Give some examples of everyday vibrating objects. Which exhibiozb2x8dk)j6 8jjbz to72agz 5k. k+qefr)x4r t SHM, at least appr5 jjkzo4g e2q2zr6ra otj8 xk.b8 b)7zkf dx)+oximately?

Is the acceleration of a simple harmonic oscillator ever * rt99*fpwt bszero? If so, where?

Explain why the motion of a piston in an automobile engine i(lor6 yclujxmu9 +y)4s approximately simple ) 9lmu(6+ yujlyorcx4harmonic.

Real springs have mass. Will the true period and frequency be larger ortnq gjbpla gfj(m6 :7ze ;v.0p)el( l; smaller thfez)l 7tj p(:qj0;mbvan;e lp.g6gl (an given by the equations for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple harmonic oscillator (SHOku g-wr* *puzs;8pt2 n)?

A 5.0-kg trout is attached to t8fs mg 5zuown9p/f:p7 he hook of a vertical spring scale, and then is releasgp9 fw:p5/7 um8ozf nsed. Describe the scale reading as a function of time.

If a pendulum clock is accurate at sea9x)wa fx9)h z b8nx8cx level, will it gain or lose time when taken to high alti x 9z8a)fxc9 xwhn8)bxtude? Why?

A tire swing hanging from a branch reaches nearly to the ground (Fig. 11–4j4;5 eprq3(tv3ifp xt8). How could you estimat tvpp 4r x;(3t5iq3jefe the height of the branch using only a stopwatch?

Why can you make water slosh back angx)u:ags w+ +ee t/b:t arafy/s89 7gvd forth in a pan only if you shake the pan at a certain frequenca7a:yv at 9g tr ub/ /ges8:xfs++ew)gy?

Give several everyday ext :/pqcod6ja (w)uir8 cpd;-t/ h7qz0-ejwexamples of resonance.

Is a rattle in a car gz gl9 :waq1-vsnuk)+3vmr0 n)k.gdxever a resonance phenomenon? Explain.

Is the frequency of a simple periodic wave equal to the freque:gu t3xpm2x/ency of its source? Why or why not?/3g:t uxe2x mp

Explain the difference between db1lqr0f l7f 0the speed of a transverse wave traveling down a cord and the speed of a tiny piece of lb d0f7q 1f0lrthe cord.

Why do the strings used for the lh,:9 tx7z 0nextyfnv3owest-frequency notes on a piano normally have wire wrapped around 9xntfev:z 0yh73 txn, them?

What kind of waves do you think will travel down a horizontal metal rod ifpo.5 :rqki,det zs/ )f you strike its end (a) vertically fr:,f/q5k r t.)pds zeioom above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase in 5s ksbij )e))gtemperature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves in air to vary with temperag)i5)ej ssk b)ture?

Give two reasons why circu3.jp9b -nb 8fkara.hzo nk/a)lar water waves decrease in amplitude as they travel awa 9nb/b .aa.kjoh83)anrp zfk-y from the source.

Two linear waves have the same amplitudeyv b wz:4e)tb) and speed, and otherwise are identical, except one has half the wavelength of the otvt:beby w4 )z)her. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sections of cord as in Fjo2vz :c97n mp:gbbr v6)awke7d( vu*ne. rh)ig. 11–33, the frequency does not change (although the wavelength and velocity do change). Explain wrw26d)rpnajnmv9) b:ov7(g k v: eue h*7.bczhy.

If a string is vibrating in three segments, are there any places you cogronq +tr)ezb/ .)s:ij6l8bme d v-wq e612 bhuld touch it with a knife blade without disturbing the motion)r/gevrto6e2j m.bhs8z1 bdni e+ -qqbw:6l )?

When a standing wave exisaoo2u h*q;nmdf: q ;7sts on a string, the vibrations of incident and reflected waves cancel ah 2na ;:o7*dqq; omusft the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was bi fay v*ixli;3 kf3.nhz 0/4gdeing transmitted from one place to another, how might we determine whether the energy was being carried by particles (material bodies) or by g0;lkixd3/*ny 3fz .av4ih ifwaves?

  If a particle undergoes SHM with amplitude(9m*9kgvhzip f5i -jl jwi (c89rn6b v 0.18 m, what is the total distance it tra (85inhg vfj*mj vi(k 9li9crz- bw6p9vels in one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangv:jhm7h8 rjsj:u/*n qs from it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” cons7 jn *8 jhmjqsh:v:/rutant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg driver ge;d,mdzfsq6 w -ts into the driver’s seat. If the car goes over aqfwz - md;d6,s bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 k gjy+;0uwov0g jo2p.cm when a 2.7-kg fish hangs from it. (a) What is the spring00 owjog+2ykj pg uv.; stiffness 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 mass of 0.60 kg is husp. 8vbk *4cxew78ssh 9g2f6d+h*yz 8hhsssung from it. What idws 6 yx z heus s4s+ kpg9.b72hs8hv8*8shc*fs its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the poshudb8vq*z u7u9w6t 13bng zk.ition x of the mass in Fig. 11–2 at times t = 0,t =u9qh 7kzz 6bwb ng*uv1u8 d3t. $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 vibrcuumpka )(nn ij4v,7 8ates predominately with a nnjiuamv8ck7 4p u )(,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 aw c; cp50f0 :bdlxq+ri spring vibrates with a frequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 Hzc;ifxwdc :b 0qp5r+ l0. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per second with / d e. / ex*enztfq-/llt3w2ena-p 8tcan amplitude of 0.13 m. Determinet*/ weexc zn-q-lndp fa./t e/8elt32
(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 aujn v(bxpspi9 ,zw 8n+s.+/ mzcaj11equilibrium is the speed of a SHO half the maximum valui /n 18sxjvpzjnu, s (am9w1+zacp+.be?$\approx$    A

A mass attached to the end of a spring is strbxq(mk )::d6 bhyh oh;etched 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. If the spring is stretche1tx3 f /0thu 2ivz; yqjvev*jgd 7hd(;d an additional 0.130 m and released, how longd1zh/hvtitv;(7qjfe udg*2 ;yjv 30x does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with spring aqwv ,sz6);vzx f2pp7 0otfu: stiffness constant k = 280 N/m and is executing simple harmonic motion. When the objecfw);: ,vvztxz fsp 2 oq076puat is 0.020 m from its equilibrium position, it is moving with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compress the spr-8)3ea x+t1vvsizes)pb o1kqq(os 3j ing of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will the ball leave theis1o)8z(q3k3-ve xstp) e j+vo a 1bqs gun?    m/s

  A mass sitting on a horizontal, frictionles2xsw3 -ltpg+ 5f2fthts surface is attached to one end of a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, the mass experif3 x-l5s h2+wgt2ttpfences 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.n:u60 x6zaoezpu +db;peg+;2e sn3o* 8kg otw4t where x is in meters and t is in seconds. Deterzosu0ntnw o d;;b*3po2ze+ 6paxg k e u68e+g:mine
(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 (v ll 1p2 2pi8nu0zmwlis the energy of a SHO half KE and half PE? vlu1(28 plznwpi2ml 0±    A

  If one vibration has 7.0 times the energy of a second, but their freque+0 qca-uwoau m u2n1pl/o +g;yncies and masses are the same, what is the rncga m12wu yu0++lp/oa u q-;oatio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vecuk+ *u-vxrsq9 ba wj.9)byh *rtically hanging light spring once every 0.65 s. -r+us y)9a9bwbchk*.qx*u vj
(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 vertical sr 7a( .tn- r cumlt*oic/t:tx9prings, each with spring stiffness constant k (Fig. 11–49). What w*m xol t tca7r(u ti/rc9n:.t-ill be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t where x is in y4re f-qop(z-s:s 8vbmeters and t is in secondsb8p4vey s:-rs f-o( zq. 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, la f cz3x9c0h:w)ihy.e;1ypx pn 9jiuf 5beled 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 q+ d(hrhq(0vlrest on the end of a horizontal spring (k = 124 N/m) is struck by ah h0q(q+r(dlv hammer, which gives 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 stig l :/d;news8* mthj7nbes.g b.b3:yzx 4*lxoffness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it.b7.jx:ngm;h :lt/e obb*g *zdexn8 swls.y34 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 spr/1ctpkr9y /*0kqndkt89p- d r fkmo g4ing 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 fixecet)+ yfc 3p+od horizontal spring whose spring stiffness constan f)y+cco+t e3pt 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. At0j knejq 81w(fter reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m belwq ej0j (nkt81ow 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 7 vx9h6/gm rns7d 56ci2uvlyfis its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum rdxaunc 8++ 5 oyenfw(jk03x1 be if it is to make exactly one swing per second? (That is, one complete vibrationu5k nncdfayjw 0 xr8(1+xe+o3 takes exactly 2.0 s.)    m

  A pendulum has a period )lz3 lqtg5n 5p2ck/hoof 0.80 s on Earth. What is its period on Mars, where the acceleration of 5hg /)5onpq c 2k3ltzlgravity is about 0.37 that on Earth?    s

  What is the period of a simple +um 2y)si4socpendulum 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 m, tmg0dwb -ue ux7 zivff**.vv(+he pendulum bob has a mass of 365 grams, and it is released*-7u+*bv. evz0dmf ixuw( fg v 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 b8qdbnk x594 u,gdj2 ,fvs 9adthe clock loses half a minute per day, how should you adjust the length of the pendulum? shora4 s9ud8jknx9b f,gvb,qdd5 2 tened by    mm.

