Give some examples of everyday vibrating objects. Whixwrm9v(s t09wch exhibit SHM, at least approx(99vtr mwsw0 ximately?

Is the acceleration of a simple oii kh-o hdc) o-2j;c(harmonic oscillator ever zero? If so, where?

Explain why the motion of a piston in an automobile engine is approximately sib cnf6-fqr8yecq1 yus3 +b.u1 mple hu 81ue-y3yq1qsc+ .fnbc6f r barmonic.

Real springs have mass. a 5bbm7jkq3ln1 klq)t1s:7 vuWill the true period and frequency be larger or smaller than given by l v7k: 35st)u7kmn q 1qb1bajlthe equations for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple harmonic oscillata r.gero4,l; xor (SHO)?

A 5.0-kg trout is attached to the hook of a vertical . ajlgw30mom hhnl7 th 9ha1:4spring scale, and then is released. Des:hh13n4j 07m 9agoml.hh l atwcribe the scale reading as a function of time.

If a pendulum clock is accu k.sy;ld9 t t8i/jje-frate at sea level, will it gain or lose time when taken to high it ;kydst/j- jl.8f e9altitude? Why?

A tire swing hanging from a branch reaches nearlyr--j7 3fupaeu(q2x4 s wb u9gu to the ground (Fig. 11–48). How c2 u u39b 4xr7u-e(jpguf sa-qwould you estimate the height of the branch using only a stopwatch?

Why can you make water slosh back ani/uvwl:d9c ju7 z8 i w lpajd,9va 1)wg0ig;+nd forth in a pan only if you shake the pan at a certain lzniaigji9cv l w w au:8p j7dgv+,/9duw10 );frequency?

Give several everyday e *h/:x.e hxiihxamples of resonance.

Is a rattle in a car ever a resonance phenomenon? Explaid8l.ja,rws et,2tf; j n.

Is the frequency of a simple periodic 4l ht z4;lcuft.y5x4 iwave equal to the frequency of its source? Why or why not?.;4it4xt y uzfc5l hl4

Explain the difference between the speed of a transv 9gh jx dvd).k6avno42erse wave traveling down a cord and the speed of a tiny piece of the cord.j k.692 aovg )n4xvddh

Why do the strings used for s9jetipmnnh )q6 63 jqir 5h4)the lowest-frequency notes on a piano normally have wire wrappedjn9665r) tipq3 )eij mhsn q4h around them?

What kind of waves do you thiqk( jbm xu6e7lnq;(o4: q dgb/nk will travel down a horizontal metal rod if you strike its end (a) vertically from above and (b) horizontally parallel to its lengteub n(b/q7qx g;(:q lk dm46ojh?

Since the density of n*gw.q*u).me efff o5air decreases with an increase in temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves in air toqufne * ) .m.5*fgowef vary with temperature?

Give two reasons why circula,7 uf14cefdxyz1(v gxr water waves decrease in amplitude as they travel away fromzeucy( 41dxf 7vx,1gf the source.

Two linear waves have t+x 7wgw xl47y/.1zimzvwmx x .he same amplitude and speed, and otherwise are identical, except one xy.xlx7mzx.4/z 1i mvww+7wghas half the wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary bet e 4qa)+dpgi3tween two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocity do change). 3a4p +iqdteg) Explain why.

If a string is vibrating in three se 8u y/9n*oveq-a yex(zgments, are there any places you could touch it with a knife blade without disturbing thx9v-q uoae / eyy*n(8ze motion?

