Give some examples of everyday vibrating objects. Which exhibit SHM, at least ape , 71 p:w*esmyp,ssvupp p:s* es u7y,s,1wvemroximately?

Is the acceleration of a simple harmonic oscillator e( q8ua;j6iry6 i3z ajhver zero? If so, where?

Explain why the motion of a piscf a;a,0ok7 jkton in an automobile engine is approximately simple harmonf,jak;7a0ok cic.

Real springs have mass. Will the true period and frequency berqb ,v .jh7gi, larger or smaller than given by the equations for a mass oscillating on the end of an i h. q7ib,rgvj,dealized massless spring? Explain.

How could you double the maximum speed of a simple harmonic oscillattl-)naoz/ jbz ymv+*6or (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scale, and then is9-rq sb mw2)os released. Describe qsr9)mos2 b- wthe scale reading as a function of time.

If a pendulum clock is accurate at se nvl+5b1 izy1 cgw6d3ta level, will it gain or lose time when taken to high a1b+ivn1y3 wct5dz6 l gltitude? Why?

A tire swing hanging from a br;hvq--w2zo8 3u::bh j ,4bo kspbitj yanch reaches nearly to the ground (Fig. 11–48). How could you estimate the height of the braojuht;2-b:b :zs3 k,qiw h pov48-byjnch using only a stopwatch?

Why can you make water slosh ba(ob89hof7n unb s+xqu p(8r;eck and forth in a pan only if you shake the pan at u n7 +(98qsn eufpx8bhor;(oba certain frequency?

Give several everyday example6mz:jjwnm8 *r s of resonance.

Is a rattle in a car ever a rj zyl4o/ewrf4v /:l b0esonance phenomenon? Explain.

Is the frequency of a 7lh ++3;r hknlvxj,o xsimple periodic wave equal to the frequency of its source? Why or lx+vn3ohl+ j;,k x7rh why not?

Explain the difference between the speed of a traub nmzwe/ 8l2a);2lwvnsverse wave traveling down a cord and the speed of a tiny piece of the )z/2wn a2ellbw; muv 8cord.

Why do the strings used for the lowest-frequency notes on a piano noab9m**ufv:+2a:lv g zzmf6inrmally have wire wrapped mal:nb2a9 zvgz*ifm+u v*f :6around them?

What kind of waves do you think will travel down a horizontal metal rod i8t ) kravu/r5rf you strike its end (a) vertically from above and (b) horiz r5u k/tva)rr8ontally parallel to its length?

Since the density of air decreases with an increase in temperature, but the bulkx sz3;8fhy( gl modulus B is nearly independent of temperature, how would you expexg8f ( y3szlh;ct the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decreco6m2h3- fz 3y( srxxzase in amplitude as they travel away from tcxzf(zh3my-x26o 3 r she source.

Two linear waves have the same amplitude and speed, and otherwise are identica;e*baev7 byu/b, eau1a4 w j4iid1y*il, except one has half the wavelength of the other. Which t417 b1weybai *iu/ju iaa4bv eyd;*e,ransmits more energy? By what factor?

When a sinusoidal wave crosanev i7ws584 zses the boundary between two sections of cord as in Fig. 11–33, the frequency ds vn5 za4i87weoes not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there any placeiax u vlk ;q nvaa45rl*;(ua83s you could touch it with a knif4(kulr ;ua aav xq8la*;vn 53ie blade without disturbing the motion?

When a standing wave exists on a string, the vibrations of incident an9 ,-kxx/ac* cyrxj -q9uw)sh nd reflected waves cancel at the nodes. Does this mean that e-xs/nkx-u a r, *w9xqyjch9 )cnergy was destroyed? Explain.

If we knew that enerxjiizlfq:(+)zfv )l5 gy was being transmitted from one place to another, how might we determine whether the energy was being carrif q+l5jvx (l)i)zf:ized by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is /24 kcwoffkosk+2cn* the total distance it travels in o4cc k swkff/n2*oo+k2ne period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it but is 85 cm czrb,8z2d*z )de ho6 blong when a weight of 180 N hangs from it. What is the “spring” condb* dz6zr8ohze 2)c,bstant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg driver getsv)r o4 s:e.zbr into the driver’s seat. If the car goes over a bump, what will be the frequenvb 4.)rsozre: cy of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs from it. (a) Whaf,2hsaqsc o7 *h ez/,qv+m /vxt is the spring sti aosm*f7 hs,vh/2q , vq+x/zceffness 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.tum 8 9ixfa pbs0;w+9z0 Hz when a mass of 0.60 kg is hung from it. What is its frequency if only 0.38 kg hangiuam+ x9 w;stf0 8b9zps from it?    Hz

Construct a Table indicating thelrz 2*3u (sd f-amboop .+lcm3 position x of the mass in Fig. 11–2 at times t = 02c3bll(am*od3. srfuz +-opm ,t = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

  A small fly of mass 0.25 g is caught in a spider’s web. The web vibrates predomru )8qmg 15oqt( j)v6kj egq8gr2-lj ninately with a frequency of 4.0j ojgnqjm)t-8gl 8e2g1k rqr5v 6q(u ) 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 0.88f+fg. c m xl77euglxhp7f-f.3 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 Hz. What is the g 3hfe7gcp+uf7f.x fll.7x-m value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per second with jellb6vffk( kr* h0k 03- o2kg9kv.jsan amplitude of 0.13 m. Det960f*ksk 3v(l 0kj.jr -g hb klok2fveermine
(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 spd z:c+ife, j5dgtls9an(y. 0+q f4ns ueed of a SHO half the maximum value?is c alz,u0n(+ d:ef+nj4fydg 95ts .q$\approx$    A

A mass attached to the end of a spring is stretl.acju.chx -d :d:;voched a distance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretches a vertical spring 0.315 m. If the sprpmj59c4phg)hd .y s)uing is stretched an additional 0.130 m and released, how long does it take ).u)pm p 5yh9h dgsj4cto reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a springhofy :q 6z+ shoj*,)tb with spring stiffness constant k = 280 N/m and is executing sy )6,oh*btsz +h:oq jfimple 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 tow :3lig ,fzv0esfj u8+y popgun 0.200 m to “load” a 0.180-kg bufj,ef vs g0z:i +wl83all. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface 6av) xm ez 9i(2q,znueis attached to one end of a spring; the other end is fixed to a w6q)ez ( uv9e2na ,zixmall. 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 = 0.41p wm+w*,3 5j1kummdha ew xv(5cos6.4t where x is in meters and t is in seconds. Deter* p(m1ha+kxmjw ,1 uwm3v5d wemine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equilibrium is the energy of a Sk +l;oatx+cj3zz0(4 mmawe2 5vij 4gcHO half KE and half PE? 2v40zxm4zlte c5g+ jo;jmca i(k 3wa+±    A

  If one vibration has 7.0 times the 5 3xo+.qog1czx .icbaenergy of a second, but their frequencies and massecciz o x5x.qb3+aog. 1s are the same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanchx(.m4a-s j jging light spring once every 0-ajx.(hmc sj 4.65 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 by0qb kz8ack47dh+ qp/d two identical parallel vertical springs, each withk7z08 4 dc/kd pbqhq+a spring stiffness constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation nk* iehnt 7+vp3*sznm+ ap:b3x = 0.38sin6.5t where x is in meters and t is in second +tka73nb:*nmi+h p p*zs3ve ns. 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, wha) 0m yx9uqmfn0t 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 roc*qh jze;(y0 est on the end of a horizontal spring (k = 124 N/m) is struck by a hammer, which giveeq z(0hyoc ;*js the mass an initial speed of 2.96m/s Determine
(a) the period and frequency of the motion,    s    Hz
(b) the amplitude,    m
(c) the maximum acceleration,    $m/s^2$
(d) the position as a function of time, x = (    m)sin(4.08$\pi$t)
(e) the total energy.    J

A vertical spring with spring stiffness constant(lgu0d 9m+a,o0q53t rlnt col bx/e mmh:rw(+ 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) with positive veloci+lmqoc(9e:o5/,l w n xhg( tm+dmura t3r 0b0lty at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two springs, with spring stiffness consta.4gnweqa-)5e)y ;yxxnpx- eqnts $k_1$ 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 bl.grf.8gxy3 (+ omses am0yv9l)4b llnock attached to a fixed horizontal spring whols(+egs a3ol. fvm9nxg 4r8ymlyb)0.se spring 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 65.0epx w5 )fr4dwcbk 4p.. kg jumps from a high bridge. After reaching his lowest p 5e4wxr.ppf)bc.wdk 4oint, 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 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 i no8q3as99p) od1shvc g a)0gzn exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly one swi82kcagm ;duy :yq q94mng per second? (That is, one complete vibration takes exactly 2uy gqq8k4mcda2:y9 ;m .0 s.)    m

  A pendulum has a period of 0.80 s on Earth. tp*a3so;sf qd+so0q +.km ;hjWhat is its period on Mars, where the acceleration of gravity is about 0.37 that on das0k3 +f;sj ;ps*mohq+ otq.Earth?    s

  What is the period of a*9jh8591 juabqsgmztm3o n h s-qcz ,2 simple pendulum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple penf5m91ibhl 4c .ry vdu6v81xod;piay, dulum is 0.760 m, the pendulum bob has a mass of 365 grams, and it is released at an angle of 12.08 ar5vy lob,;6 ucdyidmhi 91.fv 1xp4 $^{\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. Iehn vct7z.g) zivog t4,mxo6,-ed6t :f the clock loses half a minute per day, how should you adjust the length 4c6t vz7e g,:nve.o, hdi6txzm-o) g tof the pendulum? shortened by    mm.

Derive a formula for the maximk;m n45hrz5,lcpi-y;2f ytg fum 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 6.nciiga +fd gf6n fj/.s8g 7 prslr3*2.5 Hz. At it is released from rest starting at an angle 8sfn+ 66cil na.7r*r3 fjfg.ip /sggd of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests pass the bow of his anchored boat every 3.0u w-443ebow lxo .pn(fj pk)3p s. He measures the distance between two crests to be 6.5 m. How fast are the waves trofopexn p3 4)kl ( 4bww.u-jp3aveling?    m/s

  A sound wave in air has a frequency of 2qgo1)yjuw6/9u o5n ihgc.o/f62 Hz and travels with a speed of 343 m/s How far apar.)yjfq6 u9u/5 oh1gin/gcw oot are the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz anv5 6.;qdv8vv 2f(a1jil h*d omzjph/cd 1600 kHz (kilohertz) and travel with a speed i5j(vhmdcq/26 f;8z vhal. dj*pvo1v 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 ofg 9w(dv)hyj(: d8( 7pfonmxdhp-q9gg longitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastiokk (pzsxl4jaj(qpan 1, j: 9.c modulus, but one is twice as dense as the other. In whicnopaxl ,sk1a zq4j9.kj(j p(: h rod will the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretchedt999dlh lik2d between two supports 28 m apart. If the tension in the cor2l dkd9t h99ild 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 the top of 8q 6nj*hxu n4ypuhf q on0e1*/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 and sends a wave pulse al4/nunuoxy6 eq *80hpfh n1*jqong 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. Hex b.4c/h+i ) 6c 5w3gbbg2or.ygyda se hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. Hd 4i y.sgeg+bx).rbwo6cgb23y hca5/ ow deep is the ocean at this point?    m

  P and S waves from an earthquake travel at differezk *7 qpvo9:bant speeds, and this difference helps in locating the earthquake “epicenter” (where the disturbance toa:q *o9bkv z7pok 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 sinusoidal trantz g 7mgxtjp3 m(lea m1x)3-5vnz sw2+sverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which s mzam-gvt 2gw5 ( 1 zelx7p33xmtj+)nactually include 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 intensities, and (b) the amplitudes, of an earthni0al7pgkulf bk p9h/b;,,5 pquake P wave passing through the Earth and detectf0i l/,9,uap pgbb ph;k57lnked at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthqua3unpt*f2r0 jqke wave passing through the Earth is measured to be *03j nutfq2pr$ 2\times10^{6 }J/m^2$ at a distance of 48 km from the source.
(a) What was its intensity when it passed a point only 1.0 km from the source?(round to one decimal place)$\approx$    $ \times10^{9 }W/m^2$
(b) At what rate did energy pass through an area of $5m^2$ at 1.0 km?    $ \times10^{10 }W$

  Two earthquake waves of the same frequency travel through the same portion ofr6a++ort55pjqj9 zz k the Earth, but one is carrying twicept ra69o5jjzzq+k5 r+ the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a lcgncb r lo(-zom+p k4:(oj, 6stretched string have the same frequency, but one transports three g(o -(j4kl6o,monb cclp +:z rtimes the power of the other. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move u( ovy7 u lz3n(nwur6wv/ l:3xnp and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wavenuw6vyuz: on3l(x vr 7nlw/(3 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 movin2k+ h .bc..0pdx13cd4iclukld ga) h lg toward each other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the3b ck2gxpa).0d.lc4 kc il.duh lhd 1+ 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 atfh5xa0uc4u r1w*a b*b 440 Hz as its fundamental frequency, what are the frua a4fuxb 0 5rhwb1*c*equencies of the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294. 7hbxbje2rbz.v /e9k Hz when unfingered. At what frequency will it vibrate if it is fingered one-third of the way . xe b2vbz7r./h9jekbdown from the end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequencyo,/ r, d ;)8 rqsk6;zeis9qpfktvbt6p of 280 Hz. Name at least three other frequencies at wi6rsz),o; vq8dsk6q,k ;ttf9r pbp/ ehich 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 fre+.;j7 p*,8wzwnavk,d deo onequency of standing waves is 47 ko pv,nnd+eoe.j *;w78,dzwa5 Hz, how far apart are two adjacent nodes?   m

  If two successive overtones of a vibratinh /wuac.1l u(/c:k2: zvpzneq g string are 280 Hz and 350 Hz, what is the frequency of the funda.zp z kae:u2hlwu1n:(v//c c qmental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distance fromg862.m hd- :wjy hxrzcomfh -8 the bridge to the support post is L = 62r2jgh h8-mw cmh -6.8ofyd x:zcm and the string is under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, but it is measured n,x / jh(i s*38esj zmp,)wiycto vibraiysw/8cz*npij ,ems, ( xjh)3te at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hz, bu. 2s-orpt, lxl*vlh;ut it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency? decreased l2uo slxht* -lvp,r. ;by    %

  One end of a horizontal string is a)cei ;(9l55jaihedfh ttached to a small-amplitude mechanical 60-Hz vibrator. The s5eh)(l 5ea9jfcd iih ;tring’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 lengtk qop 5fd3ig9 5 tqu9ewbt*8.eh of the string may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may b.ep*5keo39dq tw qt9 fig5ub8e achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the waterq6p wq27/ya.t c4 jrbd3 r,fhr back and forth in a tub at just the right frequency, the water alternately at4h/ y.rwfr6 dqr2,b 7jqcp3rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a 2vi 9nrm84zfw boundary within the Earth between two z9f2 inw8vm4rkinds 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 cs/ 2 g8; eh4pfyo* kkmmodm58gsar(z4hanges from 2.8 m/s ts8gsaoehm(m45kp * f2goyk4d m; r/8 zo 2.1 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 ar6jukq.i;l2ifa -vq 0ir when it hits a layer of cold, dense air. If the sound wave hits the cold ai.qfjqvrk ;iu6l2- ia0 r 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 earthq-o(mw2zii x+x uake wave strikes a boundary between two types of rock at aixi -x(+ mzow2 38 $^{\circ} $ angle. As the wave crosses the boundary, the specific gravity of the rock changes from 3.6 to 2.8. Assuming that the elastic modulus is the same for both types of rock, determine the angle of refraction.    $^{\circ} $

  A satellite dish is about 0.5 m in diameter. According to the 5fceuq r qh7*4user’s manual, the dish has to be pointc*huqe rq47f5 ed in the direction of the satellite, 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 2kl*eb6ucwnn:7 : 8)c6ot7cdt qaro l650 km and velocity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately hoob lut:ndw6cec 7lc6 k* :r 6no)7tqa8w 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 stii3 ,: kbm. lp1ax*hhziffness 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 ofk: xp3ibhl i.h1 mz*,a 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to5nk53sj8 qcdo a fire net 18 m below, which stretches the net 1.15o d8 kcjn5sq3 m. 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 hangnvgs4 (o i-v,ting spring. The mass then falls 3(vt ivn ,4osg-3 cm before it stops and begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a spee i)0o7ztit6 ,dwya j7ad of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What i06 7 jt)waztiy7,diaos 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 c mqy y1ejeb:;)offee (diameter 8 cm) at just the right pace of about 1 step per second, the coffee sloshes more and more until eventually i b:1j)e;y myqet 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 g ldcfq 27c s7u5fcqm j9. ;d-l.gjjy.the center of a 33-rpm phonograph record have a wavelengt9- fdg cj.2q5qfjs 7ymul..dc ;gj7clh of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates acco1 n/w1pv fcgobqiw)1l. i14w/ j4bb shrding to the equation x=0.650cos7.40t where x is in metersbhi1lp/fqo1s4cnww. ig 1jbv/)w 41 b 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 oscillates with f y3kfnswal+ b9/hzc 89requency f. What is its frequency if it accelerates at 0.50g (a) upward c/ ns 39k+hwbl8azyf9,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man sv.5ln ol2r) gcetex8 7w4iy2n tands on the raft, it sinks 4.0 cecrlet4 ovnl)y 2n5 gwx8 i.72m 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 t;f2ytq nfs)y u44ug- qd-d5az uned to play at 392 Hz (G) and 440 Hz (A) fyz-qt2d5suqa d )-fn g44u;y.
(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 two0, i);t; etzl1motpyy -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 yy;,t ;o itlmt0z1e)p in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the tip of each pronild1/hr,w )6 8n hdrkmg moves 1.8 mm to either side of center. Calcu /wdk6, dh 1n8lir)rhmlate
(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 frequenc.ito m) 9 yfe)9jjy(sly 1.5 cycles per second. 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 oscillaslj ()m y99 tye.f)ijotion?

A string can have a “free” end if thatqe5py -jtq/ 6a end is attached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of sucey6/tp 5qjq- ah a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactlyqz;-iks*0bq y om::wcf jtiz- /,rj5l 2.000 s — each one-way swing takes 1.00 o t-fy /l5qj irzqb:;,m wij*s-:0czk0 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 oscillate in the vertical direction,hecy)( z6eg48b y za jkw-ra4 or can swing as a pendulum of small amplitude, but not both at the same time. Which one i4-zrwb84 jg( ),ha keazy6ey cs 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 u;evmo,de;f xn) wh+c- nder a tension of 255 N. A pulse is generated at hevx)ew;m -;nod+cf ,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 suspen6qeabpbl4 l2wx 4q5j*ded from a ceiling by a spring with spring stiffness constant k. Al44pbx jq2a *56l bewq penny of mass m is placed on top of the block. What is the maximum amplitude of oscillations that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-h8*nf.ol bb3/l0mpv njj- jh; kg car at the junkyard. The steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. What is the period of the bouncing? [Hint: Refer ;m fvloj 3*h.8jpbjnhn-b0 / lto Table 9–1.]    s

  A block of jello rests on a ,v yq bnxf9o8 88o7ucmplate as shown in Fig. 11–58 (which also gives the dimensions of,u9 y v8o8 n87fqcbxmo 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 that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz