranch using only a stopwatch?

Why can you make water slosh back and forth intny6cckk.:; x a5xy m)g0-zx x a pan only if you shake the pan at a certtg xccyk: ;kna-y)xxx 56z .0main frequency?

Give several everyday examples o1 viue*z3s6xj f resonance.

Is a rattle in a car ever a r(8(pywd9 a w er*ccc-a j a96e3pbas+oesonance phenomenon? Explain.

Is the frequency of ay*:8ko 0 av:pdor ,oob simple periodic wave equal to the frequency of its source? Why or :,d: ooa*v o0ypbk8 rowhy not?

Explain the difference between the speed of a 9b88twufmwwk6t+t z)* ja;an transverse wave traveling down a cord and the speed of a tiny piw8uw+*j m )8n;azk bft6wat9tece of the cord.

Why do the strings used for the lowest-frequency notes on a piyd8msne bl+8i,i :de0q ft g--ano normally have wire wrapped around theeqti:0bdymlg8d,8f- -sni+ em?

What kind of waves do you think will travel down a hor *: msxxi.dr;vizontal metal rod if you strike its end (a) dsv .xri*;: mxvertically from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase in temperature, b1 99(.wixur9aq8dmy fz 12dtz j qhpv9ut the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves in air to vary with y9 j9imr2f wq1tq1 8z9za( vd9huxp. dtemperature?

Give two reasons why1gt3yao tg7 l1 circular water waves decrease in amplitude as they travel away from the sourcet7 g1oaly31g t.

Two linear waves havnt 2bxd rq:(:ve the same amplitude and speed, and otherwise are identical, except one has half the wavelength of the other. Which transmits mb dqnv:t(2r:x ore energy? By what factor?

When a sinusoidal wave crosses the boundary between two sectiop((94p z1wnx jw pvq*gns of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocity do 9wz(4*v g 1(pxj wqpnpchange). Explain why.

If a string is vibrating i8m:s+asc 7ku exp0a3un three segments, are there any places you could touch it with a k a0+um8k7csp:3 es xuanife blade without disturbing the motion?

When a standing wave exists on a string, the vibrations of incident and riwgg k:9pmw6 k:*6r* vvim+khgbscld.c 2y,(eflected waves cdm v(kr6 :b.wli,+c*hw92m pksgg*cgk: 6vyiancel at the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one pla o 74owa*lk),d.7 lr eucceo)gce to another, how might we dete4g7eo.d )*o r 7oll,cukwc)e armine whether the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the total 4ndnp+eo202 vuz *.kp mc7z xbdistance it travels in one vd+nbnm2 k704.pezxz *uc2op period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from zni10 9+cde.divpn.y7t 3tjq it but is 85 cm long when a weight of 180 N hangs j71et ndn 9q .0p.dtciyvz+i 3from it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compres v;ek4s i1sn.1fa ,kzys 5.0 mm when its 68-kg driver gets into the driver’s seat. If the car goes over a bump, what will be ka ,yk z11i.v;n4fess the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.*pfghe fj+7*mhq.m v/6 cm when a 2.7-kg fish hangs from it. (a) What is the spring stiffness constant v/hq*mp7.h+ mfjegf * $\approx$    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 hfas; j,iwh,hw(zm 7ke,, b/y*8rc4 okc qa.phung from it. What is its frequency if only 0.38 kg hangs frwj(8;hq, 4y kz.,osw*m/r,7icfkh ecah,pbaom it?    Hz

Construct a Table indni,k+ 7:fdr )mvk;rqyicating the position x of the mass in Fig. 11–2 at times t +r: ;kdrf,7miqk nv )y= 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 vibrates p2l0 ph))mnxjo7hl d0zredominately with a frequency)0 0omxnhlh2 pjz7 l)d 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 ae(,+jv8o7dc ( a bsxxs spring vibrates with a frequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency idb(soe78 x ,v(x+ac sjs 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a sple4z t0 s5d2)wym- c) v2obthpring vibrates 3.0 times per second with an amplitude of 0.13 m.zt25hdo4)m- )wyc t lvp2b0es Determine
(a) the velocity when it passes the equilibrium point,$\approx$    m/s(round to one decimal place)
(b) the velocity when it is 0.10 m from equilibrium, $\approx$ ±    m/s(round to one decimal place)
(c) the total energy of the system,$\approx$    J(round to one decimal place)
(d) the equation describing the motion of the mass, assuming that x was a maximum at x = (0.13π)cos(  πt)

  At what displacement from equilibrium is the speed of a SHO half the ma,vpwuh (w*)dj ximum valwhv*w)(j pdu, ue?$\approx$    A

A mass attached to t. kped +;t; n1zuw: p4yvle;6lyctj 2ahe end of a spring 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 .r ti zh 9:*y5gflm usf 4l;x06xs6yktvertical spring 0.315 m. If the spring is stretched an additional 0.130 m and released, how long does it take to reach the (new) equilibrium posikxf 5yhsmxrt l4;06:g6zily.f 9us*ttion again?    s

  An object with mass 3.0 kg is attachuttgvs -q g)/ pp.+al8ed to a spring with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m f)qs gtl8.vut-/pag+p rom 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 a toy popgun 0.200 lh;5 f9pnh:kcf8v9z wm to “load” a 0.180-kg ball. Wit:;c f 8wkfvh lhp9zn95h what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to ah7qhgk,j-p cut om: . eq;dab8t1iz7 r7/hw/one end of a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, the mar1/wqoia/.7e hpz j, :g; 7au- hthbkqtm7dc 8ss 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 equ92f x.;er awvmation x = 0.45cos6.4t where x is in meters andr92w.ex fvm;a t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equilibrium is the energexu2cgv4( k2a:/a+m(k-axpb+ cwhk wy of a SHO half KE and half PE? m:/aehk w+ -(g (cpk2k aw4vxaub+2xc±    A

  If one vibration has 7.0 times the energy of a second, b a mav,-+3mnkgy*yaame:p *2t ut their frequencies and va:m2,* a*mn yky -pae3m tag+masses are the same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates ftt 670zqw q,qcrom a vertically hanging light spring once every 0.65 sqtwt7cqq, 06z.
(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 identicm-b m(ohst;bdw, )ra zx5x.3nal parallel vertical springs, each with spring stiffnro ;ahs(3).,tdbz5mwnm- xb xess 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 xn*g .t qd0 7(glg.nveo is in meters and t is in sg(gn* .07vglqten do. econds. 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 gc(kztn- ovs ao33:f* examples of SHM, labeled A and B. For each, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on the end of a horizontal spring (k = 1v0e2v j:5 dflqoyb* q0oe3 gr7c6a r3l24 N/m) is struck by a hammer, which gives the mass an initial speed ofeb5l*l32rvo: j cgyq 0od63q7 er f0va 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 wi7d4-u t l fb7abhsh:9eth spring stiffness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg han7f 9d7-hubb: stle h4ags 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 spring stiffness constants z;cza5ef * e 98uzcl0m$k_1$ 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 ac7 wo jcx 9n,9r,sz qdy8(,xeq fixed horizontal spring whose spridx87o,e c sx(wq,jzqnr,9cy9 ng 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 his malrxa9+btxru6b gy401 l :q1 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 l46:qxl+agr0ua ylb1 1 mrx9t bength 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 vibratiod3r.h 2jw k;d14a3;me 9 cxxvgu5rigbns 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 v fb8fd(.ppp3(*fh6eij kw/ uone swing per second? (That is, one complete vibration takffvjf 6b3duei* /hp (8.(wpkpes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. qrry 1rly i:y3nq9bxr0 x59p 9What is its period on Mars, where the acceleration of gqx x0yyy rip rrl:9 5139nrb9qravity is about 0.37 that on Earth?    s

  What is the period of a simpleb.e8 imh+z c wm pe/l.9ck9mv- pendulum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulu,la1 f/f qv0.ie1c7w ubiu y/km is 0.760 m, the pendulum bob has a mass of 365 grams, and it is released at an angle off u .v,efu7k10y ilcqw// b1ia 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 clock1 d aae v:rj:1oqm8zv+tk6w2lv/ vb8t loses half a minute per day, how should you adjust the length of the pendulum? shoaw ot 2/ad61 rl+88tv:e v1qvmkvzjb:rtened by    mm.

Derive a formula for t z)7k-osuco 0the 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 osci*x qy* it fcm;wel:a8y 1.j4clllates at a frequency of 2.5 Hz. At it is released from rest starting at an angle.al ym*;l wqc j4ye* fi:8cxt1 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 every 3.c*+5. wf-: 7nggxpn(ti t kjny0 s. He measures the distance between two crests to be 6.5 m. Hojfkw.(7c+ tyngp *-xn5gn: itw fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 26y/a8pb m2f 1inqjk.8 xf*f a)bqv*,z z2 Hz and travels with a speed of 343 m/s How far apart arxyzai8z q f82vfb*j1mk p q,)/.fab*ne the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 t3z)ji aj3q6nkHz and 1600 kHz (kilohertz) aj 6a)33tnzqij nd 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 longitb md1ku jg-u; f0ce9lr+g 6a47grl n:g,0qubdudinal 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 t90zgato)l ,l5b k.xa twice as dense as the other. In which rod will the speed of longitudinal waves be grea.btx al 0olk5z )tga9,ter, and by what factor?   

  A cord of mass 0.65 kg is stretched between two suppo.6rfbtrd h91xpauje*ju6q* b )86vlw rts 28 m apart. If the tension in the cord is 150 N, how long willr61 a*66dj qfbjewhrpx b)u uvt9.8 *l it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to the top of a hill by a steea ct1(zh,es8d l cable of length 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and sends a wave pulse along the cable. It is , 1(t cahsz8edobserved 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 hipeni, 9dgds*b(we/e3v 3 yt 8wpv4ct2 s ship just below the surface of the sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s latpc8 ddebtw4t sie9 ng *,2/vv(pw3ey 3er. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at differcs 2-dxgmb x:jfr+z;+11cp qs ent speeds, and this difference szxp rcq bc;-+s2f1gxd m:+j1helps 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 surface wave can be approximated byi:4h h,cs( 3qwyrx; ac a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of freh,s3cc:(a 4;q hiryxw quencies), 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) the ampdyy6+n;x o y1glitudes, of an earthquake P wave passing through the Earth and detected at two points 10 km and 20 km from the souyx;d1 gy+6on yrce?(a)    (b)   

  The intensity of an earthquake wave passicwoicx:. )n y* lmth(9ng through the Earth is measured to be omxln:h(tcywi c)*9.$ 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 portio2mhojy-6x*)b 6uk c 4f 52hs c-sl;lofaiko i9n of the Earth, but one is carrying twice the energy. What is the ratio of tcs k*6a fhiohl2o sxufycj4l92 6 -i -)bkmo;5he amplitudes of the two waves?   

  Two waves traveling along a stretched strijrm h0p y81l7xng have the same frequency, but one tr1m7rpjh0 8 xlyansports 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 observed to move up and 3f.t61epu6e,7po hv n axb-dodown a total vertical distance of 6.0 cm, from 17pn a,vxt63h.p6bo- eeuf od the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown i9 vylgd9 g6*v-l/g rshn Fig. 11–52 are 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 oth l/ gd9g9l-g6 svr*yhver, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundamental frequency, what are the -fj( dr8uxvtwl+d-g4 frequencies 8wgl--d juvr+d4x (t fof the first 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 itrmx 0t5n7ssy; vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of t;5y7x tms 0rsnhe string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequencsqhupb5g7x *cuan nf o; 3: sj+ rpqgw,t)5;i4y of 280 Hz. Name at least t)r: ,3gqsnuj p h nxb47g+;wq*o ui; c5fpsa5three other frequencies at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If th1;be) fquc .c0gtvbq 3e frequency of standing waves is 475 Hz, how far apart ; .301 gvfccue q)bbtqare two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 38mnf(broszd-wo ,/ vb rb,8 a250 Hz, what is the freqao b8z-(fr2vmod,/r,8wsbnbuency of the fundamental?    Hz

  A guitar string is 90 cm lon +,w x:3* dlxkc3z in/tayej8bg and has a mass of 3.6 g. The distance from the bridge to the support post is L = 62cm and the string is under a tension of 520 N. What are the frequencies of t3: 3awtjy /lix,k*+edxc8bz n he fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrmybxf3)gpb7ck/rcw7m f/ h: lyz b 701ate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct73c:0w xb y71lkfc)y b/7z/ fpmrbgmh the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed w:bz75luln 7pc3o8 vbg n )z0lto vibrate 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 t75ub:zznl w3)8g l op vblnc70he frequency? decreased by    %

  One end of a horizontal strinu:jjjcl.9mx o0sbk3;v jx n3( )2aojjg is attached to a small-amplitude mechanical 60-Hz vibrator. Tjxu.jjsc9xb jnj2v)k( ;aloj 303 mo:he 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 s ayql tnn.(.a/tring may be adjusted by moving the pulley. If the hanging mass m is fixed at 0. ty/lna.n (a.q080 kg, how many different standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water 6okd.pmz2)9 qqj y1jf back and forth in a tub at just the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65fzdqm. y1kqj2 6j9 )op-cm-wide tub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave travelinguabr2b ck:a9x8p 1wq + at k.0 km/s strikes a boundary within the Earth between two kindaqk+br a 1:bp8 xwc9u2s 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 velky,g96v sa /ljocity changes from 2.8 m/s to 2.1 m/s If thvj69 y/aks l,ge 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 aq8-ptg: hki8fg)v wy0 ir when it hits a layer of cold, dense air. If the sound wave hits the cold air interface at an anvp:0- i 8y8kw)qhgtf ggle 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 betwee :x-, j.ijbxfgn two types of rock at ax jgijxb ,f-:. 38 $^{\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 diamh k octkdkf992o5z7 i6eter. According to the user’s manual, the dish has to be pointed in the direction of the satellite, but an error of about 2 to69k hf7zkdk 2ci5o9$^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 2yhh uh7+:.wb/i u u8u(wzuco4 50 km and velocity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, peoplw7+4zuou/ h 8:uu(yi.cwuh hbe have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness constant of 550 kie54op1 cc ;xjN/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 (approxima15ixc4o pcj;etely 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from b xq 4rl 91nqy)7u4iqna window to a fire net 18 m below, which stretches the net 1.1 m. A4q1q yqxn9i47ur )nblssume that the net behaves like a simple spring, and
(a) calculate how much it would stretch if the same person were lying in it.    m
(b) How much would it stretch if the person jumped from 35 m?    m

  A mass m is gently placed on qu sm(j) 1yq.h0hrwd0the end of a freely hanging spring. The mass then falls 33 cm before it stops and begins to rise. What is the frequency qq) y(h 0h1rdw .ju0msof the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s pbefu na/r x.2fq/ /6tcgwo47 (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffness constant of the gupqb6/x n.2w7e4artffoc// 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 ,m6s:a/o jk uzgao.k*right pace of about 1 step per second, the coffee sloshes more ao/ m6:oaaku.ks* g,jznd 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 ceno; tt+i9 pbqqq))dku8ter of a 33-rpm phonograph record have a wavelength of 1.70 mm. What willqt+k ;dbtpo 8qi) u)9q be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equat.1dljxw+sj6 1oguzq+ion x=0.650cos7.40t where x is in meters and t in secq j1 +lwzgu +x.sd6jo1onds. 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 f y5m5okrlu; 9.syi ao4..oc nvrequency f. What is its frequency if it acceler . yma;.4vioyo rc5k9su.n lo5ates at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft float3q nxqd.-suy 3s on a lake. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps ofn x.duyqq- s33f, 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 Hz ( i1;tvi dbc857cr7ec/r a wz2 dsh+y3wG) and 440 Hz (Aez2icyd7r aw3cb7c1 ds/ 85+h twvir ;).
(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 stretche2td ad:ytx9o1d two-part cord of Fig. 11–33. Determine a formula (a) for ta1 d:dox2y9tthe ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the ts1yf 9s6)nm enis,0gnwek /r 0ip of each prong moves 1.8 mm to either side of center. Calculat )in/0,yss6eswmfknn0 eg r91e
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simp/x3-bqf 5m1 4mojy1jcb,bu nn le 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 place3 bnuj/jy1qfc-om b1m n45,x bd there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” en()5:yt lo5( k-+hsvujrs1j sjwo; yo yd if that end is attached to a ring that can slide withouk -)ys(5rs5( ovo:o yh+uj;lj1yws t jt friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.0juv-:8 p+kxvj9y:qq g00 s — each one-way swing takes 1.000 s. jy9+ x-:q 8vq:vgu kjp
(a) What is the length of a seconds pendulum in Austin, Texas, where $g=9.793\mathrm{m/s}^{2}$    m
(b) If the pendulum is moved to Paris, where $g=9.809\mathrm{m/s}^{2}$ by how many millimeters must we lengthen the pendulum?    mm
(c) What would be the length of a seconds pendulum on the Moon, where $g=1.62\mathrm{m/s}^{2}$    m

A mass hanging from a spring can oscillate in the vertical direction or 4ze0+u6rib 4odib 1yscan 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 of the horizontal swings r y eib4+6bo0s1z4diu, 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 m8q5triv. f9v of 255 N. A pulse is generated at one end, and 20.0 ms lamrv9vf.it q8 5ter a second pulse is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended fromox6a-(q9mlz 2cfm.lpng-3 z c a ceiling by a spring with spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillations that will allow the penny to jumalxmq2f-6-oc c g znp93 l(z.st stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. Th0hi o,*d0e7 ekbckj/* j.19a safsnhhe 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 bouncing? [Hint: Refer to Table 9–1.] 9n*.kesk1fa/ca00 s,j*boehh7hdi j   s

  A block of jello rests on a plate as shown in Fig. 11–58 v4oes3n ) bbaygroc+2;b (7e a;:n nuf(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 vibraenbob 2;s (n;v4u n7)3yf:ocbra +ga ete. 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