Give some examples otx z55/y6oinw2bf.vao ) k9vwf everyday vibrating objects. Which exhibit SHM, at least approximatel6b ty).kwwvvn/ xfi 5o2z59oay?

Is the acceleration of a simple harmonic oscillator ever zsf()nu,deau81pt7x a ero? If so, where?

Explain why the motion of a piston in an automobile engine is approximatelyu (7y 0bmhn9gq 7 a*ye:6kzqqn simple harmon70 km6qgz(any*b yqq:e79 uh nic.

Real springs have mass. Will the true period and frequ3 btk)6v:p sj34 tgklvency be larger or smaller than given by the 6 4:lstvb33jpkg vt)kequations for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maipz0nfxh t0s/7p4q 1r ximum speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attachr w-gv( sb3a*oed to the hook of a vertical spring scale, and then is released. Describe the scale readi(roa wb s3*g-vng as a function of time.

If a pendulum clock is accurate at sea level, wqkclt x*:fh 2d xltugk1 6,7n4ill it gain or lose time when taken to hig cfklxdgtk*lh7 n q,4 t6ux12:h altitude? Why?

A tire swing hanging from a branch reaches nearly to 7sdn:ho j)cj- the ground (Fig. 11–48). How could you estimatec:h d)nj -jo7s the height of the branch using only a stopwatch?

Why can you make water slosh back and fi4mpx 3rp4o4/g/s jio orth in a pan only if you shake the pan at a certai ip g/x3prioo/ jsm444n frequency?

Give several everyday examdq v(4,qzl 0/sfrzo,b ples of resonance.

Is a rattle in a car ever a resonance phenomenon? Exn f )qw+q +00t/d+c q-frbfncq/jdx8kplain.

Is the frequency of a simple periodic wave equal to the frequency of its sourcuxwvb f);,mj+e? Why o)mbu+ x wfjv;,r why not?

Explain the difference between the speed of a transvers9m) 1js y,*dbg7ii:urplz: cke wave traveling down a cord and the speed of a tiny piec*:cusm7:p19iiykjgzl,d) br e of the cord.

Why do the strings used for the lowest-frequency notes on a piano nyvxuy u,xjc44h+b :6 yormally have wire wrappbx4:y6jx+u ch y vu,y4ed around them?

What kind of waves do you think will travel down a horizontal metal rod : w.bj;02;zds sxvkd mif you strike its end (a) vertically from above and (0.wvd mk2:j ;s;db zsxb) horizontally parallel to its length?

Since the density of air decreases with an increase in temperature, but idr) z3a pr76,roqbt9nk-1y r the bulk modulus B is nearly indepe,7idqarznrpt)93o- 1ryr k 6bndent of temperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decq ,u609 cj q;:qo rh(v0moxnaarease in amplitude as they travel away from the s0 ovo:qq69 na(x qmh, cju0r;aource.

Two linear waves have the same ampliaa 1ic70yc w+jtude and speed, and otherwise are identical, except one has half the wavelength of the other. Which transmits more energwy ic 0ac1ja+7y? By what factor?

When a sinusoidal wavemtf d1qc7h j(tn r.*hgpu+ btd9i,)5 h crosses the boundary between two sections of cord as in Fig. 11–33, the frequency does not changu1pt*5c b9 hnih)gt 7m td, (rjqh+.dfe (although the wavelength and velocity do change). Explain why.

If a string is vibratingtokti4 (s e9-*lge5wkp(1pg4 zmkmy ( in three segments, are there any places you could touch it with a knife blade witho(4pi t 5w4*y1(s9e- z(pmkeggk omtklut disturbing the motion?

When a standing wave exists on a string, the vibrations of incident and rdg26lrpbca5 -a eid0 c q;-d;hm cmx2)eflected waves cancel at the qedm5d gm6 c02xhidc-a;-bc r2 lp;a) nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy+.,oe* q6 dtupq(jfi hf/os:xjtsl) + alu -e9 was being transmitted from one place to another, how might we determine whether the energy was being carried by particles (material(e x) q9:jqj l e-shuau fidp*+tt+slo/6f, .o bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.ia t qc*ik e- wnp*9-1dj4jyw;18 m, what is the total distance it travels in one day-t49i c-*j1 * nipqkjw e;wperiod?    m

  An elastic cord is 65 cm long when a weight of 75 N dw*/o c; iwkyt 9kwa5)hangs from it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” constant k of this elat9aw;) kyco* wiw/5dk stic cord?    N/m

  The springs of a 1500-k vr5(j zdm xx*enqs g uc0z*3-y:wj35og car compress 5.0 mm when its 68-kg driver gets into the driver’s seat. If the car goes os3ur*e* (5xj:yzn jd3wgovmc 05qx-zver a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs from it.uw 8fn) lv/zu. (a) What is the spring stiffness con/wnlz uu).f v8stant $\approx$    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 of 0.60 k9 x(xmou- wkg5g is hung fromk-5( x uowx9gm it. What is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of theg;yuvbm i0o6uv0 (zpy 9f35d;y3gfv / qfy(fe mass in Fig. 11–2 at times t =(zvu3 f5yvp3g;9i /qe uy(y bfyf0f0gmd; 6ov 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 5dt nl k .:b9nludv/e8in a spider’s web. The web vibrates predominately with a frequency of 4.0 Hz. :nb 8.v9/d delkunt5 l
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a spring vibrates with a frequency of 0.88 Hz. When agao6qcka lhb0vbi*i)b9, 1l ytd. 3c:n additional 680-g mass is added to m, t9c3g1hco0ilia l:6dt.)b kv*qabb y, he frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of u6oiy*f yn3n0z,i jzfy9v( z4vb3c7na spring vibrates 3.0 times per second with an amplitude of 0.13 m. Deteiin73u4b ,y9fvc0fn jz vy63 *z yon(zrmine
(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 ha8d i xohg xmxs 2/-,iip1sf.b pl681lwht)y:olf the maximum valsdiioh.s1) i81mt yl hx,lp f-x6x/ bo2:pg8 wue?$\approx$    A

A mass attached to the end ofz)qj +qesh-5d br*xz6 a spring is stretched a distance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretches a vertical spring 0.315 m. If the spring is stretcujnp nlf.u ,t4t3 0 -exty(v4yhed an additional 0.130 m , pfen-t 3jy (ntyuvt40u.4xland released, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with spring stiffnessl nn,gr6-(t+ojzy5 lk constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 6tl5n-z korl(n,gj +ym 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 9/vwy9kcz ep1ofwb 90 the spring of a toy popgun 0.200 m to “load0kp19o w9y9 ewv fz/bc” a 0.180-kg ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is b,1z5o p2d jixattached 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 maximum acceleration of ,p 52xiojz1db 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 equatie-z5+ uie jag ;rn il8w8*7dowon x = 0.45cos6.4t where x is in meters and t is in secondrd;ieae5 w-i+*ngw z8jo7u8l s. 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 jx o ,6jzkfjr:9-wdr+equilibrium is the energy of a SHO half KE and half PE? ±+ -:6zkdf xr,jj9owrj    A

  If one vibration has 7.0 times the energy of a secorj d*(sk 0pv-g tl+qk)nd, but their frequencies and masses are the samkd0t rj s) kq(-*lp+gve, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vekqvti.h0asv4po ;/ y1rtically hanging light spring once every 0.6qivt4v. 0s hakpo;1 /y5 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 supph,fxhr q:s(eqj4 .i3 + 7yrb gwr11qvzorted by two identical parallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What will be the frequency of vieq1vh q:7f.xqi ,+wr4gr r hbs1(jz3ybration?

  A 300-g mass vibrates accordi;* w/ wyalf8m7tp6gtxng to the equation x = 0.38sin6.5t where x is in me/wt 8*a 6tpxyf;mlw7gters and t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows two examples of SHM, labeled A and B. For each, l)cw;6ym9 ccdwhat 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 2 pgut ;d5+0fw 3nyvsi)oc8u oend of a horizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.96m/s Deterfop32uo;8u0)iy+c dsg w v5nt mine
(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 sqlnq+x/5j e v*pring stiffness constant 305 N/m vibrates with an amplitude of 28.0 cm when qq*+/5vx ejnl 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) with positive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to *(fsvv+i3r 6 seyg9xo two springs, with spring stiffness constants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes a 0.600-kg block attacoc.zmlpb,fm *s g 8rbg790u,ro8o6rphed to a fixed horizontal spring whose spring stiffness constant is gg,o po 0rczl ,rp78 ro9ubfmms8.*b6 $ 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 with6sz;rfwia7zh,z ,1t p mass 65.0 kg jumps from a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes zir7 t61 f,p;za zhws,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. What is p 31k4bqao o9o37glld bjz-q2its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly t8a 2a3 .feuo6m 14vhpyx wso-one swing per second? (That is, one complete vibration takes exactly 2.0 s.) av 2fe1pt.a-38x m46 w oohysu   m

  A pendulum has a period of 0.80 s on Earth. What iss teh8yy9sv k7 t c+f(0znkt38vd9u;c its period on Mars, where the acy;k7 tc 8ft9y9ct(s08hnzv 3+dvuskeceleration of gravity is about 0.37 that on Earth?    s

  What is the period of a simple p/(pgo4ja i eoz (;jlbtr )6q;hendulum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 m, the pendulum b txyh ;oe.b1ia* e7w3kob has a mass of 365 grams, and it is released at an angle oo*.t1i3 k7ebhaye; xwf 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 pet(m i )dfp)qs0ictl-+jdj4k *ndulum has a length of 0.9930 m. If the clock loses half a minute per dafjdj iqt4di c)0lp-k*tsm) + (y, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximum spee+gu2(nnk tz:dd $v_{max}$ 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 releasedip p04ntzxxi14 ct4 *g from rest starti nxipx 41c tp0*4gti4zng at an angle of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests pass the bow of his anchored boat every 3.0wz/oi0zkws 1p kd 378h.f mquj2ge6z. s. He measures the distance between two cre7 /3uj w0f 6.dm.zkzhqse8ki 2oz1wg psts to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz ansz x jo1-v)hk,0 otaf,d travels with a speed of 343 m/s How far aparxso v tf0aj)kh,,-o 1zt are the wave crests (compressions)?    m

  (a) AM radio signals have frequencie/0g zoc8 qjbhn1p-q9h t:s,rd s between 550 kHz and 1600 kHz (kilohertz) and travel with a jg doh 9-qcbtsq0h/nzp,r8: 1speed 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 londrqcioe ln: ,sknr5-+4(of +sgitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one is z0vbl3-*o -hxmx6vdc twice as dense as the other. In which rod will the speed of longitudinal waves be greater, and by what factor?o6dhzvcxxv- 30b*l -m   

  A cord of mass 0.65 kg is stretched between two suppork. xt ptxk)1t(ts 28 m apart. If the tension in the cord is 150 N, how long will it take a pulse to travel from one support.x1 (xtkk )tpt to the other?    s

  A ski gondola is connected to the top of a hill by a,x1( /lyx,aks4voykiv ;1og h 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 v41 yoxo/v1y ax(gk;h ikl,s,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 surf 3v3p.+ul4 / dbhuqenk(j.g yface of the sea. He hears the echog/eu.(ylnf3k3 j4. bu v+ hdpq of the wave reflected from the ocean floor directly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at dy(-wh;7r-osns ,bofr ifferent speeds, and this difference helps in locating the earthquake “epicenter” (where the disturbance took place).o s7( -foyr;nswhbr,-
(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 approximat/:3 mngvn* .k)fobqbevo rh 56ed by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Snqkvm:.r5oe )bnb fgh/* o6 v3et the acceleration a>g]    m

  What is the ratio of (a) the iagp )n) /5hs lffu3+xantensities, and (b) the amplitudes, of an earthquake P wave passing through the Earth and detected at two points 10 km and 20 km from th3s)x u af)f+ /pl5nahge source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth isv)0l*bjvcffd j 03 (yn measured to be *3f cdb(ljfyjv0n )0v$ 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 icy5.5/yyzsrxya8b (s gr/knu uu4;- same frequency travel through the same portion of the Earth, but one is carrying twice the energy. What is (/bc u4x5a gussy;iu n8kry-ry/z.5 ythe ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same frequency, but onc)s vj 6 +q;9k,xwnqk1ou1vfk e transports three times the power of the other. What is the ratio of the vvo;6ck,w1+ qk)s unf9qj1xkamplitudes of the two waves?   

  A bug on the surface of a pond is observed to move up and doml 6u q+a+viv-,xbb ;ywn a total vertical distance of 6.0 cm, from i lbm-bq;+v6,+xva yuthe lowest to the highest point, as a wave 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 mo:o03h)dt : slmea/jvsving toward each other. (a) Sketch the shape of the string at the moment they directly ov3d hme:vjs0l/o ):s aterlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 4m1rr z a9f4,*p uedcf540 Hz as its fundamental frequency, what are the frequene mr14a ,u fz5pf9r*cdcies of the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 23)9 vgmovrakp9 zf9 x994 Hz when unfingered. At what frequency will it vibrate if it is fingered one-third of the way down from the end? (Thamxko 9p3rf9g9v )v z9at is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four la-1i,m*jvhha5m9j-mc nx z :m oops at a frequency of 280 Hz. Name at least three other frequencies at wh, 5amh*xjm mjc9i-- h:azvm1 nich it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the frequency of standing wts h v 9vpal9w3gub v4)1fi3a9aves is 475 Hz, how far apart are two adjacent nous1b9gtva 93plh) 9 vi v34fawdes?   m

  If two successive overtones of a vibrating string are o;esobd,dm1b y9k mr/y6*yh+ 280 Hz and 350 Hz, what is the freque /1bb,koo;h*rmdd9m6y+ys e yncy of the fundamental?    Hz

  A guitar string is 90 cm lop j.jfgdq vw*m;**vd:ng and has a mass of 3.6 g. The distance from the bridge to the support post is L = 62cm and the string is under a tension of 5;vd * gdmp*qvj.w *fj:20 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string iajp5.lle4 3di.iwmk g i7 pb65s supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the f4 ei p.li.miw75j p5al3gkb6drequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibratbx;dou zqon*8x 52 0dgjs 9(gue at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should thedod2bx;juuz(nq* 508xs 9ggo tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-amplitudc2ttc;znb4e*0x9j j jz ce.i6e mechanical 60-Hz vibratorjb*.tz e 60i jj zn4;txecc9c2. 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 the strlks 6 f brltwchd0 j-z-39:ez.ing may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patt-0dcf r wt .h:-bselzk 36jzl9erns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at -ctfgpkh7a2/ just the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm htfcka/ 2p-g7-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 th4*. pivg oqmo 4sa((2 -dhdlvoe Earth between two kinds of material. If it approa d 4-o.d((v4*ogqiv2sl mo aphches 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 veloc4(vsxz .:yq+fflm+f aity changes from 2.8 m/s to 2.1 m/s If the incident wave crests mfffyzq:vmx a (. +sl+4ake 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 la0) mq0o,0woa(xo rc/iqn1.a cl pvt;g yer of cold, dense air. If the sound wave hits the cold air interface at an ang/(paio;1goo mrqvl0 . w)x,ta0c0cnq le 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 +1d.963rasc.dae isvk6;dvg4rvyhbw 4 6r f nwave strikes a boundary between two types of rock at a h i 6s 4v9 gwd4; vk bdsferd6aa6rr1+nv.c.3y38 $^{\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 user’s mazm 3,8e/vdo ocm1xr i*nual, the dish haxme/*v83i oz 1r,odmcs to be pointed 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 250 km and velocity 750jl qrq+ )586h7wwnpuc km/h travels across the Pacific Ocean. As it approaches Hawaii, j6qn+h)5lcrw8 7wuq p people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness constant of 550 k e zjhnz9 u3wa9rl1,x;N/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: 3l;9 nxzjh w,eazr 1u9Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire nen-z.d2qv6kp e t 18 m below, which stretches the net 1.1 m. Assume that the net beha .q6edp-zn2v kves 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 8*- ow6hx4ihf r/(g7cl5iy,ok gnwcg freely hanging spring. The mass then falls 33 cm before it stops a*c,7 4 og (ghxf ir/yln-oih5ww86k gcnd begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a u3 l4g4+i7kw8boqrhtix3 w4qhuge spring at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is3iquxohw4w4b7ri8 gqk 4t l+3 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 c r c 4*w553 njz6s-gqvdx3wk4xrhr, brup of coffee (diameter 8 cm) at just the right pace of about 1 step per second, the coffee sloshe-g4 rr4 b 3v5xwqwj5,cz3 6dhrxsnk *rs 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 :tsn/r-m. m dbfrom the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequency of the soundb/nsm. : mrdt- emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t where x is im ;6hl8,m--i k+u9g qal*hnr vd4 iumjn meters and t in seconds. Determine lj;8iurd* h9mmnuai lhg 4 6-,qk+m-v
(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. y.3(j c(o bqicWhat is its frequency if it accelerates at 0.50go q( 3cjb(ciy. (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on the raft, it sizr2,em 8j* kjinks 4.0 cm deeper into the water. Whenje2i,j m*8k rz 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 instrument7 ev f2*xplzix dx38a+b;c: pmsfh :a0 are tuned to play at 392 Hz (G) and 440 Hz (A). :emfi0 c+sa ab8 v;7xxx*p3 h l2f:dzp
(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 travkb)kqsj;8,mx4 2x 0iyr -iz pueling 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 liyujkrqi,b p-02 x 4si;8)kzxm ghter 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 a7ksa ;hb8fv5)xq23wxs e z0 cst a frequency of 264 Hz, and the tip of each prong moves 1.8 mm to either side of center. Calculate c ks sxhv8xw sqeb)7a52 f0z3;
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillatfa660uf f f1zjes with simple harmonic motion of 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 boarda6zfj0f 1 f6fu during the oscillation?

A string can have a “fregwofl vt9wd,x .82(rbe” end if that 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 such a string wi ,.8v(dtfxb 2lwworg9th one end fixed and the other free.

  A “seconds” pendulum hasys 3080x5e,r0du hx( cwjzmrk a period of exactly 2.000 s — each one-way swing takes 1.000 h8d5kws c 03(,mxrje0 xuz0ry 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 io8.a6c-e jxuc uy * cbd,spt(d5*du. on the vertical direction or can swing as a pendulum of small amplitudec6xd -cujtood, c ud b(se py*.a*u5.8, but not both at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontal swings, and by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

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

  A 10.0-m-long wire of mass 123 g is stq:i r81qf;gj, qtv -hase6xo, retched under a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at the opposite end. Where will the two pulses first mee: qjx-,hr1qoiqav; g f t8,se6t?    m

A block of mass M is suspended from a ur 9nb0c38j /c8lnai kceiling 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 oscillati/ancn 9r bjku0 388lcions that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyai8usr/hcw6u* sc .fjiy ,6c+t rd. The steel crane cable is 22 m long and has a diames c6+t 8/*iusfr iwj6chcu,.y ter 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 to Table 9–1.]    s

  A block of jello resyrte (8, mser*ts on a plate as shown in Fig. 11–58 (which also gives the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this vibrste *emy (,r8ration, given that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz