Give some examples of everyday ydv./ pj,ys5u vibrating objects. Which exhibit SHM, at least approximately?uj y/5p ys.vd,

Is the acceleration of a simple harmonic oscillator ever zero? If so,oc h98b+wnyr ewaoe7hr u.w+z*y87s + e:w(et where?

Explain why the motion of a piston inuw2etxtus 260 an automobile engine is approximately simple harmont2e6 s2tu 0wxuic.

Real springs have mass. Will the true period anf(; 4nj ut s-1rkvg1xej0;t azc5tww;j7yt ( nd frequency be larger or smaller than given by the equations for a mass os t;wjaje-(ct4;7 u;fzg w rtxvk 1n0njs51 (ytcillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of ar0zhby 8ci-m3xfi *b/ simple harmonic oscillator (SHO)?

A 5.0-kg trout is attlyel.y3t f/ p2 4 evd5erlay:8ached to the hook of a vertical spring scale, and then is released.pl4:5f/.r vteay lyy3 dle82e Describe the scale reading as a function of time.

If a pendulum clock is accurate at sea level, will it gain o zx) 3pgtu5m-pr lose time when taken to high altit-p)xz3ut5p mg ude? Why?

A tire swing hanging from a branch reaches nearly to the ground (Fig. 11 u6x 0 a4a4cyqovv6frpd9-1 w 9.aeerf–48). How could you estimate the hqoae496rva1.v r wpxae6uyfcf-d409 eight of the branch using only a stopwatch?

Why can you make water slosh back and forth in a pan only if you wztj.kf 0wigp kw55cs;6x)viime4* 1 shake the pan at a certain fre 6i zwcs i)gpi*f01etkww k;j4xvm. 55quency?

Give several everyday jfijhe k6g9:pw9 txq*-tp+) z3*prd rexamples of resonance.

Is a rattle in a car ever a resonance phenomenf 6 0mk1:w im7gin*ahpon? Explain.

Is the frequency of a simple periodic wave equal to the frequency of its(rp i*7tny (j:ekgq u- source? Why or why not?7k(jrte*qu(:n ipyg -

Explain the difference between the speed of a transvers48geyr0w zd j n8owr7e52/* i/50jjfgaxhk nve wave traveling down a cord and the speed of 47jkrvw5hgr /dw5n8g0z x/njae0*o2jye i 8f a tiny piece of the cord.

Why do the strings used for the lowest-frequency notes on a piano norma+ k/50lq8cu4ekh r )jh yu.wsplly have wire wryqhr08j)k p+ceul54w. hsu / kapped around them?

What kind of waves do you think will travel down a horizontal metal rod if you 9ba-- t--* empiakeov7r)k iwstrike its end (a) vertically from above and (b) horizontally parallel k-ep7o -ai v-9 t r-*)bikmewato its length?

Since the density of air decreases with an increase in temperatug,xfyj097s 2)o7q9 xb nkhj2f,fygeh1(x ggire, but the bulk modulus B is nearly independent of temperature, how wn,0,y f9 ih)gq7kxgs9 j j1by(gh7gex o x2f2fould you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decre t yh ev,4j(h7octudoqw.0*,rase in amplitude as they travel away froh, jw*cyu ,4(7 v.hqro 0tetdom the source.

Two linear waves have the same amplitude and spe1xnli q (dz,tirq. ;4yed, and otherwise are identical, except one has half the wavelength of theqq(t4,id1 x;l. rynzi other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the0b/ a ,enfg zmtr6kzk4+ :yuvljka4 6/ boundary between two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and z+j zv6 /ra4t ynabke0u:m/gklk, f46velocity do change). Explain why.

If a string is vibrating in three segments, are there any places you could touc glzs dp,e+k c h7/dbx(m9i*g*h it with a knife blade withzbmc sg 7p *exddg/(,h*ki+l 9out disturbing the motion?

When a standing wave exists on a string, the vibrations of incident and reflect ;ggo/0;bhigcis +g4. wu,mxe ed waves can+w;.cigb4g hx; ,/ 0uoimeggs cel at the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from o25 z9b:lk fk,v8ig/5b8c qjpiz: ktjkne place to another, how might we determine whether the energy was being carried by particles (material bodies) or ,b:gk iq8 59fk kiv l25kt/jz :bjz8pcby waves?

  If a particle undergoes SHM w8flkcv g9pz/ 6/k dl5fith amplitude 0.18 m, what is the total distance it travels in one perp lfl95f68zg kc /vk/diod?    m

  An elastic cord is 65 cm long when a1gt j-uaa d1/m weight of 75 N hangs from it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” constant k of th /g-m1uaatd j1is elastic cord?    N/m

  The springs of a 1500-kg car compress 5 zd0bwvga :9,j.0 mm when its 68-kg driver gets into the driver’s seat. If the car goes over a bump, what wil,j dwv0b9az:g l be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fis,tkr /hmymo 3,k- v.ckh hangs from it. (a) What is the spring stiffness const hckr/.vkmom,k-t y, 3ant $\approx$    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 vibratesjp:j9d/4xtbdgpm kb2er,2: e with a frequency of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its kppm2 tjdbjr:/9 e,dx4g2:eb frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. 1*sjp-8 rsvhfler .5n61–2 at times t = 0,t r6fsh .58j-* nplvesr= $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 predomfii l+*kk1km tyl+;1lewz0 r/inately with a frequency ofl rl/1; i*ky ilwte+k+ mz1k0f 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 spr7yze(-x igz q5ing vibrates with a frequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 Hz. What isyg -7 q(ze5zix the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates (21g bgwu(ai ofdvx:o z g10l/3.0 times per second with an amplitude of 0.13 m. :gg u/lxw((d1ifoa0 o b1vz2g 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 p)ccwkxe5dhr 9y84ph av :+zi7ju3 4ehalf the maximum value?z4ce3ux4c9r k8 ie+wyd:hjhva5p 7) p$\approx$    A

A mass attached to the end of a spri-3gp ez mt:ah:ng 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 stresffo//zwr:k )jtjo ug fq3 22.tches a vertical spring 0.315 m. If the spring is stretched an additional 0.130 m and released, how long does it take to reach the (new) equqw /u3ko :gfj/s2r.fz2t)j ofilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring wvs1j 22av5th9ta ;pq lith spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the obj ;p2qa1v95hatljv 2stect 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 afr v,vtf; 2+ze5ipf-):i azb of a toy popgun 0.200 m to “load” a 0.18t,;f2ziav5f+rfzv b ):i-e ap0-kg ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frik,w+tqwl wb*+ ctionless surface is attached to one end of a spring; the other end is fixed to a wall. 3.0 J of wor+w ,bq *ktlww+k 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 = p2y1emmq59 p(j0 v6u7gy9ftux8bhj o 0.45cos6.4t where x is in metersmjy(5t6v 1gf b0jy2up xq9uhm79p oe8 and t 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 is the energy of a SHO half KE and half Pb:k(z1zdlo u3t .yx ,hE? ±1.:z3zdhxto u(kb y,l    A

  If one vibration has 7.0 times the energy of a sen4y/qsk(xcz9rr + e4 kex6ox,cond, but their frequencies and masses are qycxxxn+4korre, e(649 / ksz the same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically h kth0)9pyh7 )ew6j +y:rxr zdranging light spring once every 0.65 s. r r6yk0 :+w)h 7)h ptdreyz9xj
(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 ide. pma292pfz 9q g)fpointical parallel vertical springs, each with szfp2 pap.i9of 2m)9qgpring stiffness constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t whe4jvii ,b :d4ihre x is in meters and t is in seconds. Determine jhiidi v4:, 4b
(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 andqczrimr 1(k1)/+ bsu o 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 en j (c:rhqu;vffhl 9/t2.v vx)69tc fswd of a horizontal spring (k = 124 N/m) is struck6 v(/:t)u9 h;fv l cft2sxcrvf h.9qwj by a hammer, which gives 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 305 N/m vibrhhf ;h-veqkaaf00 n kls301x(ates with an amplitude of 28.0 cm when 0.260 kg hangs frok1saqe -0vx0a n(h 0hfh;k3l fm 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 stiffness con i jbi;6;rznx9stants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes a 0.600-kg block attached to a fixed horizontal sprk jb 0,(acy1pning whose spring stiffness constj,1b(cnyka0 p ant 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 qu8 ,acq/ lwaa+it69 g65.0 kg jumps from a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 38g,9a+awi l6qqu8at/c .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 in exactly 60 s. Whatw+g.i95aiv de is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if ih-us 0z,t3bq n n/vh7wt is to make exactly one swing per second? (3hnqv/7s -, wtnuz0bhThat is, one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on n;zv* nxd -3blMars, where the accedz* b 3n;n-lvxleration of gravity is about 0.37 that on Earth?    s

  What is the period of a simple pendco/puidw8:h f37i8 ( m2 sphqdulum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is2mqr jasm t)h-56 )niw 0.760 m, the pendulum bob has a mass of 365 grams, and it is rele-62mwrij5a qs m )h)ntased 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 w g-lc ghqdk, 7s6fo3u;bl9p*has a length of 0.9930 m. If the clock loses half a msq 36lgb 7pf 9g,olud;- ckwh*inute per day, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the max /6lcqd ,-5kfmuk.wir imum speed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at a frequency of 2.5 Hz. At it is releaszsyhzf0w:6 mzjcq;8jb+ d7 1h ed from rest starting at an angle 0b1+j 6zscd78yqzhfjmzwh :; 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 evt:mwdw cjib)o,0 gmo*yv39err 1/b 8 aery 3.0 s. He measures the distance between two crests to be 6.5 m. How fast are the waves trave)b :0wo mio mr*9c/jv,a81 3rdwbe ygtling?    m/s

  A sound wave in air has a 9e8g/qg/ ;nq hmpy-umfrequency of 262 Hz and travels with a speed of 343 m/s How far apart are the wave crests (/8m/n hqg9-y;g u qpemcompressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (kiloh 2;q-hvq qjxd,ertz) and travel q;q j2hxd-,vqwith a speed of $ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

  Calculate the speed of longitudinal waves 3obmn :t0 ov0r,p7cnr in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same el)*w qdswi5v+ qastic modulus, but one is twice as dense as the other. In which rod will the speed of longitudinal waves be greater, and by what facdw5*wsq)i q v+tor?   

  A cord of mass 0.65 kg is st.hwyg,m +5l 2 gylq5ukretched between two supports 28 m apart. If the tension in the cord is 150 N, how long will it take a pulsel ,wug yq52ghl.5+kmy to travel from one support to the other?    s

  A ski gondola is connected to the top of a hill by a steso- how: (qdmrt;/xb*j8 w m9ael 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 along the cable. It is observed that it took 16; xmqb swro8j-/:9 tdm*(owha 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 hi ctq+5beggfd69v,ph) s ship just below the surface of the sea. He hears the echo of the wave reflected from the ocean floor directly be)de5g9,v f6 htbg+p cqlow 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at differei uyx03m2, rrjnt speeds, and this difference helps in locating the earthquake “epicenter” (where the d,rxm2 3 0irjyuisturbance took place).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced surface wave can be approximated by a pd 3nrl9lnx y lb1n,r ;r(hz;(sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that 1n(h lrnl br;r,lx( 9zypd 3n;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 eart8b xzs5wtm/u 8*hg) 8qolzxazw t*; k9hquake P wave passing through tougl xt89h5z;k*b/ *wzx)wq8 mtaz8s he Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Eart*za /9 ou:/+g2;y gqemmrf gifh is measured to be e+mf g:2gy9z ;mgruf/*iao/q$ 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 of t1hnbc. vw* :gb:dq 5na.7hvjshe Earth, but one is carrying twice the energy. What is the ratio of the amplitudes of the two.7:gjvwd1.h5 c*h qnb nv:s ab waves?   

  Two waves traveling along jm sdujm 5b- -ij8wl( f4fi4j-a stretched string have the same frequency, but one transports three times the power of the other.i-i854f -jl ds mjb( 4jfw-mju What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is op w+ /ps(e (r)(e+p zvxd7wjcobserved to move up and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the rep+cp+ odz)w(( re/(w spvxj7ipples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each other. (a) Skes7t pbp2 x8crr2l*q7 mtch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight. What has happrp7 b2t m8pl72scr*x qened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundamental frequency, what are the:m,vdbr9pnpub9m3x *e hbs: 9 frequencies of the first four harmonic9mvdb p ::peh,39xbs *9urbnms?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 ta0+a j e(*onsHz when unfingered. At what frequency will it vibrate if it is fingered one-t o0ej+an ast(*hird of the way down 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 frequency w:fjz5l1r)blof 280 Hz. Name at least three other frequencies at which it will resonatelr:fjl5 z w)b1. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the frequency of stac5()uvz3 udpd2vejiit fn0 54nding waves is 475 Hz, how far apu if)ct 0 d3pd5n(5iu2jvvz4eart are two adjacent nodes?   m

  If two successive overtones s7mu: +6b h3k i um(uofrfw1)oof a vibrating string are 280 Hz and 350 Hz, what is the frequency of the fu7uukmh1 (+36 ifof b o)srmu:wndamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.:le uf 6j6t-pf6 g. The distance from the bridge to the support post is L = 62cm and the string is underp fl6 fj:te-6u a tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed tkqeg-c(zc+(vcoy 3 s1+f ry4ao vibrate at 200 Hz, but it is measured to vibrate at 205(1q(+ac4g ry3-+fc e o kyzcvs 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 2ev:dejc 0f*+ .vowzlej 00s8 t00 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tensevo+*cjfet8 0 s.v: 0zjed 0wlion in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal*zpz35g4s*rrvg6num4 mww ac 6o ),vk string is attached to a small-amplitude mechanical 60-Hz vibza r5 spw*n6v4 4r)uvg 6m3wzc,kgm*orator. 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 le- 4yz fdm0v1s8z; midyn/j9)qzsla3o ngth 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 mmyln) o ja/d z;imfz3 y8vs4dz0qs 9-1ay be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at just the right frequenca*kltt7bef;r5 ,xf 8b y, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose ;k7abff*8 e,b5rt tx lthe 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.7-y suy3*gyq(esi4cv::6 y a +j f +uivyrid9x0 km/s strikes a boundary within the Earth between two kinds of mifvvy:+ ac6* rs sy y4u(xu ygii+9y7ejq3:- daterial. 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 t3).fwkggam, m/s to 2.1 m/s If the incidwk fggmat.) ,3ent wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveetl/+jx l54 ctling in warm air when it hits a layer of cold, dense air. If the sound wave hits the cold air interface at an anglett/45 +lxjc el 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 boundary m9et(k4ur z-t)brib 8 between two types of rock at a m()bb- 8zi9re4r kutt38 $^{\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 ilyuf fys 6b4f-t 1+w1pn diameter. According to the user’s manual, the dish has to be pointed in the direction of the s f1yuf1sp yt6l4+-bwfatellite, 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 su-hr ku60;mvmn/nb 0 velocity 750 km/h travels across the Pacific Oce;0rh nm06n/vs mu- ubkan. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car -m:m*dbnxg x/rha-: ubumper has a spring stiffness constant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collides* m:mg- x:/x-hrd uban with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 1w)))x hwm z+on8 m below, which stretches the net 1.1 m. Assume that the net behaves like a simple spring,w)x)o +wmn )hz 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 x*diazj; 2pi+ -a xnz3a freely hanging spring. The mass then falls 33 cm before it stops and begins to rise. What is the frequency of the oscillatiozx2+x*dz n-j ai;p3ian?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/;/no .dvrvzb5 v8zv7ts (Fig. 11–54), compressing the spring 5.0 m. (a) What is the sdzr5vv . tvo7b/zv8n;pring 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 cupgxf3d 0yn5lic 65lh( j of coffee (diameter 8 cm) at just the right pace of about 1 step per hi d3n 05lcl5x(6 jgyfsecond, 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 fr4fd rz6u m9is y5fn-q)om the center of a 33-rpm phonograph record have a wavelength of 1.70 mmffq mz9ui 6r5)4dsn-y. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t whe;/ w ki*a hlfrv/bp/2vre x is in mf//v*lrp2 vbwiha k/ ;eters 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 frequency f. What is its frequency if it a-v.9 sgy (qwdaccelerates at 0.50g (a) upward,v.a qd9- gyws(    f
(b) downward?    f

  A 220-kg wooden raft :-n46imsfspt)y. t scfloats on a lake. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into th s-ytmnp6f)t.:ss4ci e water. When he steps off, the raft vibrates for a while.
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a musical instrument are tuned to play at 392 Hz (G) and 44pqimo)n : i.d2e*0 (gc2yu hv g/e4tkq0 Hz (A).e2q gtdi0hy4 /v*p uik(c:2onq egm).
(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 traveljy0e yj.4n,ehing 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?y,0he . yjn4je) (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 /qd5+bv 1z2fpx6srh 7wmnu5mof each prong moves 1.8 mm to either side 1wp u q5nmdrsh5f+v6x2b7 /mzof 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 oc-e5m )wgxw 4ff frequency 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 dur5e-4wxmfgcw )ing the oscillation?

A string can have a “free” end if that e( m::crcp z phgu)12qtnd is attached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations ofp(1cht zm:r) :2ug cqp such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each one-way swi* xq1ufc. kjf+ng takes 1.+j .x c*1ufqfk000 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 vertic3bu,95t)m- la qtzk.s4 h vci6ss*buial 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 oscillatia *hlisib z6u )5s sm,3tq-buc9 tv.k4ons 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 under a tens4 6e4ziiqh2m uion of 255 N. A pulse is generated at one end, andm2iqi4e4u z6h 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 suspended from aalvyahk e,p01p sa:() ceiling by a spring with spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillations that will allow the penny to just stay on top of thea ksp0(v: paea) 1,hly block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel cb,mnhu 7fc45 )oz y(;hc)sr rcrane 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 ofyrm5u(;onscb h)7)4 ch cfrz, 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 th+ye8vdm g.4qie dimensions of the block). You push it sideways as shown, and then you let go. The jello s8dgmy+ .ie4q vprings 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