Derive a formula for the maximum speedem utl1a *qj:3 $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at a o*3 hpipvi63c frequency of 2.5 Hz. At it is released from rest starting at an3ipvh*pc o 3i6 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 b w9t4j*e:p ,q2e2/kqxos n0 osa0pglcrests pass the bow of his anchored boat every 3.0 s. He measures the distance between two crests to be 6.5 m. How fast are thex g ,*ejpns 2p ewk q/o9:sl02aq0o4bt waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and cy i,qer d0jye46)bt,0uj ,sgtravels with a speed of 343 m/s How far apart are the wave crests (come0tj ie q),4c,,s6djy g0rybupressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (kilohertz) + s+wmww rp*f:bq5 kl0, 3 srg*zeacp,and travel wita0segz m ,p*br5l+,w3r:spf cw* kqw +h 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 longitud wezine62+(bypeb2-q3vc- 1b oih2zminal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one is twice as dense as the+; j+dgzf5cdn other. In which rod will the speed of longitudinal waves bed5+ gzdnjc;+ f greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28376lf jie 2u2i,oqnedb i c;r* m apart. If the tension in the cord is 150 N, how ln 2u2dii *jib3olq76 e rcf;e,ong will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to the top of a hill by a9(d4b0wi sd5lxocbdl -e bu5i- i g3j/ 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 sends a wave pulse along the cable. It is observed that it took 16 s for th sd5cg0jdl4-9l/ i3bwbdii -uebx (5oe 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 just below the surface of the sea. Heqpx. q1sp3ylzq/w yq0x50 f8t hearsw0q80fx 35t q ly/1pyq qzpxs. the echo 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 f0oj(w4o6uvp9 ,mdkttravel at different speeds, and this difference helps in locating the eat(6po4vdum9 f0 o,jwkrthquake “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 approxiiv;)1rzj5 uchvvqc5 3fz:y k+ mated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixtur;+5j:3k 1uvyzivfr) hcq 5zv ce 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, fkv,5x t7 er8s)6yzvzand (b) the amplitudes, of an earthquake P wav8zfyrvx, )6etzsvk7 5e passing through the Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake p+r)yj:gl4z2v i he4cs 3a hc4wave passing through the Earth is measured to be 2yli c z4av4 )3+p:gsh ce4rhj$ 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 wavesf .x:k)prh) mlezb:w7 of the same frequency travel through the same portion of the Earth, but one is carrying twice the energy. What is the ratio of the amplitudes of the two wavr7 m:.e wk))xbf:lph zes?   

  Two waves traveling along a stretched string have the same frequf-slah/b0 4dd ency, but one transports three times the power of the other. What is the ratio of the amplitudes of th4f/dh -dsl b0ae two waves?   

  A bug on the surface of a pond is observed gg5:jj;l-m 0 6 w;sgbg fcttg:to move up and down a total vertical distance of 6.0 cm, from the lowest to the hgb mw-tj :j5cf t6lgggs;:0g; ighest 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 s1v;6er g xd(fFig. 11–52 are moving toward each other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketchr6f(;evxd 1sg the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundamental frequyzsvjsefo/ w(r -n-4:ency, what are the frequenr:(vnw4/fz e-s -soj ycies of 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 oy uy*zyk1( r)what frequency will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds o1k)yu(ry* yz of the string vibrates as a standing wave.)    Hz

  A particular string resonates in fodt3(ponms wz8so+8m gz(zh* .ur loops at a frequency of 280 Hz. Name at least three oz8h(3tzmm *sn o8 s.g+ pz(wdother frequencies at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the frequency of standh s6x uma07j1oing waves is 475 Hz,j6m7u ox01ha s how far apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 350 Hz, what il9 )a 8j )2;hrsswoblps the frequency of the fundame 8ho;jlsp9ws)b )ral2ntal?    Hz

  A guitar string is 90 cm long a )fufzlh:5sbcw8y q;wnq ztxx9vl)81v x:0j6nd has a mass of 3.6 g. The distance from the bridge to the support post is z8bx qu j01n:xf8v); 95c:x)lqzfwh6l y svwtL = 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 vibrkry g,ohc ,,e2ate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to ck,2hy,eo g rc,orrect the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hz, bugq 5n+(rj5 o qpc/mp3ut it is measured to vibrate at 20cp(j 3q 5 r/npou+g5qm5 Hz. By what percent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal strinjzenixjcwcgly*9r7ba )v1 x 8 d2j71.g is attached to a small-amplitude mechanical 60-Hz vibrator. jyi1lbca) .918xjx*rzjnc 7wgd7e2v 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 lengt,uumws 0r59 phh of the string may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be ac0mw uu5r, ps9hhieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back has;0 d3r*ipb;erxe+and forth in a tub at just the right frequency, the water alteaxr ;*s;ei3e +ph dbr0rnately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundar*yf0l0ye5dv* kq* mi/cn5rh v y within the Earth between two kinds of material. If it approaches the blhkye***55m 0n0fvc vy id qr/oundary 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 ve,p jh. 1 f4gc0cbzrj3klocity changes from 2.8 m/s to 2.1 m/s If the incident wave c bg3r0jkzfj ,1cch .4prests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is travelpv.jh mfjdmr:3+2y hig8 kb0- ing in warm air when it hits a layer of cold, dense air. If the :+ pmik3hrg8 bjdhj20my.-fvsound wave hits the cold air interface at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave strs + zp9hdo2tq9ikes a boundary between two types of rock at a 3 9 t92ohdpqsz+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 0.5 m in diamadp9 nom5 ;q85i r;ucneter. According to the user’s manual, the dish has to be pointed in the direction of the satellitc; m5r8do9n 5;npa uqie, 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 tray+x,g kppjk9:cu 8w0laj,kd. nb/ t)qvels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the ha cal:p9+8k/p gkkjnb x)dtqwj,. u,0yrbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper hjfdq+0sf: txz1 h by z3::c 24trot/itas 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 2.2xt0:z qyt+fjzft32t : obdi/ :sc 4h1r m/s (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a windo*uwh4j34st3; pjlmk 2joim ,sw to a fire net 18 m below, which stretches the net 1.1 m. Assume that the net behaves like a simplek*so4j2 m33 ;wtuhslpjj,mi 4 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 spri 3ncvci:xv/ v,mw8i j1ng. The mass then falls 33 cm befor:x 8icvv/ ivmj13wn,c e it stops and begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 11–54), compressin6vcgi+/u8zq (l 9h7ri2ej n bsg the spring 5.0 m. (a) 2 +/gz(7hqsul j 9be6vr cii8nWhat is the spring stiffness constant of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of ckq1 l c9kw*jp-2 1ji zm0exbm76mzk* voffee (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. 11– k9*1vjkj*im2c1 zz epm7bkwq0 -mlx655). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from th*hfw: j.:z3 8y 0jf1rdei qyjze center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequenc8j:qz rj1w z fe*3fhj :yd.yi0y of the sound emitted?    Hz

  A 2.00-kg mass vibrates 9ee85 zqs8kpn according to the equation x=0.650cos7.40t where x is in meters and t ine98nkzp8 sq5e 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 frequp+ pgw:whn u*f;p0 el:ency if it accelerates at 0.50g*: ehwn0+ ;ppw lpufg: (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floatm12ej.f9 kj/ y mv ffyimq)9i;vt-+mks on a lake. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he sf m/ k+yeit kjim2qm9-1f;.9mvj)yfvteps 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 idrs,(ol (mhfqz7g9ik e9wwi3; )a*u392 Hz (G) and 440 Hz (A). ,; f(q9l7osz dg)wi9ima(hi3wer *ku
(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 tj , p1t0np4htvwo-part cord of Fig. 11–33. 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 the two sections. (The frequency is the same in b0pnj4tv tp, h1oth sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates atn0mu zm, c:9r./meq- jl ghcj6 a frequency of 264 Hz, and the tip of each prong moves 1.8 mm to either side of center. Calcugc.m nmr 0zj cj9qml-h:/e,u6late
(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 of6l z6ts/vx8asftu9a3 7y :,d6y g sibn frequency 1.5 cycles per second. What is the maximum amplitude with which tz3yss yv9l,8 bf7/6nastaut g6:i6 xdhe end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that end is attztrl e)dd*1 f6ached 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 string with one end fixed and tzr)flt d6*ed1he other free.

  A “seconds” pendulum has a period of exa x. n6a5w6hdra. s(vnck5d 6vmctly 2.000 s — each one-way swing takes 1.000 srnwa 5mh.vx5s66n(cdk6 d.va .
(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 oscillat-h*hjbu.7zvnat z0-buh z ;2we in the vertical direction or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontauazth-0u2.7hb bzzwn ; -*v jhl swings, and by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

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

  A 10.0-m-long wire of mass 123 g is stretched under a tension of 255 N. A fabb 7eq-6o:kpulse is generated at one end, and 20.0 ms later a second pulse is generated at the opposite end. Where will the two pulses first fo:6ae 7b-kqbmeet?    m

A block of mass M is suspenxij- ngkjmnr;/0, c: yded from 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 just stayn0j/-m ji;gcrkx: , ny on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel crane cable is 2wqpv b3,2o)(u ed*fh z2 m long and has a diameter of 6.4 mm. A breezup)zh(o v,q f*d23e wbe starts the car 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 plate as shown in F* +iujrnk- .3xk*sht*epnt*z e;6 sjuig. 11–58 (which also gives the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs nxrsj-*k; *uzk*th *se+upit j.en 36 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