Give some examples of everyday 3ux 9oq0jx9ab vibrating objects. Which exhibit SHM, at least approximat b3o9 uax0xq9jely?

Is the acceleration of a simple harmo6c2n+ jxggqw6-gebj 5nic oscillator ever zero? If so, where?

Explain why the motionv:;k7 5k lts2*uc:4 tc6a4h xki bijbs of a piston in an automobile engine is approximately simpleav 6i5kbij:k*sbuh 42 :xc4t ckl;7ts harmonic.

Real springs have mass. Will the true period and fr0 cr; e21r6z xyjxkz)8mjec b.equency be larger or smaller than given by the equations b cx26r 8r k).1mzxcyzj;eje0 for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple harmonff11w :okq9u q6kdwv:ncp- 4f fe b(v)ic oscillator (SHO)?

A 5.0-kg trout is attached mk6)cr gtrxxb krt0t9*6 iqa p w*+r54to the hook of a vertical spring scale, and then is released. Describe the scaleiw*56c 6xm rg 9*)at04+rxpk t krtbqr reading as a function of time.

If a pendulum clock is accurate at sea level, will it gain or lose time when t- *p8tw18knl kmo hydpp56/fk aken to high altitude? k1/m- l 58thopdk*w6yk8npfp Why?

A tire swing hanging from a branch reaches n;uo9 +mo,).ble;de id jdqb6jkg(y, kearly to the ground (Fig. 11–48). How could you estimate the jdekojd l,e;y6;u9 )md.ik bo,b+g(qheight of the branch using only a stopwatch?

Why can you make water slosh back and forth in a pan only if you shake th 8qkl0)r 6nftne pan at qnr)ln6k0 ft8 a certain frequency?

Give several everyday example*x 5j)n lpwiv9s of resonance.

Is a rattle in a car ever a resonance phenom/8u un,h4nglmenon? Explain.

Is the frequency of a simple rm66*ow xas h/gpxtim./j2x 4periodic wave equal to the frequency of its source? W s6xx/ 6omtgjx4iw/ *rpa 2hm.hy or why not?

Explain the difference between toij7j5 jt-4mr he speed of a transverse wave traveling down a cord and the speed of a tiny pietjj5 7-iroj4m ce of the cord.

Why do the strings used for the , 73jqf.mebzn lowest-frequency notes on a piano normally have wire wrapped arounm e7zbjn .f3,qd them?

What kind of waves do you think will tzb uio a;oqd+q-;60jjfw; dy1ravel down a horizontal metal rod if you strike its end (a) vertically from above and (b) ha;+j-;o60 jddqo;y1zifqu bw orizontally parallel to its length?

Since the density of ac558fyrnvznk rp;c 0* ir decreases with an increase in temperature, but the bulk modulus B is nearly independent of temperature, how w0n kycr *nrcv8p55fz ;ould you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in amplitude as they tra0bi j9 uo vp7fb-;uxv3vel away from the source.u90iov f;b 3xp jb-v7u

Two linear waves have the same amplitude and speed, and otherwise are identicay jc9-hp20wwi l, except one has half the wavelength of the o 9 pjy2-w0iwhcther. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sectionsl7i n1 u*m1r 52ppejrn of cord as in Fig. *i5p n j11rm7nrlu2pe11–33, the frequency does not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in rqaohh1um slyb:* ,r -q2o ,:gthree segments, are there any places you could touch it with a knife q a uh,qo:2r1 h-r*mb,oy:ls gblade without disturbing the motion?

When a standing wave exists on a string, the vibrazp685 k.tt7(nm/ry:;v6ite mg zryl ftions of incident and reflected waves cancel at the nodes. Does this mean that energy6tzr(:5tmyy8pf nk t; .z/lm6evri g7 was destroyed? Explain.

If we knew that energy 8.k3 rk +l9v7qsqx ft 1usu8gy. fd;irwas being transmitted from one place to another, how might we determine whether the energy was being carried by particles (material bodies) or by waves?7qli9fs k3t1fdr;yr x8+u.q8. vuskg

  If a particle undergoes SHM with amplitude 0.18 m, what is the total distance itlx084j(8yr g)h g bra,blu-qr travels in one ry)40qbul( l8xr,ajg 8 b-ghr period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it but is dzl )2g*4ax mc85 cm long when a weight of 180 N hangs from it. What is the “spring” constant l4gcm*xz d2a) k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-k cd -d,hik+(zcg driver gets into the driver’s seat. If the car goes over a bump, wh+ hci -d,ckdz(at will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.5ni j s/+k* ne)m+ctpg7-kg fish hangs from it. (a) What is the spring stiffness conske5/n)n+i c*mptsj + gtant $\approx$    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 vibrate ;2x sadsv9:cb 5btlx+s with a frequency of 3.0 Hz when a mass of 0.60 kg is hung from its 5bc: tl xs+va9;dbx2. What is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the positi u j.lks(k/j)bon x of the mass in Fig. 11–2 at times t = 0,tk)/j b u.sjlk( = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 g82zgtsys spm lq:v-): is caught in a spider’s web. The web vibrates predominately with a frequency of-gv:s:s )pqt8ys zml 2 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 ) *tdtf+y mtk9rrbajpy8 j:to( p8e ;1spring vibrates with a frequency of 0.88 Hz. When an additional 680-g mass is addedtrjeyy+ dt;9k8otjt(afp *p)b :m 1 8r to m, the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibra 3r2 xgjzgd(cs16r5gz/s w mn2tes 3.0 times per second with an amplitude of 0.13 m. Deterz 6zw3g2m 2(x rdj s5cn/rsgg1mine
(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 speexz u6mb*fer23d of a SHO half the maximum valm 2xbez63*f ruue?$\approx$    A

A mass attached to the end of a sp hn zyzw-gx6m1:3/s jkring is stretched a distance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretches a vertical spring 0.315 m. If thu2q a +nggt-cig 6i:t*e spring is stretched an additional 0.13g-ui:2i+6 *ng g atqtc0 m 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 spring with spring stiffness constaif ivz +ta.d(o5e ),ytnt k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m fro+z toi.vat d,) (fi5eym 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 Nm j6xoysae*c,(2w1 tj to compress the spring of a toy popgun 0.200 m to “load” a 0.18 2e jc1woj t,*xy(asm60-kg ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to one end o2rn e wdch1;**me gdy:f a spring; the other end is fixed to a h y** c 2gmnd:w1;eredwall. 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 vibrat srrhwspz.5 ;6es according to the equation x = 0.45cos6.4t where x is in meters and t5r.ss;zw r ph6 is in seconds. Determine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equilibrium is3g ;dqc, n m5d.jrbejcap-9s- the energy of a SHO half KE and half PE? ± j-c-;bqmn,5adjscpe 93r.g d    A

  If one vibration has 7.0 times the energy of a second, but theirj4faka8 h dlms- g+m/( frequencies and masses are the same, what is the rg (/aadj4mm8s+fl- h katio of their amplitudes?   

  A 2.00-kg pumpkin oscillates am*m. k n6/01x duglbyer)zv.from a vertically hanging light spring once every 0)uv kmey 1bl r*60a.nmzd x./g.65 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 xh17q2+ qmfqoparallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What will be the frequency qo 712qfmh+q xof vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5nq zcipa-49vw/3/ubz w.,e uzt where x is in meters and t is in seconds. Determi.,pn cwvwu/ea3i zb9- uzq /z4ne
(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, labe4w 8vdcnqkwai-r94i8led 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 horizontalh3 neh/wx6 av7,+0qx nmbwxd, spring (k = 124 N/m) is struck by a hammer, which gives the mass an initin 6 a/xwh,x,wx h7nd+3beq0 vmal 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 witf tm/va2lkv+ g7sm cjkp-n- .4h an amplit7g cm jvvsnk4kaftl. + /--2mpude of 28.0 cm when 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 stiffnu,ibc ;ng7-hz ess 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 fixedyhv5mk*ol.n2-ka d61cz v hw,ole d. 3 horizontal spring whose spring stif o.elah 2ho vn -.ky w,dczv*m65kd1l3fness constant is $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with mass 65.0 kg jumps from a high bridge. After reaching his1t2x0hx +p zca5q-x)1v pfhrp 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. Calculate2c 1hh51r+vpf-p pxaqt0 z)xx 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. Wha0c5rl ;q4orzs22wnebrhr19 ac+ n d s9t is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly one swing p:misld ) )do6q97 rtgoer second? (That is, one complete vibrat) dmol:ird g)os7t 96qion takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on E//krt-wc)zxl 7 4 ffwlarth. What is its period on Mars, where the acceleration of4lf-/w 7x lf k)ctwz/r gravity is about 0.37 that on Earth?    s

  What is the period of a simple pendulum 80 cm longxdodn611y31 fxhi tz.
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum ivet u)2dtod 9v3 ct)qq. v3;bps 0.760 m, the pendulum bob has a mass of 365 grams, and it is release93utoe b2.dc;)vtq qdv t 3pv)d at an angle of 12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’s pendulum has a length of 0.9930 m. If the clock losesh d5mwg5:s /; 5g7she)l 4ge bccntrd) half a minute per day,sg ec: )r4wm5h)5n;7lsg /ce bd5d thg how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maz hen ql;qrwx 7/2z/o+,q 3albximum 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 ofvo,1 lgh 83ym--att7wt ,id vz 2.5 Hz. At it is released from rest startingiy,1a7vmh,3-d ttvw zlg -o8t 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 pass the bow ofhw;gs51k es *c7f f1do his anchored boat every 3.0 s. He measures the distance between 1sec5*1 7ogfswh fk;dtwo 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 speed of 343 mpxyhcjf m1+/ 0/s x fm1p/ c+0jyhHow far apart are the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between o0.r(xeiydj ri.c-m:550 kHz and 1600 kHz (kilohertz) and t:jiyci .rxr (-mo 0de.ravel 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 longitujfh f dmn1;z2*dinal 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 1* xv 7 bac ;9tdo(pdpam+lud7as dense as the other. In which rod will thd *a1vbpd ouc7m(xd l7+t 9pa;e speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched b:ov9(,wv-vm a sa wfv py8q8w0etween two supports 28 m apart. If the tension in tww-sfvvv9 p m8q8,a wva y0o(:he cord is 150 N, how long will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to -ifgah)ccc9 ;7zec0un+zl e9 the top of a hill by a steel cable of length 620 m and diameter 1.5 c7z a9u lci- fgc)0enhczc+e;9m. 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 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 below the surface of the sea.:f, (uk2-vx7fixlloe He hears the echo of theivl(7xf2-l fox,e: uk 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 earthquakjjdj5io8 n9y. p)z l:ebt.s;me travel at different speeds, and this difference helps in locating the earthquakz di :)9jjl.. 58p;myesontbje “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 sfqcn x9cn/wegz vq+(wo 9sl 01h b*1+wave can be 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 needbge90 f wqq( 9osncw1 *h xlc1+sz/nv+ed so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplitudeshte8d,fr +hff;, fakx0yv+ d9, of an earthquake P wave passing through the Earth and detected at two poiak0etx9fhf+ , 8;d yvdhfr,f +nts 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing thupk2l eu imwk9,gwl*4m 5j t)6rough the Earth is measured to be m6jgl54u,uwl2m kw9k) ip*te $ 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 travkyvt6uxj 12y9 jyop, 3el through the same portion of the y36j1xjvk o 9,p u2ytyEarth, but one is carrying twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same ;av) yko p3i2dfrequency, but one transports three times the power of the other. What is the ratio of t32dyaipv) ; kohe amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move up and down a total ve6:l jmwfh 7*jkrtical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decreas*jk m jlh:f6w7e to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown ink x;tro/o)o: rp-+j pi Fig. 11–52 are moving toward each other. (a) Sketch the shape of the string at the moment o) :/t+opopxkijrr-; they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundamental fre1wbw1ohv 8)o o/k/enfquency, what are the frequencwwen/f/o1h k1b8vo) o ies 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 what freqc * s1n*9r(uyal6rtk suency will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of the string vibrates as a stanu cs*6t1yn s k*ra(rl9ding wave.)    Hz

  A particular string resonates in four loops at a frequency of 280 Hz. Namn 8(di 8(iyyjjef8bc.e at least three other frequencdyb(. ycf88iiej j8n( ies 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 o pi-e ki4v0dcsi+g 3626rpeaqf standing waves is 475 Hz, how fs di6e+6-c03g2rap i 4ekpv iqar apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string 3memf o 1 w+xwie3-te t0qf/d4z(kzf 1are 280 Hz and 350 Hz, what is the frequency of the fundamental? wfm1tk 1tioe3mw0f ezx+d3/qfz(e -4    Hz

  A guitar string is 90 cm long and hasyd nx r,9+yuw8 a mass of 3.6 g. The distance from the bridge to the support post is L = 62cm and the string9ny,x8yu rw d+ is under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is sul- ebuc 90,vl )/knfospposed 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 fre nle, ok) f-l0cvu/b9squency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hz, but it is measured ;5c6n s* ddijz m kdt,p7)1)i .sotelfx.*dbjto vibrate at 205 Hz. By what percent shol1 d;zkd7s6f *c.d)e, jm*bio)d p xjtti5s.n uld the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal strj.hl2 yrvp:po,gy0n 2ing is attached to a small-amplitude mechanical 60-Hz vibrator. The stripjo,lrvy ph.20yn :g2ng’s mass per unit length is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of the string may be adjusted ;ky76 qw lj1bmkc smm pa8,3ap(7lgg6by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by( gmc3psmakp ab,ylm7g 8kqw;lj66 71 varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at j ,a1oy d7a/qwrust 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 stand/r7qo,ady1 awing 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 boundary wit3gwcgd:9 ;,tj8nd3ix qivf-5p 0cz cehin the Earth between two kinds of material. If it approaches the :jcp;i5t3f ngv- 3c ,80izedgw cqd9xboundary 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 fbiwzemd6p w: t/g: -y2s+ 4of7nc )utsen m9c:rom 2.8 m/s to 2.1 m/s If the :cbm:mp+9fy wnot/2isz -:ne 4u6c)7ts egw dincident wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air when it hits a layer of cold, dense air.oo3mxcqsa3d9ad9 xko - 3f/ ;t If the sound wave hits the cold air ind9ok oq- 39tcx f3/ma3ox a;dsterface 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 striiolkd:k2hkde6 9g q28kes a boundary between two types of rock at a 38klk:69h2o2ddeik g8q $^{\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 mpstl phs h -et:l0p+58k,dh:x in diameter. According to the user’s manual, the dish has to be pointed in the direction of the sate, :h+sl k-hdptlteh:p580xs pllite, but an error of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 250 km and velocity 750 km/h travels across th -yiir,02ijtl5 m s+abe Pacific Ocean. As it approaches Hawaii, people observe an unusual decrism5tyar2i0,j +i - blease 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 stiffnesf 8d/(veqcvsj8h 22 ids3 nw1ws constant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (appro sji v3q dwf2d2e8hn1w(/v8cs ximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to azw4p.z p.(raxdd5 wf9 pz)( tl fire net 18 m below, which stretches the net 1.1 mp.p(rza d .wtfxw54)pdz(9l z. 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 hangibm*ofw)o7 6a ) fjwe;wng spring. The mass then falls 33 cm before it stops and be jw o*b;6afew)w7of)mgins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 mv rbb11sij fmg4 7h0i3/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffness constant of the sprinisv340fjb 11im 7r hbgg?    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 ;wd;4s kgtfv;cup of coffee (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. 11–55). Estim v;kw4stfg ;;date the speed of waves in the coffee.    cm/s

  The ripples in a cerw q/, m laqisdep8*c*.tain groove 10.8 cm from the center of a 33-rpm phonograph record have a wavelength cs./ dwi8eqplma*q*,of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates accordi pz 8)fq5,hikmng to the equation x=0.650cos7.40t where x is in metek8i5h m)pf zq,rs and 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 oscilla.s t3xez(1x rztes with frequency f. What is its frequency if it accelerates at 0.50g (a) upward, xsxzrz1t( .3e   f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on 6 9c7 xinp8u4w 6rulk /baib(ithe raft, it sinks 4.0 cm deeper into the water. When he steps off, the raft vibrati8p49(bnac kil ru6x/w7 ib6 ues 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 an (s *dvfmkjb1 88:kdtt 392 Hz (G) and 440 Hz (sd n8*vdk:j8 (kbfm1t A).
(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 c lf5e sn387lmf1.7ttp/smh8 eu* yodhord 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 sec8l/*e71 lt3monseh.5fh d8smpyuf 7ttion, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the49- :9otaygb gpbtg4n tip of each prong moves 1.8 mm tt94ggo b t 4-gynb9:apo either side of 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 simple harmonic motion of frequency 1.5 cy29cq )p, jy 0b1erjafxcles per second. What is the maximum amplitude wiqp2eycjj0ax9) r, 1bfth 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 end is attae;c;p +xw9pk wched to a ring that can slide without ;kx +pw ;e9wpcfriction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each one-wayjh 27-zpujt:)() q,vdi dkk m,* oglmg swing takes 1.0jkg)-mi(,g7zjvq )t2p: h* duo dm,kl00 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 osc 7+ye6r 6 hy(ke itmj(*czmcd .(*lmdhillate 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 e(k6h*6d.h*j7ct+myr mc(iez my( ld 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 is2 mcjy6:3riibad5i +yl (3r nz stretched under a tension of 255 N. A pulse is generated a rd5 y:+lc(z3r 2yi6aijbmin 3t one end, and 20.0 ms later a second pulse is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is;k ms 1tyxqu2) m3c1eb suspended from a ceiling by a spring with spring stiffness constant k. A penny of mass m is pq3c xye)2 ;mst1mbk1u laced on top of the block. What is the maximum amplitude of oscillations that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel crane cable is 2w -1.uz nzh6.+8k8zuh9oodimn( aptf2 m long and has a diameter of 6.4 mm. A breeze starts the car bou +o(ki8n6uw9 ntz1m -.hhapu o.dfzz8ncing 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 Fig. 11–58 (which also gives the gwi+gu;.+yqo /: cedb 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 vibratiowe ./g;:bu dcy i+oq+gn, given that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz