Give some examples of everyday vibrating objects. Which exhibit SHM, at leas:8c ;n n vg/nym7k+v81w gzdt(y;dn mgt approximate;t1;nm8 gvwk nn7:nz d 8 ygyd+cgmv/(ly?

Is the acceleration of a sim ; +bditgu or)k30gsdo6j1f:mple harmonic oscillator ever zero? If so, where?

Explain why the motion of a piston in an automobile eo( 89(wvte xodngine is approximately simpl9(vdx(8ot weo e harmonic.

Real springs have mass. Will the true period and frequency b1w vl7 h7hhk.ke larger or smaller than given by the equations for a mass oscillating on the end of an idealized massless spring? Exlkh7.k v1 w7hhplain.

How could you double the maximum speed of a simple harmonic y 0 zrj:;6s zkv4oy/gooscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spri9f/oplk/q86psnyuz3j w .d/xng scale, and then is released. Describe the scale reading as a function of timedsnf/9j/pyxk.ow3z/ l6q p8u.

If a pendulum clock is accurate at sea level, will it gain or l10:bamuuxc:hkco q s5 .;7inm ose time when taken to high altitude? am0;: xo1mhq5ucci.u bsk7 n: Why?

A tire swing hanging from a branch reaches nearly to the ground vpi-i6n 5+.wx4mzv gq (Fig. 11–48). How could you estimate t xz4vi65q g.mp vi-wn+he height of the branch using only a stopwatch?

Why can you make water slosh back and forth in a pan only if you sh 5sl3*uy qj.nqake the pan at a certain frequenc*n3j.lqy u5sqy?

Give several everyda 5vqy8n53zhr 2gvlz8uy examples of resonance.

Is a rattle in a car ever a resonance phenomenon? Expcrvq3 v x6vhmq3pu)4. mwj (yk84sr *elain.

Is the frequency of a simple periodic wave equal to the frequency of its soun,hmhgi5i0d :gs h,a( rce? Why or why no5 d,:agh hisi(hg,0nm t?

Explain the difference between the spuk *03zyfdoi.,o lov.eed of a transverse wave traveling down a cord andk0ooyvdiulf *. z,3 o. the speed of a tiny piece of the cord.

Why do the strings used for the lowest-freqiad +o j82eqf-1c7tsquency notes on a piano normally have wo-ia2 f1qq87t ce+djsire wrapped around them?

What kind of waves do you think will travel down a horizontal metal rod if you hif7de4aw;72)rfan ystrike its end (a) vertically from above and ;4h )fedirya 27fnwa7(b) horizontally parallel to its length?

Since the density of air decreases with an increase in temperatu*jsb2hrvjb :4 re, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound wave:rbb2hj sv4*j s in air to vary with temperature?

Give two reasons why circular water waves decrease in amplitdwwfwkd7(:su+a q62aude as they travel a+62s a(d 7ww:wa qdkfuway from the source.

Two linear waves have the srz4 s)2b z2z j,to+kreame amplitude and speed, and otherwise are identical, except one has half the wavelength of the other. Which transmits mz rjt)2k 2ozebr4+sz,ore energy? By what factor?

When a sinusoidal wave crosses the boundar*/2un5: m-oxfi v k wv2o2tdpuy between two sections of cord as in Fig. 11–33, the frequency does not change (although the wvfo kd- p :mv2 uxtwun*2i25/oavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are 6so;98s zk d.vrg4p;yhc,wo ithere any places you could touch it with a knife blade wi,v4w; zrhs9s8kigpo6cdo y.;thout disturbing the motion?

When a standing wave exists on a string, 4/ zr-eql5j asthe vibrations of incident and reflected waves cancel at th4zqjea /sr-5l e nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted fk4+o s- mn1v,qrtvqn9cy)m.2 qcz.sdrom one place to another, how might wevq-s,c.+ovnr1cq2q z .)n9dmy k t4ms determine 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 tk 2ltul3 -rkand6 t -r2 u;)iozx9x.neotal distance it travels in ornude- x-;rulxnt6 tilk2ao2.9 )k3zne period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs frqa qycl80;qt7om it but is 85 cm long when a weight of 180 N hangcq l ;0ayqtq87s from it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compo3ygkh * 5dg+aress 5.0 mm when its 68-kg driver gets into the driver’s seat. If the car goes over a buma gk3yg+5*od hp, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangscxxl )kzs316l3 f; zgn from it. (a) What is the spring stiffness constan 3x6zcsz;l) knlx3g 1ft $\approx$    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 freq2 4vg 0. aa,7c a6tjifcrvswl)uency 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 from ia)a6lt.7 jsrca2iv,w40g vfc t?    Hz

Construct a Table indicating the position x of the mass in Fig. 11–2 0cz9-h l jjw-4pnxuk +at times t =nj c x-k0z94ju+hlp- w 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. .*6 :ypembv fuThe web vibrates predominately wit6: u*y v.mefpbh 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 afze 84 mfvy8+e sb.me9dditional 680-g mass is added to m, the frequency is 0.60 Hz4y .mzf +e9e 8ebmvs8f. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring v*waox8j 0xkn1 ibrates 3.0 times per second with an amplitude of 0.13 m.1n8ka0o wxx*j 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 mai yq po,vzb (-3wgj9yn7oly6-ximum val-p,( ovy9wnizg7yy3l- qj6 o bue?$\approx$    A

A mass attached to the3xo, ;fwbnx n+ 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 stretcheis6ko9(r5w9zll rw6g;gbx k( s a vertical spring 0.315 m. If the spring is stretched an additional 0.130 m and released, hogkwi59r6 6k l9 z(w(lxobs;grw long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with spring stiffness *x:gw vstn1x1 constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, itg* xn11xvs :wt 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 ofd9cp88ci941 ohoplav a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will the ball leave the gh18cv9i c8ld p4pao9oun?    m/s

  A mass sitting on a horizontal28, ul fy*.nsa dcy(vk,6x qy9tez nu uqq/)v5, frictionless surface is attached to one end of a spring; the other end is fixed to a/qunf8vx zeqanyu.69s,yu) 5lcqk*dv2 t ,y ( 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 experiences a maximum acceleration of 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates according to the equation x = 0.45cos6.4t where x is iiv4f b e6s cl.to/:*own meters and t is in seconds. Determinlfvt.4 c*6 oib/ swo:ee
(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 ic jjc6fp f115c3m6: j,ackpj +k f8rwms the energy of a SHO half KE and half PE?56cmcjf,p+ kj1:fp 1am wjkcjc3r68f ±    A

  If one vibration has 7.0 times the energy of a u zzy spdd:3)*second, but their frequencies and masses are the same, what is the ratio of their amplitudes?s:)dzyz *3dpu   

  A 2.00-kg pumpkin oscillates from a vertically h3t rfh5g/:juq anging light spring once every 0.65 s. rgt3 j:/5hquf
(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 springs, ealzz.z):2:mc+ - jxu 0 bzvngvrch with spring stiffness constant k (Fig. 11–49). What will be the frequency of vibration? zg ::vc.zr 0zjmxun-2blvz+)

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t where x is ive0 guq6yu7g38uxzn2 n meters and t is in s62 0znxeuqg3vu7y u 8geconds. Determine
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows two examples of SHM, labeled A and B. For each, what is ; -yx1 u xdo;rf;6askb
(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 sprw1 n1vy reqs7 r+1etc/jd s/8ning (k = 124 N/m) is struck by a hammer, which gives the mass j/yqe+ s78nnwd1rc/r1st1ve 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 spring984efu 8dqsht1 b zcp9 stiffness constant 305 N/m vibrates with an amplitude of 28.0 cm wheef9c 84u8b1hs9qzpt dn 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) with positive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two springs, with spring sti z9c87g:e3ayir xoex 9wpyq /3ffness 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 blb:ggp:e3pp j+ ock attached to a fixed horizontal spring whose pjpg:+ eg pb:3spring 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 jug,q9w+r3 a dvsmps from a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He f3gvwr 9,qas+dinally 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 vvv:se/9c9iblz6ss-0s hk1 tr-2e om is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple ziy4 ov+ge15nub4 y4z pendulum be if it is to make exactly one swing per second? (That is, one complete z4e1o5ug+y4 n4ibvzyvibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on Mars, where th/hdxy4 3zbxxtyy9 k ,:e acceleration of gravity is about 0.37 that on Eartd x3zh y9x4y t/xk,by:h?    s

  What is the period of a simple pendulum 80 cm lonv90 iz6hum8mcic *r/ ig
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 m, the pendulum bob hol;hg o e a) rnpk0o)axd89m5(as a mass of 365 grams, and it is released at an angle oen))05l(g9ramkd ;h ooaop 8xf 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 clock lov1euc 0 ;x3vbwses half a minute per day, how should you adjust the length of thvu ewv 0bc;1x3e pendulum? shortened by    mm.

Derive a formula for the maximum1lp( 1qgnsvhb /de2sp aoy + ps-b37/p speed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at a frequency of 2.5 Hz. At it is released from 7 fr:oad:d1gdfzhsxe.5mz9h t9v ,8ores:tafmez :,od v79xdo9z hsf1dr5.h g8 t starting at an angle of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests 5cy*bnd e po5b82d4uf pass the bow of his anchored boat every 3.0 s. He meas5d4neb uc 8bod *fp5y2ures the distance between two crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with a spe/5 6 lrli i9frirj:4hbed of 343 m/s How far apart are the wave crests (compressions 5r 9jbr6l4/l:ir hifi)?    m

  (a) AM radio signals have freque0;; 3ad 0jsgb5z .:t bygbd2v crjqp.tncies between 550 kHz and 1600 kHz (kilohertz) anp gd.ry.2c 0 gq ;tv 3;bstja5djbz:0bd 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 ok g flpz4/8.pmar)q;cf longitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elast rt29hcb..jm5 mzvxv tg/f .9ib zma-9ic modulus, but one is twice as dense as the other. I.frzm 9 g v.m9zivhxmb25.a bt9-jc t/n which rod will the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between/nuzb2e z*,e ;prpiu- two supports 28 m apart. If the tension in the cord is 150 N, how long will it take a pulse to travel from oneeuen pz*z ,;/rub i-2p support to the other?    s

  A ski gondola is connected to 2.rg*2bsraoyqef ygo(f . 66b the top of a hill by a steel cable of length 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal f rgbs(ryqe.fyo6*6.b oa2 2gand 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 jusgb z(1wj. 4ae-5equ kst below the surface of the sea. He hears the echo of the wave reflected frgwb ja( 4s5q.kee-u z1om the ocean floor directly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from anh+5sc cpyrl5wujp. )cs 65fl+ earthquake travel at different speeds, and this difference helps in locatl +uw6cc+5.5fs ypl)sh j5rcp ing 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 j 7vt,9xwp-o* t bq .-lxed-mqbe approximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the acceleraojme -vb--*t,9pdq7x. xlqw ttion a>g]    m

  What is the ratio of (a) the intensitied+z zo*kc7q:n s, and (b) the amplitudes, of an earthquake P wave passing through the Earth and detected at two points 10 km and 20 d+ ocznq*z7k :km from the source?(a)    (b)   

  The intensity of an earthqu4 eoo0dsk.yc+m+eh h 2ake wave passing through the Earth is measured to be +.kee2co +hm0osyh 4 d$ 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 tjb oc4(a)e 3haravel through the same portion of the Earth,heja(3o )ac4b but one is carrying twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched st ctk/zmf)zp+j jeblok9z-g(t34d u9.ring have the same frequency, but one transports three times the power of the other. What is the ratio of the amplitudes of the tgkz u o ./+zd()b39p9ktel mtjczj4f-wo waves?   

  A bug on the surface of a pond is obsexizpfyp1p4. e(yz i:f +w)m3e rved to move up and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a pzye.ye4i:p ifp mw3x )1+fz( wave passes. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are movin rk0t l32zdciec8 z2b*g 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. Wkdzl2zcb e0* t8 3r2ichat has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fun;gobn s4cwya,k 5z+o9aw jw +fu: ,w;edamental frequency, what are the frequencies of the first four harmo+4 9csj ; k,o+ guyzww5wefw:oa,;a bnnics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294s7f5 lr j*k(sj Hz when unfingered. At what frequency will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of the stringr7 l*j(5sjkf s vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequency of 280 Hz. Name at l zxv+x3 *b;pdz2xm m;ffohg 0(eaozpmvxzgf;+2h( fx ;x*30db mst three 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 9e ;b 4tmgv7;jxd4oqo:2m/s If the frequency of standing waves is 47mxv4qb:o4 t;gdo j7e;5 Hz, how far apart are two adjacent nodes?   m

  If two successive ovea: y5 /9e7 ffulygg g7m*pkbw.rtones of a vibrating string are 280 Hz and 350 Hz, what is the frequency g e7f9fl/p5m: gg.kw7ya* u byof the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. Ths* nu:6cugafjp 0 m23w:jf5nte distance from the bridge to the support post is L = 62cm and the string is under a tensi*w:u ut6cng3 fj2np:5fj a0m son of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supp8vu.q0hq/xgg)xp xbh5z 1hj 6osed to 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 the freque1 0bh )pzj/ hxvq8x65 gx.gquhncy?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is su0+ja rvt7t1bspposed to 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 the frequency? dtj70b r1av+ tsecreased by    %

  One end of a horizontal string i0 b /7 bqhiwa7j.kv;hj .wju/cs attached to a small-amplitude mechanical 60-Hz vibrator. The string’s mass per unit length is wbqb;kh.vaj/7 . c j0uj7iwh/ $3.9 \times10^{ -4}$ 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 adjuste+htie*dcwjb u4,2 6 exd 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 betwe*+2ij x46 ,etdbcew huen 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub ala3i3rec 0 zc/t just the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the fclr/ai ze033c requency 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 bouniy( g1;nz /71) (sxgednottcrdary within the Earth between two kinds of material. If it approaches the boundary rg ct(ey1tgz; 7/sxi n(d1)noat 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 veloci+vmc3x/hq 1flty changes from 2.8 m/s to 2.1 m/s If the incident wave crestsmhcxq 1l v3/+f make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is travelinacy l/5jsy;kmm 2yd4m-rp5v5 g in warm air when it hits a layer of cold, dense air. If the soun5lvmy p5/ myyj;54d-2 smrk cad wave hits the cold air interface at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave strikes a bo19qs9c (wbr7zgiks. ai4y7 ltundary between two types of rock at a 379 zkb(iitwrl .4sgc9a7 1 qys8 $^{\circ} $ angle. As the wave crosses the boundary, the specific gravity of the rock changes from 3.6 to 2.8. Assuming that the elastic modulus is the same for both types of rock, determine the angle of refraction.    $^{\circ} $

  A satellite dish is about 0.5 m in diameter. According to the user’s manual,c7 men,,-y ikaj2(zgz ua,ro4 the dish has to be pointed in the direction of the satellite, but an erymn7 j,- c(a zg4,aruk2 ,eizoror 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 tr4mpp*3c 9kmom avels 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, people have died during tsunamis, som4pm pomk93cm *e of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness consta-*;obxttm(c. dl l9 cycs1)qtnt 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 (approximac( tycl ql) .bx 9-1;cstdmot*tely 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m b2 ;au1;p9n .3 kri:qvgnqddasii se9*elow, which stretches the net 1.1 m.;qk; siq3 .*rnud : de vspn12gai9ai9 Assume 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 the end of a freely hanging spring. The m npzs.+k n4j,j ks)/diass then falls 33 cm before it stops and begins to ,/j.isd4 zpnn)+js kkrise. 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), compressin06b5-ok myvl:mes 3(6 vp ; d2 5z2zebzsfzpfog the springf 0y2; 3f v me sozolpp5k:vze(25d6bbmzz6-s 5.0 m. (a) What is the spring stiffness constant of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of coffee (di0zt3+5m txwo;mm9 w pmameter 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 them3m xo+m5; 9zwtpt0 wm 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 ofw5 u2vthm+0u8hg+as i a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequency of the u 52gh+stha+mui 8wv0 sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0e bqtni8ei s),2 51q;z reza+f.650cos7.40t where x is in meters and t in secondsni8z fzqr 2ie,t b5e q1se;a)+. 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 frequency if is3 qx1kvvk,;z* re l0vt accelerates at 0.50g (a) upwav,01vzr *es k;q3lk vxrd,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on tbkgou() ,k gg5iz+1bxhe raft, it sin,gi+ b1kgkg( b) 5ouxzks 4.0 cm deeper into the 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 instrument are tuned to play at 392 Hz (G) and uri 7(zerl 6gu,00q ep440 Hz (A). rpe7igqeur( lz0 0 ,u6
(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; y dkkrf djbch8j1mygmfei196h 060( two-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 both sections. Why?) (c) Is the wavelength greater in the heavier section of cor0k( khemy90ij mrd f1ghjbfd y81;66 cd or the lighter?

  A tuning fork vibrates at a frequency of nvl2,)n ulv0 m264 Hz, and the tip of each prong moves 1.8 mm to either side o,nnmu0l2)lvv f center. Calculate
(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)pmhv4.ez0 d kle 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 zh 4pve.d0km) a pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that end is attached to a ring that can slx 0ud5 y t leaj;/9+fwsejt)z(ide without friction on a vertical pole (Fig. 11–57). Determine the wavelengthsjtty9 )uwsx; d5ajz/l+e(f0e of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — eacczv+tpe)coyqk hde25 4 uoh 3+r4 +9pkh one-way swing takes 1.000 s. p o 2prvuc+ +hkqzeyo h9et5k)34cd+ 4
(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 vex7 emx2z-z y,lrtical 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 horizonta2x xyl,zz7 e-ml 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 tensiono i85*u o0pg,xs:ydvo of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at the opposite enux5vp0: ysoiog 8*d,od. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spring with spring stiffness d(.la rmi:c+ -(h*e uscrnfb/constant k. A penny of mass m is placed on top of the block. What is the maxim s- mrhf(ci*(+uleda n:c/ br.um amplitude of oscillations that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at d 3 qd*7x)1t,zszenelthe junkyard. The steel crane cable is 22 m long and has a diameter*7xdlzzeqs n )e3d1,t 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.]    s

  A block of jello rests on a cit(bkwc4)msc7 (lxi6: wh/e plate as shown in Fig. 11–58 (which also gives the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this vibration, given thabi )6kecx(i twc h(:4 ms7lcw/t the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz