Give some examples of everyday vibrating objects. Which exhibr,a)e /0mfhbqit SHM, at least approximatel,fqe /)rmahb0 y?

Is the acceleration of a simple harmonic oscillator ever zero? If so, i9* 3hkk v hnpyv()47.unyh lywhere?

Explain why the motion of a piston in an automobile engine is approximately sh/up1n. , golvimple harmo/pv .1ghn o,ulnic.

Real springs have mass. Will the true period and frequency ny+ qi84hx y4cbe larger or smaller than given by thcy+n hi xy4q48e equations for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speerrrk ;r.w,kvt: 5hrs.d of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertica+)pbe bmywm e080db: kl spring scale, and then is released. Desd)mb +:kyep80mb bw0 ecribe the scale reading as a function of time.

If a pendulum clock is accurate at sea level, will it gain or lose lry* hvt0/o;b time when taken to high a0oly ;t/hrbv* ltitude? Why?

A tire swing hanging tl5hstsh1 nx- 9xbnbcu/erk :+4lv(+from a branch reaches nearly to the ground (Fig. 11–48). How could you estimate the height of the branch usinx-sb s k:4r+ l1/95xne+lub vtch n(htg only a stopwatch?

Why can you make water slosh back and forth in a pan only if you sh,kpljg)uho. 7ake the pan at a certain frequency?plg jk.7ho), u

Give several everyday examples of resonao.vt pxgaim j+pdt 6 r6n-31p7nce.

Is a rattle in a car ever a resonance phenomenon? :pc 8g5i7ltdr Explain.

Is the frequency of a simple periodic wave equal to the frequf. :yu/c- zyte0hpd4b ency of its source? Why or why nb4c/y-eypf0zu:d. t h ot?

Explain the difference between the speed of a transverse wave traveling dojaq fyvu1(5(2hatm, c wn a cord anqtyj(caum ha5(1 v2f, d the speed of a tiny piece of the cord.

Why do the strings used for the lowest-frequency notes on a piano n-; v hokc27:smyw .freormally have wi e:7k ;cysm.v fh-rw2ore wrapped around them?

What kind of waves do you think will travel do.yfod m dw+ +g,3wm3nrp1o7se wn a horizontal metal rod if you strike its end (a) vertically from above and (b) horizontaomw mno +yegw1 ,3s7.3r+pfddlly parallel to its length?

Since the density of air decreases with an increase +fx0m7+t 1.sdytm zmrin temperature, but the bulk modulus B is nearly independent of temperature. mr7 tzm+mft0+1dsx y, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease igrc1mw(1 9 ex -jytr3u/y: ude*jxr5s n amplitude as they travel away from tryy3w /(: xcr5d ee9u11rj gt*-ujms xhe source.

Two linear waves have the same amplitude and md:+s,vyxru pz.i 6: xspeed, and otherwise are identical, except onei su6zmr .,:+xd:vpxy has half the wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sections of cord u;.fomc om 7(kas in Fig. 11–33, the frequency does not cm mk(oco ;7u.fhange (although the wavelength and velocity do change). Explain why.

If a string is vibrating in ;*e)u,g6u4 gh 8hmpp-w v ro, ilitc1qthree segments, are there any places you could touch it with a knife blade )ui1gg; 64qw hh* ,op,vrti8lum -pec without disturbing the motion?

When a standing wave exists on a str/4to5lmplc d;fr19gi1-jmv b ing, the vibrations of incident and reflected waves cancel at the nodes. Does this mean that energy was dep;c i1drm 1b/t l5og9ml4vj-fstroyed? Explain.

If we knew that energy was being transmit)j/d*nluz ae) pl0 dc k*e(q1hted from one place to another, how might we determine whether the energy was being canlddp0e1he)ujkzcl(* q )/a *rried by particles (material bodies) or by waves?

  If a particle undergoes1h ((tz /2rmv+zbskcj SHM with amplitude 0.18 m, what is the total distance it tm( (vscj zt+/1k2 rzbhravels in one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it but .x45mo6zoo zy is 85 cm long when a weight of 180 N hangs from it. What is the “spring” z.ooz5 m xy64oconstant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg driz(k 8y 9xso8nyver gets into the driver’s seat. If the car goes over a bump, what will be k x8 znyys(o89the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hang(cfry j re+*j0s from it. (a) What is the spy+ ef( rj*cj0rring 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 wh:o*ui z3imtpbg d) 3o9en a mass of 0.60 kg is hunbg)* tpi i:d33mzuoo9g from it. What is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in 0oxvq5o)h yo .twtp5u:ecr1 57ge m;hFig. 11–2 at times t =)t er:;5cq u51pmevooh hygx 07.t wo5 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. Thnh o+ hs g-a700b2dbhhe web vibrates predominately with a freb h07 nosdhbh0h2 a-+gquency 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 Hztr*,np8z5p p 4s5 jaqd. When an additional 680-g mass is added to j,p * 8a4qn5z5 tdppsrm, the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end o76lw 0r.2stqm6otv 4gn()bzafy bf 4o f a spring vibrates 3.0 times per second with an amplitude of 0.13 m. Deterql7ma on 4sb.rv0f6 yz2owbt46f(gt)mine
(a) the velocity when it passes the equilibrium point,$\approx$    m/s(round to one decimal place)
(b) the velocity when it is 0.10 m from equilibrium, $\approx$ ±    m/s(round to one decimal place)
(c) the total energy of the system,$\approx$    J(round to one decimal place)
(d) the equation describing the motion of the mass, assuming that x was a maximum at x = (0.13π)cos(  πt)

  At what displacement from equilibrium is the speed of a SHO half the maximum vk4*wh0jf6 ( tmzrd-gvaluejrz(v - 0 mhd*tfg4kw6?$\approx$    A

A mass attached to the end of a spring is stretched a distancqzgui2uh (9( be $x_0$ 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 strethsc1x-chs 9venz+w7 ;ches a vertical spring 0.315 m. If the spring is stretched an additional 0.130 +hv1 sxhccz; 7e9 sw-nm and released, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a sprv/p ch 0;h*as3g i0yoxing with spring stiffness constant k = 280 N/m and is exe3 asco;vhyp 0ig* 0x/hcuting simple harmonic motion. When the object 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 spring of a toy popgun 0.200 m to “c5p ti 59;c;uc.vol cqload” 5vco 5lcu9qci;;.ptc a 0.180-kg ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surnfbzh mj;:q gi:fk8;4ihl3:iface 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 compresseg fl;hjm::4ifikh3in;: b q8z d, 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 whfo vwau9;+*ct)2a/ red ves-lere x is in meters and t is in seconds. Determic9o2vw*;)l/f+reatd -sua evne
(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 e3yg9vm1nrh hku b(:0xeys( q)quilibrium is the energy of a SHO half KE and half PEmxu v3q b hk((91 er0nys:gyh)? ±    A

  If one vibration has 7.0 times the energy of a second, but their frequencies d)vq l z1eq64:u y2qowand masses are the same, what is the ratio of their avo dqq ew)q612y4 luz:mplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hangin hfcxu1/ g l-3im*l)z9xq-g0s ju sptw44lyu0g light spring once every 0.65 c) - lxjpus4ll1uwqs m *0g9ty0/xf3uigh 4z-s.
(a) Write down the equation giving the pumpkin’s position y (+ upward) as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. y = (   m)cos($\frac{2\pi t}{0.65s}$)
(b) How long will it take to get to the equilibrium position for the first time?    s
(c) What will be the pumpkin’s maximum speed?    m/s
(d) What will be its maximum acceleration, and where will that first be attained?   $m/s^2 $

A block of mass m is supported by two identical parallel vertical springs,u,ya1q 8x vkvo)*ju3dvkbhzb2 2-f2y each with spring stiffness constant k (Fig. 11–49). What will be the frek182h a2 yuvokf*3 v )qudyb2x vjbz-,quency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t where x i hysu sg0crp,yl.8y5 +b,h+n ys in meters and t 8urc l yygys0+ yhp,b+,nhs.5is in seconds. Determine
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows two ex 997lr0z j.mzgg mp)5bsaeqh6amples 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 = 124 N/m) v 7fuujps7urf24gz1qa( 8am 1is struck by a hammer, which gives the mass an iz71u aa jg8p rqmff(7uu4s v12nitial speed of 2.96m/s Determine
(a) the period and frequency of the motion,    s    Hz
(b) the amplitude,    m
(c) the maximum acceleration,    $m/s^2$
(d) the position as a function of time, x = (    m)sin(4.08$\pi$t)
(e) the total energy.    J

A vertical spring with spring stiffness constant 305 N/m vibrates with oortw8brb+8q+ct8 , can amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium po+twrb8c b 8ooqtr,c+ 8int (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, with34z 0eo9 gzxesor a5ypa+7 2pv spring stiffness constants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes a 0.600-kg block attached to a fixed horizontal s:spp.vg92s) qwrps: ipring whose spring stiffness2sr:v s.q p wp9:sip)g 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 bris) 4n8s-v:dvz7.xffh oiyz 4fdge. After 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 below the level of the bridge. Calculate the spring stiffness constant and the unstretched length of xvof-s:ndf fv yz4 hz.i)784sthe 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 is 4a0u ( p5d if;hrcie6uits
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simp9ri0/iwx5m3 ) w1pvq;nkz ilile pendulum be if it is to make exactly one swing per second? (T ;3 vqnw9rk/mlzp iix05i1)wihat is, one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What vj-pbwud x9jx4y+4d) is its period on Mars, where the acceleration of gravity is abouvy9bx+)x 4j wj-dpd4ut 0.37 that on Earth?    s

  What is the period of a simple pendulu *9+griop9ph.5hg, ty b; m5 -tug +k5ceekjgnm 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,w9 pk6.i w (5v6 tle1k.m6 kzymhkmt6m the pendulum bob has a mass of 365 grams, and it is released at an angle of mkk6. m6ve9wkt5lz 6h.iywmm k(61 tp12.0 $^{\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 pendulu1om)21yznfz wm has a length of 0.9930 m. If the clock loses half a minute per dan11mzf o wzy)2y, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maxiq;0l-sd uob6 jmum 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 oscilq 8r-z7qzo-bam,c :vla;zr d.c20 sphlates at a frequency of 2.5 Hz. At it is released from rest starting at an anglhvdzp;a-7l0saq-qz. zo:r2bmcc r, 8e 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 t j lypx v-81h2 qqamh4/6fel,chat wave crests 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 the waves trave 61,laqqvf 8 -2yhmxhje 4/lcpling?    m/s

  A sound wave in air has a frequency o dr*.j-kk/g4cfay8q7e kt1sz f 262 Hz and travels with a speed of 343 m/s How far apart are the wave crest.17 8jdak/gzq*y-sek kc4rft s (compressions)?    m

  (a) AM radio signals hr alb8*n m gab,w9,.niave frequencies between 550 kHz and 1600 kHz (kilohertz) and trawn igla98bnr .b,,m* avel with a speed of $ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

  Calculate the speed of longitudinal waves injj8 w,3ps 1enz
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastfdv ,3x8t25q xjtgca0 ic modulus, but one is twice as dense as the other. In whicgt 8ax d053fctxv,2 qjh rod will the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched betwee* caq+nv yiw5-n two supports 28 m apart. If the tension in the cord is+inycq5a-v *w 150 N, how long 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 a steel carb *t;mvp4i f7ble 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 observr7*ti 4bp v;fmed 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 just belo/ uew5-n( beiseu l*bs20o1 qvw the surface of the sea. He hears the echo of the wave reflected from tho v*(le u1-0ns 5 qsuebw2e/ibe ocean floor directly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at differen-tcvu1t/ r2 p ne1vbo6t speeds, and this difference helps in locating the earthquake 6orv- et1bc2ptn1v u/“epicenter” (where the disturbance took place).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced surface wave can be approximated by a sinusoid f 5:qbdhz*l:6b0tx d1vpr5a yal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually ib tx0rb fv6d*:pal1:y55 qzdh nclude a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the ioj8kq1 0q/d* gf axml3ntensities, and (b) the amplitudes, of an earthquake P wave passing through the Earth and detected at two points8q/ g0fm*kj d xoqla13 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is measured to b+ h7snjsk :uldm0b1( ae h70laju d1b s nm+ks(:$ 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 wavesebw x4dto ::1b of the same frequency travel through the same portion of the Earth:dbwb1 4o:txe, but one is carrying twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched shqb 42r-v;qjcg xdpwe .(q r,-tring have the same frequency, but one transports three times the powq.hvr2e c;p-x, b q(wj4 grq-der 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 down a total verticalqwwylrd-22 .t distance of 6.0 cm, from the lowest to the highest point, as a wave passelwy.- wq2 2drts. 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 moving toward each othery szr 32i,xe,w1n-0oxl.pqk ay8(xf a . (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few momenta2i(x1 n, xfkps, 0-a zo3.8wyeqlxr ys 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 frequenc *r6cnw;dpinq/*n(9 jrd f r6gy, what are the fre*w6 ijq;( pcr9rgfd6/nn* rdn quencies 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 wha4mv p0;, yv xkxkkg7;at frequency will it vibrate if it is fingered one-third of the way down from thex;v7m, gpk0k;yakx4v end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequenz,0/yni4f t/z1y mriycy of 280 Hz. Name at least three other frequencies at which it will resonate. ym n r0iyi 41f//ztzy,$f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s q:2 3mbsk vtxh:12iypIf the frequency of standing waves is 475 Hz, how far apart ark22::mit bvs31xy pqh e two adjacent nodes?   m

  If two successive overtones og:2j yet2yx+cr9 cy)nunko( 9)zp3* qk r/a jlf a vibrating string are 280 Hz and 350 Hz, what is the frequency of the fundamental? p2zr j+:n9t9rlxy ge) uko)ny/( cj ayc2qk3*    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The dist7b -h3qvcif 8rance from the bridge to the support post is L = 62cm and the string is under a tensionribf3-8h7 vqc of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is suppoe:,.ex *sxga msed 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?So the three fga.*eexs, m:x requencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar st9p zp3z1is s7jo/ux+ering is supposed 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? deup+ 1 ozspz3/ j7x9isecreased by    %

  One end of a horizontal lkh9a( -si) 9gzhkxlbb l5:5k string is attached to a small-amplitude mechanical 60-Hz vibrator. The string’s mass per unitk x5)lk5hs9gbl k9(zbal h-i: length is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of the string ma0vprxe:p -,qkmfu+ my* eo 8p0y 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 achievq8+rekmmo yp ,*0:evpx-pu 0f ed by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tubbdr;d j-i-z s+yv0 (kv 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 65-cm-wide tub is 0.85;j (diz bdv -srv-k0+y Hz. What is the speed of the water wave?    m/s

  An earthquake P wave travelitxnfknro0: -( ng at k.0 km/s strikes a boundary within the Earth between n xn0:krf ot(-two kinds of material. If it approaches the boundary at an incident angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “shelf” where the velocity changes fromh- c5)/e 7gccm2pwuh b 2.8 m/s to 2.12h7g5pcem-/ ccubh w) m/s If the incident wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air when itqp qut4yl9hdab4/1*b hits a layer of cold, dense air. If the sound wave hits the cold air i1ay/ qbp4t u qb49hl*dnterface 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 wav z /s.pzzzw/01v2jr +htq)cp oe strikes a boundary between two types of rock at a 38)1 2s +/vt.hzzjz0pz/ co rwpq $^{\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 3tstedg+n4+ 8coa rx-the user’s manual, the dish has to be pointed in the direction of the satellite, but an error o c nxtda3+sr-4etog8+f about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 250 km and velocity 750 km/h travels across,zk * l1ro21 otfx*-ij7xuapy the Pacific Ocea*pzk1,7royjolxtf1 a*i - 2uxn. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffn)ud bon)e1f y/ess constant of 550 kN/m Find the maximum compression of td /eo)1n yb)fuhe bumper if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fihn vobz;* .a. qfq:-wore net 18 m below, which stretches the net 1.1 m. Assume thatzfv; -b.:ho*qw q na.o 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 frds3v6d 5ocuxz:kt 72;,ybis,(dg . kjfc4nkreely hanging spring. The mass then fallso 2kix 4z fr, cdgs,t357s .6ynkvu;:cbkd( jd 33 cm before it stops and begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge springi zqp ug.ip7q, e.a4teu8v h73 at a speed of 22 m/s (Fig. 11–54), compressing the sp4hqq i3 e8uei.7 p7zva tp,.ugring 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 ntz .cza9pgc;,r+8g eof coffee (diameter 8 cm) at just the right pace of about 1 step per second, the coffee sloshes more at rac8npg e9zz g;,.+cnd more until eventually it starts to spill over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the center of a 33-rpm phonograen3 snb3vgu9 3ips2v+n yrr2 9ph record have a wavelength of 1.70 mm. What will be the frequency of the vps3gu3ev29b9sr32n + rinynsound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.4o9+p/ tapgnl-vc;9f xgj+c m, 0t where x is in meters andt+f/px n-l 9cg+ 9g;v ocmpaj, t in seconds. Determine
(a) the amplitude,    m
(b) the frequency,(round to two decimal place)$\approx$    Hz
(c) the total energy,(round to one decimal place)$\approx$    J
(d) the kinetic energy and potential energy when x=0.260 m.(round to one decimal place) PE$\approx$    J KE =    J

  A simple pendulum oscillatipi cn/75w8hges with frequency f. What is its frequency if it accelerates at 0.50g (a) upw 8phin7 ig5c/ward,    f
(b) downward?    f

  A 220-kg wooden raft*vsnw8s 9ne k8ggz;3 p floats on a lake. When a 75-kg man stands on the raft, it sg gvs*;nszne w38p k89inks 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 instru6qolmdd3a/;is/ u wh- ment are tuned to play at 392 Hz (G) and 440 Hz (-qad/diwmh 3o lus ;/6A).
(a) What are the frequencies of the first two overtones for each string? G : $f_2$=    Hz $f_3$=    Hz A : $f_2$=    Hz $f_3$=    Hz
(b) If the two strings have the same length and are under the same tension, what is the ratio of their masses ($m_{\mathrm{G}}/m_{\mathrm{A}}$)   
(c) If the strings instead have the same mass per unit length and are under the same tension, what is the ratio of their lengths($L_{\mathrm{G}}/L_{\mathrm{A}}$)   
(d) If their masses and lengths are the same, what must be the ratio of the tensions in the two strings?   

Consider a sine wave traveling down the stretched two-part cord of Fig. 11–4z(/oks*n cbi(bw-p z33. 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. Wh (/won bziks(*z p4-cby?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the tip jttvz/kq/ha, . ,rq l.of each prong moves 1.8 mm to either side of center. Calculate /zjq,qal k/vt.tr .h ,
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simple harmonic motion of 4e h*2 jgo50xj0xc epg v;kzb:frequency 1.5 cycles per seepgojx*be502kx4: zv;gjc 0 hcond. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that endi5pn1fqs(m6:cv s8lbb d0 fn4 is attached to a ring that can slide without friction on a vertical p4blvp sc fn(fq6s8i5d :mn b10ole (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 m, ::v5a 4waub s2p l vw7:yb,mxfg(gchas a period of exactly 2.000 s — each one-way swing takes 1.,wpb7y,:b:s(2l5fx:mavg4 a wcm ugv000 s.
(a) What is the length of a seconds pendulum in Austin, Texas, where $g=9.793\mathrm{m/s}^{2}$    m
(b) If the pendulum is moved to Paris, where $g=9.809\mathrm{m/s}^{2}$ by how many millimeters must we lengthen the pendulum?    mm
(c) What would be the length of a seconds pendulum on the Moon, where $g=1.62\mathrm{m/s}^{2}$    m

A mass hanging from a spring can osahljl1) uqnq(dq9 +v 7cillate in the vertical direction or can swing as a penu qd( v1j+9nll)qaq h7dulum 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, 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 underr3il9o( i; ljl6mdxcc5u.5s t a tension of 255 N. A pulse 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 mcmd6r jxt;uc3il9s (l lo i5.5eet?    m

A block of mass M is suspended from a ceiling by a spring with z(drprj( )-fc 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 alj drc(-p( zrf)low the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car 7- 7wzlr:jp vwj,+vy.5)neuzuuja s+at the junkyard. The steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts tvs :nz+5,r7 zwuuj+l7u)j p-yjvewa .he 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 sho5tgsath6e*h /: sfu2pq s( w,dwn 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, estimate5d /ep,:6fau qsg 2ths h(wst* 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