When a standing wave exists on a string, the vibr.r z:( x/xqmuuations of incident and reflected waves cancel at the nodes. Does t: x/.qm z(xuruhis mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one place to a.ms*qyd3czoon 34jl ,wo. jr7nother, how might we determine whether the energy was being carried by particles (material bodies) or , dnj wq3 cl4.z3rys*o7omjo .by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the total distan6ivgdmw lb7zal)* 3:q ce it ad3l) i7q *vgzb:lmw6 travels in one period?    m

  An elastic cord is 65 cm long w2ak bc*m ;y:0h v9j2hqwnq+ iehen a weight of 75 N hangs from it but is 85 cm long when a wqwmy ;h+ k bc2j29ive0*q:hnaeight of 180 N hangs from it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg caot8ah +e8j0 rir compress 5.0 mm when its 68-kg driver gets into the driver’s seat. If the car goes over a bump, what will be the frequency of vibrationse8+oa0i8 rjth?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs from it. (a) ux -suj0-xgs*What is the spring stiffnesgxssj-0u- xu*s constant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a frequency of 3.0 Hz when a mass )pil sap*r(9r of 0.60 kg is hung from it. What is its frequency if only 0.38 kg hangs f*al ps ri(p)r9rom it?    Hz

Construct a Table indicating the position x of the mass in Fig. 11–2 a-78kvnh2d ly: t5; psm ungno+t times t l:u- 8m5dhg ;27nk+p tvy nnso= 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. The web vibrates predzs2 ) e.,kj6vcab60 eplq(m7k dq xvp+ominately with a frequed.26apev( plxs)cz mv q+k7 jbqk,e6 0ncy 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 vi- c7bjdu/.k)s wy6quza obh 79brates with a frequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 /dko u7 y9sb -w)z.b7uaj6qch Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 time.*id.5:/dax q8ui ;jtofl ymas per second with an amplitude of 0.13 mitajm au.f5do:; iylq./xd* 8. Determine
(a) the velocity when it passes the equilibrium point,$\approx$    m/s(round to one decimal place)
(b) the velocity when it is 0.10 m from equilibrium, $\approx$ ±    m/s(round to one decimal place)
(c) the total energy of the system,$\approx$    J(round to one decimal place)
(d) the equation describing the motion of the mass, assuming that x was a maximum at x = (0.13π)cos(  πt)

  At what displacement from equilibrium is the speed of a SHO half the maximum vala; /chibcl* 8eu8c ;ibehl*/a ce?$\approx$    A

A mass attached to the end of a spring is stretched a v ml ,o)x, :ibwtq8j.xdistance $x_0$ 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 smyuiv71b 4:kuso8 v 4wpring is stretched an additional 0.130 m and released, how lwyk4im vv7ob: su1 84uong does it take to reach the (new) equilibrium position again?    s

  An object with mass 37a2 1yaivdk1 :scr/sg g 6u5e;grka x3.0 kg is attached to a spring with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, icr 1ks:56/rgei k gdv3a;ya x7s 2aug1t 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.v es5dax yw- wsficy+k1qc0p0 +h;58 x200 m to “load” a 0.180-kg ball. With what speed will the ball leave the gu-c5h+x5 p swa 0vxy80k;dqefsiy+c 1wn?    m/s

  A mass sitting on a horizontal, frictionless surface is attachdtr kdfdgnp4 ys53-68q q( )rbed to one end of a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, the mass experiences a -ndr 8grfsq3dk( p qb5dyt)6 4maximum 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 whers(x4/0 pwxdkg e x is in meters and t is in seconds. Dexwd0 k/(gp4x stermine
(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*2wb5ofb9ost3 (l; 7ynhdxbw from equilibrium is the energy of a SHO half KE and half PE? ± 59lw(*fxy3 hd b 7o2 s;ntbowb   A

  If one vibration has 7.0 times the xymo :toz,9/ ;fvo :kfdt18b uenergy of a second, but their frequencies and masses ym1 u/::9o ox;zot,fvb8 dktfare the same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light spring once eveo1d .wspojw,nzu 9hc 6 t7g7d6ry 0.o 6gu7w9z p,7sc ndj1 doth6w.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 csvm:9ym.0d d-nh rjeqpn275ap u0 n /two identical parallel vertical springs, each with spring stiffness79dj-yha/pndq 50rm0n:.mn secuvp 2 constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.er7qqx0mam5o qk jl/dfa0z-e:3 u47s5t where x is in meters and t is in 07q/0emu4jk3fas:r d75xl-q a eoq mz 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 examples of SHM, labeled A and B. For each, whate)0- jsbah4+ voso(k z 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 4 ;mal6fc(rxm (k = 124 N/m) is struck by a hammer, which gives the mass f lm;a6(c4mrxan 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 stiffne 6 k7phq.ou9x-bx6 (r)1zawl behzvg*ss constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from i lx qx1 rhzbv)o6 -.7gakp9ueh w(6*zbt. 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 stiffness (ua9ysgw.a87sr jur:h w3 tr8constants $k_1$ 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.dgl,n,1c8xg a*+tfd d600-kg block attached to a fixed horizontal spring whose springdg,f,nlgx c1d8t*+ad stiffness constant is $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with mass 65.0 kg jumps from a high bridge. Aft zwwu:z+b39qder 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. Calculww:3b+ 9dzuq zate 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 t no0 epmk81qnqsa-(2 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be ifu,5v6 zv i;wit6ny2ep it is to make exactly one swing per second? (That is, one complete vibration t;iw6i 6,z2nuet5vyv pakes exactly 2.0 s.)    m

  A pendulum has a period ofuz 9rc72pndt4tq r2+k 0.80 s on Earth. What is its period on Mars, where the acceleration of g29 7 z rcpqrdt2kt4+nuravity is about 0.37 that on Earth?    s

  What is the period of a simple pendulum ph(4tx6iyv ;q8m y6h uxf.,yn80 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, the pendulum bob+k fr.1/gkuuvs1v ;wt has a mass of 365 grams, and it is released at an angle of 12.0. wvsuv1ur k1;+g tf/k $^{\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 c6eys3 8ux(zd *5oz ,3wxh(akilu)qr clock loses half a minute per day, how wc( 8*,3(erih zxq35x)6 udszoa lky ushould you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the3:2ffqvq4n mh maximum speed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at a frequency of 2.5 Hz. At qfx qw g 2uoi607ep h7qjaktr )*js4i;b(+w*l it is released from rest starting at an ang*qes(buap ofwg q07w)qjriji ;lt 4+ k2hx6*7le 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 e/62slo 9ih wgx e,nv ;78o.gicns+oithe bow of his anchored boat every 3.0 s. He measures the distance between two crests to be 6.5 m. How fast are tn lw. ,goiio9hvg 2o+exc 8sns/i7 e;6he waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and1z2-tb7ay lnku*6vx a travels with a speed of 343 m/s How far apart are the wave z nayax7vu l 1t-26*bkcrests (compressions)?    m

  (a) AM radio signals have frequencies between 550;;h43nb2r3khilu w u e kHz and 1600 kHz (kilohertz) and travel wit ie;23 l nwb34hhrkuu;h a speed of $ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

  Calculate the speed of longitudinal xvtmc7dp 8x)2 waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the samet e ;i*5 p3ur;mkpr:ua elastic modulus, but one is twice as dense as the other. In uiterp;ur amp:5*3k; which rod will the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched be:xvq x qn7ly8azak3d/ v*ps6(tween two supports 28 m apart. If the tension in the cord is 150 N, how lon qlx/6 zp (8 q3k7xnas*:dvyavg will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to the top o;u r( tnnb-8w 4 ww(l-qd,qbxif a hill by a steel cable of length 620 m and diameter 1.5 cm. As the gondola comes tow ln;-( n,u4 bdtqqbx- (8iwrw 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 kx3zcccn. 0ahr gzlpnn(5h at-t)))8gkn +-csea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is the ocean at th +gncxcgc)0k8a.(- chrz k npn-l5t)zht)a3n is point?    m

  P and S waves from an et.kqr;e9 *hw earthquake travel at different speeds, and this difference helps in locating the earthquake “epicenter” (where the disturbance took pla9eh ek .w*;rtqce).
(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 by2y8f c q49nwq p;r 8p)i4yx1uvvn1s hp a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequq yvxp v8w4n;i1uyrq9p1h 2nc 4)8pfsencies), 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, .7q/ a 4vn yc7bniwd+8j:wg afof an earthquake P wave passing through the Earth and detected at two points 10 km and: a.w w/4+ygvjfna7 8di7q cnb 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is measured vhk. 7 co ud)1jo+gvd2to be go27 1.hdkj )cd +vuov$ 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*ysp+ y71bcxpe/ g/o q the same portion of the Earth, but one is carrying twice the energy. What7eycsy bp+1g xq o/p/* is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the samz+2v wlfy7y4o e frequency, but one transports three times the power of the other. What is the ratio of thz2 ov4y+yl w7fe amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move up and dzgy tb;.hltrdk,jq e; ;c8w++ own a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm, by ,8+b ;e kjlztt.+dhg;rqw y;cwhat factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving tow i iluraz87;f4ard each other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Skfli uz47a;ri8etch 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 viv/x -qsz 34m+ivg v,kdbrates at 440 Hz as its fundamental frequency, what are the frequencies of the first four harm mxs4gdvz3+- ,v/kq vionics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what frequency will it viufm)rc+1gh1al2n+ yim tq2d6 brate if it is fingered one-third of the way down from ah+t)r u f16+i2ynq 1mgcldm2the end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops as4pkz)9 fcx. )f ejyd qi97*pvt a frequency of 280 Hz. Name at least three other frequencies at wh*zp 9fqi)9 7kdpex yv.jf cs)4ich 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 If5qak9 1ftvt+u es7.acx2w6d phs ae-+ the frequency of standing waves is 475 Hz, how far apart ar1 hkp +s a+ev- s96acf.t5dtxw2aue7qe two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 3wjc.l,qfgyo4g0(g d d)1. he j,anm;s50 Hz, what is the frequency of the f)whl;jg fydam1sjng d0,.( qg, oe4c. undamental?    Hz

  A guitar string is 90 cm long ay 7vuh o/b,;rznd has a mass of 3.6 g. The distance from the bridge to the support post is L = 62cm and the strin bu;z 7hor/v,yg is under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string +dts 3ajo g e97y/-w8 av39qe xpkjp)iis supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent shos839d p7-iwty+jovexp)je/gk a q93 a uld 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, but it is meax(g13 m;adl nksured ln( ma13kd;x gto vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a0:rqp pu 0xvm5knhn28p ( l.gr2+gcbw small-amplitude mechanical 60-Hz vkb2pg :qrgwmc 50x+n.r h 8( 2nupvp0librator. The string’s mass per unit length is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of thz.ad-2u omf d)e string may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many diff.u2zm d a)of-derent standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water bact5khe4xk;fz o.:u g-ck and forth in a tub at just the right frequency, the water alternately rises and falls at each end, remainh. ;kezg xtf-u :k4co5ing 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 boundary within the E tg;ap c n(i)/z/23lkq)wp elfarth between qk (n3pl/c/2 pf awetzlg)i;) 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 from 2.8 d8 dpkm lt.1u.lxwr3s8,9wcm m/s to 2.1 m/s If the inciden8p su. drx1t m. kmdc8llw9,w3t 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. In7s(1hhqp e9w ix* ns/f9e*s 17xwsiph/q(nh n the sound wave hits the cold air interface at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave strikes a boundlys/vyz86 8lqary between two types of rock at a 38 /ls y8zq8vl6 y$^{\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. Accordin d ,4v(gj8r6er io2sh8cou;kf g to the user’s manual, the dish has to be pointed in the d6o;ourd2 gc884h se v(j i,rkfirection 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 250 km and velocity 750 km/h travels across the Pacif cw6lei04 gkg*k05hcq ic Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsuna w0clgge5 i* kk46cqh0mis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness constant of 550 kN/m Fi*9/f w)7j)l fafnszlu nd 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 (approximately 5 mi/hff )7sj )lu 9nwfzl/a*). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m below, which stretj. gposugfho3u*4( i1 ches the net 1.1 m. Assume that g ig so* 4o.u3ph(fju1the 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 ha:u60g b,bnpia(x )lvoz,(ortnging spring. The mass then falls 33 cm bef)bonlora ((b xt:6 uip0v g,,zore it stops and begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 11–54), compressihyvk4 :;0f aghp-*p2/mi bz/fkl5kkx ng the spring 5.0 m. (a) pz k2lyg0v- kax* i5 pbhk:/f4 /m;kfhWhat is the spring stiffness constant of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of coffee (diameter 8 cm) at gd3 ,n3 fp7.a rx npvyt7x3se0just the right pace of about 1 step per7 gnnxp3afst,p0xv3 7re dy3. second, the coffee sloshes more and 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 phonograph p3p /0-tnstek record have a wavelength of 1.70 mm. Wha/-pn3t0petk st will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.4*y: wliu5,t t2wc1gf. jilsc48h8rl k 0t where x is in meters and t in seco hcwlgl5.4 l8fwr, s2:k*18tjiu iyctnds. Determine
(a) the amplitude,    m
(b) the frequency,(round to two decimal place)$\approx$    Hz
(c) the total energy,(round to one decimal place)$\approx$    J
(d) the kinetic energy and potential energy when x=0.260 m.(round to one decimal place) PE$\approx$    J KE =    J

  A simple pendulum oscillates with frequency f. What is its frequenchg 66n,zmw cv9l9yf2 vy if it accelerates at 0.50g vfgm6h9 n, y wc2v6zl9(a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man ovj :fo mxk;((,a ngsqbf 33eu:au)w5stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the raft k,: 3en 3s) vqbua (o:xf(fum;oa5gw jvibrates 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 atfwd b/z 62nkc hvp.1*s 392 Hz (G) and 440 Hz (kb wpchvf6 1n.*s/d 2zA).
(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 tr dnenjzgm*w6b+ lp:+ a //n)rzaveling down the stretched two-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the hgwe*+zlb/r:/ 6ajp nnm+ zd)n eavier section of cord or the lighter?

  A tuning fork vibrates at a frequency ofaa4a 4s 9 1yla(k;jgfw d k3d4vn)j4mp 264 Hz, and the tip of each prong moves 1.8 mm to either side of center. Calcula41v9m4ksjwg a)a4kdfy; lnpa3(j ad4 te
(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 cy8i1lt ;,kflaf cles 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) lat;il,1 ff8 kwill not lose contact with the board during the oscillation?

A string can have a “free” end if that end is attached to ag ,nr/mw;eaoje y2ym6c r, )b* ring that can slide wi6mr reba, 2y jewo)m*n,;g /cythout friction 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 5 0spu259hqaxa hf:kp of exactly 2.000 s — each one-way swing takes p xh:9ha0fu2s 5pqka51.000 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 springhxo2nl 6*,3)(-x rh:gu5htmn /mlip v pcydi 7 can oscillate in the vertical direction or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontal swin *)mi-o2h3(mx, r hglhy5l:pnpncu7d6/vt ixgs, and by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

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

  A 10.0-m-long wire of mass 123 g is stretched under a tension of 25 86 -gueif,ypj5 N. A pulse is generated at one end, and 20.0 ms later a second pgj, pf 8-uyie6ulse is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended(kvdt -b kio)c,6o lv1 from a ceiling by a spring with spring stiffness constant k. A penny of mass m is placed on top of the (v,b- ol1k)vc toi6k dblock. 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 1202g*3vgdtsf/ m0-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 periosgtf3*2mgdv /d 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 4z6ukr 0zt-y s5zza bk5,hsf4also gives the dimensions of the block). You push it sideways as shown,t0 z sa4 s-k5z ,zzhrk6f5yu4b 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