Give some examples of everyday ,ymcgc1cp i4 en60nb :vibrating objects. Which exhibit SHM, at least appc,c1pn i6m0g:ec y4 bnroximately?

Is the acceleration o2 .yn9y1j,wawte ye p:f a simple harmonic oscillator ever zero? If so, where?

Explain why the motion of a piston in an automobile engine isdff7-v xssmy;maf4/4 approximately simplsaf4 d/ff ymvm7x;s-4 e harmonic.

Real springs have mass;fd:k4adtehk j, *fq8. Will the true period and frequency be larger or smaller than given by the equations for a mass oscillating on the end of ank :, f;d4fedtkjqa 8*h idealized massless spring? Explain.

How could you double the maxim hrc9.m4er;lw ln(x7lum speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical sprin /1),rmxw er.r;scvy ug scale, and then is released. De.v wre1mxsr uryc;/, )scribe the scale reading as a function of time.

If a pendulum clock is accurate at sea level, will it gain or lose timefzadcbp0 x7uvp:5p2m :qrl *p /k+;pv when taken to high pv *:lrx ppzd+5a cb2;7vpf0mpk u/:qaltitude? Why?

A tire swing hanging from a branch reaches nearly to ,yj77*7ku)c vu; pnrs/cz5(udrtsbcthe ground (Fig. 11–48). How cokcj/su(t5vc *srcn)b ,7dy7puzr;u 7 uld you estimate the height of the branch using only a stopwatch?

Why can you make water slosh back and forth in a pan only ifk8-j4 g m9kr7cpj+k auta/s1 w you shake the pan at a certain frequency?j4k k+j/8tk- r7pgw1a casm9 u

Give several everyday examples of resonance-b1mzd (r l4hh.

Is a rattle in a car ever a resonance phe.aa6 j0u5 fyefs1 t7chnomenon? Explain.

Is the frequency of a simv ,v94;g.ar if mywb2qple periodic wave equal to the frequency of its source? Why2byqf vri4mwa,.vg;9 or why not?

Explain the difference betweed; 9zt 4;utagpd,h a7qn the speed of a transverse wave traveling down a cord and the speed of a tiny ;agudt 7zt,dqa9;4ph piece of the cord.

Why do the strings used for vg1 yq/6wc pqld*zf32 the lowest-frequency notes on a piano normally have wire wrapped around themyg lv2z3pq*dqc 1/f6w?

What kind of waves do yo w glh81)2kohau think will travel down a horizontal metal rod if you strike its end (a) vertically from above and (b) horizontally paralloh8 whag)1k l2el to its length?

Since the density of airi,e/j: .5 tjzcmhga8 a decreases with an increase in temperature, but the bulk modulus B is nearly independent of tem :jg, ea5jz mt/ah.c8iperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves dr;*baj jhu/sg zr*k+: ecrease in amplitude as they travel azurshr kj/b *g;:ja+*way from the source.

Two linear waves have the same amplitude and speed, and otherwise are identicali,d:;x2jzj9p7i h xr , n6sydtuve*a9, except one has half the wavelength of th:*9vxyi t7ernx6j,disd hj;9 z,p ua2e other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary lds4w,c( wr o5between two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocity do chango4wl,5cds rw(e). Explain why.

If a string is vibrating in three segments, are th(z k jj7ijqd,uh; 2/rhh:sz y:ere any places you could touch it wjsu2r(ih ;dq:hzyk,/:h j z7j ith a knife blade without disturbing the motion?

When a standing wave exists opt+ ;7 pyrbjl;n a string, the vibrations of incident and reflected waves cancel at the nodes. Does this mean that ybrp;l;+jpt7energy was destroyed? Explain.

If we knew that energy was being transmitted f3c8: hpjrg mrmnb,s7(rom one place to another, how might we determine whether the energy was being carried by particles (material bodies) or by c 7:8mj r(3nh,bprsgm waves?

  If a particle undergoes SHM with ampli p1r4ym1u ywx+hp(1matude 0.18 m, what is the total distance it travels in one period?a1w( r+my x14pump1 hy    m

  An elastic cord is 65 cm long when ps1dty0n6jjr8s2mkn y4+cjg0yr w-2 ab;w2 za 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”+j8nbnrym4jcypkdr 20;tw0a1-j6y gs zs2 2w constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm wm6gd8zfz1fne 1y. w* uhen its 68-kg driver gets into the driver’s seat. If the car goes over a bump81m fgu. *d6ynz1fz we, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs .z uy+bpw82u su0o5a afrom it. (a) What is the spring stiffness constant 2 ysa 5uw.zba0ou+ 8pu$\approx$    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 H1*zm bvso x;hf1tb/ sbylu41 4z when a mass of 0.60 kg is hung from it. What is its frequency if only 0.38 kg hangs from it? lm fzsbs b xuo/ hvy;141t*1b4   Hz

Construct a Table indicatw c)0:zg+a-rxwo, xjming the position x of the mass in Fig. 11–2 at times t = 0,t0) ,+cxm rwa-gxj wz:o = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 0.21 - jxw)ct/pkn5 g is caught in a spider’s web. The web vibrates predominately with a frequencx-w/t )j c1npky 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.2dt 23ionui i a spring 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 id.2o2i iiutn3 s the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per second with an amp7hlug5cv1 p49zvg 6/ lt;qvg zlitude zglt;96chvvg 4/zp v 1q 57ulgof 0.13 m. 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 displacementkyc/ 8evzde/2g vac -6v0ar:p from equilibrium is the speed of a SHO half the maximum valued g6 rz0v/p:2c/c yeakev v8-a?$\approx$    A

A mass attached to the end of a spring is stretnx: et m ) pfyifzw,*dj16h2.vched 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 stretc wbkhtzs1 f44cn0l d:g8xe6 t1hes a vertical spring 0.315 m. If the spring is stretchesc4b6tfkw0 1tn:dzh814gx eld an additional 0.130 m and released, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with spring2boi hzwcj3zv p7,zwrj( y 3fo*3w,4s stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, iti,33cswhw, y f(r*v23z zj zo4jwbpo7 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 0.200 m to “l v0 armz2bqu: wz0;fgj43zt-s1 t3 bozoad” a 0.180-kg ball. With what speed will the balt33zr t0;quf sao :gw-zzjv10 z4m2bbl leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is atta/ :k7kl)kvqhtn l- mr-ched 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 b/lhvk -nm-qk7r:t k )ly 0.12 m. If the mass is released from rest with the spring compressed, the mass experiences a maximum acceleration of 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates according to the equation x = 0.45cos6.4t whh xatz*b7y /n1ere x is in metersby n/ 1h7zxa*t 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 e5k+v e 95wyqotnergy of a SHO half KE and half PE? 59ot5+ek qvwy±    A

  If one vibration has 7.0 times the energy of a second, ;pph2 pw ;qq8*emryb0but their frequencies and masses are the same, what is the ratio 2;q8;w my* phrpqpb 0eof their amplitudes?   

  A 2.00-kg pumpkin oscillates f4prr)kze6a 5a p-da a3rom a vertically hanging light spring once every 0.65 5)4r - 6da3k apzpearas.
(a) Write down the equation giving the pumpkin’s position y (+ upward) as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. y = (   m)cos($\frac{2\pi t}{0.65s}$)
(b) How long will it take to get to the equilibrium position for the first time?    s
(c) What will be the pumpkin’s maximum speed?    m/s
(d) What will be its maximum acceleration, and where will that first be attained?   $m/s^2 $

A block of mass m is supported by two identical parallel vertical springs8d.esj ri a/v53fw,fh, each with spring stiffness constant kf. er85ash i/f 3j,wvd (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t where x is in me8jv, -l.wzkvrynn5l 0ters and t is invnn8,z-v l0krl.yw5j 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, what is 8mrg)rf-6*iv9z*fr jn b3uig
(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 resnuwd8)ex9y bh:w c7 +q53f nykt on the end of a horizontal spring (k = 124 N/m) is struck by a hammer, which gives the mas: f y +wnwq nh)d7839yubcke5xs 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 wit c gc4er/y3lxi q7e5;ih spring stiffness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hanryl e7 xc4ci3 q/g;i5egs from it. The mass passes through the equilibrium point (x=0) with positive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two springs, with5jfp-oji sy 0y4nq0b / 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 strikecmzz h5yy v04uujc:wuxa;t,yh3,. -p s a 0.600-kg block attached to a fixed horizontal spring whose sprzp xzy-,uy0ua;:m34cvhw.c5 u yj, thing 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 mggd klt vp;60.ass 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 to rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the unstretche0. dlv kg;tpg6d 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;e1kx+v(7 kt*swok (gig7 8zkqgxlh1+g 5kpj 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if i8t6x1:*wno j y:: le zga6bjxrt is to make exactly one swing per second? (That is, one cx:lo8 b6a1jt: 6rzjwe *:gnyxomplete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s3 l;wtxnc0y8n on Earth. What is its period on Mars, where the accelty8 3cn wxn;l0eration of gravity is about 0.37 that on Earth?    s

  What is the period of a simple pisl0hpjs n ;-cqct429 endulum 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 bob has h gj;.q gx)ww1+n8jc ma mass of 365 grams, and it w)g.; 8nmgc+ hq wx1jjis released at an angle of 12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’s pendulum has a length of 0.9930 m. ud3rtzkvmm t 6ls23z g(v+r,4If the clock loses half a minute per day, how should you adjust the lengt m4vt+d(3rguszv 3tk2zm,r6l h of the pendulum? shortened by    mm.

Derive a formula for thevpni(. 9.:cmu -ft cfb *adf1p 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 it is re :z8jttk8o84zar- xa lleased from rest starting at anr84z kj8:al ttza-8xo 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 h .0ze0toou* wtv/c gr*is anchored boat every 3.0 s. He measures the distance between two crests to be 6.5 m. How fast are the waves/c*gu*e w0vt. r t0ozo traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travelszj7xo (no. 7yl with a speed of 343 m/s How far apart are the wave cresoxo(. znj7 7ylts (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (kiu pu5(67jwgpeeqn5 rj( r5h89cr txy 4lohertz) andp (5 9 y wqhrxj4 8rg5(ecturj56upe7n travel with a speed of $ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

  Calculate the speed of -eux)su27-qw e0iur;uovh 9gk- 6isw longitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modd,i/o-89 wbzfj 9 uisrn 4puo4ulus, but one is twice as dense as the other. In which rod will the speed of longitudinal waves be greater, and by what fi/n9po wb84z 4,rduufo-9i sjactor?   

  A cord of mass 0.65 kg is stretched between tl/- s*vt c/hvlwo supports 28 m apart. If the tension in the cv/s*htl l- c/vord is 150 N, how long will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to the top of a hill by a steel czq)tsojxs 6w1u - 4nlh sw.e9 (x/8ewzable of length 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, w tez8(9o)-1.u wslz/hjxx6 w4esqns 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 t, l t rvbsf6;r:zu7by/xm z0d6he surface of the sea. He hears the echo of the wave reflected yldb;7xbr,6s /z: rfzv mt0u6from 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 dify03; .-ukdn,k;ua)shb d wrh09 yxhwpferent speeds, and this difference helps in locating the earthquake “ekw kn)yrh-.h3 ,;0 0pdya bxsd;wuh9 upicenter” (where the disturbance took place).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced smx :e0xtqv aco-m4kgl:zq,m-g g74k /urface wave can be approximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the acceleration tgk,/gc 7aq4x xokml:m4 em:qv-- g0z a>g]    m

  What is the ratio of +qs/y3pukj* r(a) the intensities, and (b) the amplitudes, of an earthquake P wave passing through the Earth and detected at two po 3uys*jq/ k+rpints 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquak cfkintve-sq/hcun)x:5 c- /t4:; jede wave passing through the Earth is measured to be /:vf- j4/-:hdecti nu cce) q5nxkts;$ 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 t gsq.xxfn7,k myb;) e0ravel through the same portion of the Earth, but oqsbn0f 7me)k,;xg. xyne is carrying twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same frequency, but o 81y/ze7h5,swrlt rptne transports three times the power of the other. What is the ratir y/ze,1rlp t8 wh7ts5o of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed hu hm55z(xt w6to move up and down a total vertical distance of 6.0 c 5xu5zt6mwhh (m, from the 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. 11–5 6k9- h2qaiibr+klz1 s2 are moving toward each other. (a) Sketch 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 eai azhqs li1 2r6k-+kb9ch other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundame 57l+ )/mr)+esy74knb0i2 xe rwmzi/dipm axlntal frequency, what are the frequencim+w7 7i+/leyxxr)a2 ziks0l4m)/ r pbidne 5mes of the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingdiz ti ,v fu)691dxf h*dxj3.hered. At what frequency will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds ofd91 v6f h*fh)d ixjx.diut,3 z the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a freqfrvnjtkipib3* l-vl r0w;d0 ,q k3knh3 .7 y2kuency of 280 Hz. Name at least threfw0vpvri ;kk lyrki.0t ,*n3b2h7 lnk- d3qj3e other frequencies at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the frequency of standinz-v a aso v 6:d,4nx122ztgelzg waves is 475 Hz, how far apart arev an-dso:l z1za 42ve,gz2xt6 two adjacent nodes?   m

  If two successive overtones w az x5)1f :pvka3yiiq,ux(j,b:b(f oof a vibrating string are 280 Hz and 350 Hz, what is the frequency of the f: :fab op((bfj,q)i1kiw a3yxz5x, vuundamental?    Hz

  A guitar string is 90 cm long and has a mass /rkv:9;x:6( r flbfksmtxgx ;ogo .2v of 3.6 g. The distance from the bridge :rxg; s:f(vb9 /.xk rf2votkog;ml 6 xto the support post is L = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hw ora/go82j j ox1,ho:z, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?g :o/o ,aj8or2o1xhwjSo the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate a eex 0epd+.n vzi(/lzc33ie1mt 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tensio. ei3+zilzecp30mv /e de xn1(n in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-amplitude 9gs -g w878)mdbloayk mechanical 60-Hz vibrator. The string’s mass per8l k)bgys gmw7d-a9o8 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 lengthe6bhrum ld 0o7g, j4p7 of the string may be adjusted by moving the pulley. If the hanging mab7 hr6l4oej 0 ,upg7dmss m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the wat7:d uycfdx, s*er back and forth in a tub at just the right frequency, the water alternately rises and falls at each end, remaining relativ7 ,yd :dfc*usxely 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 r v z4ah-0vi;sboundary within the Earth betweenvsi 4-rzh;a v0 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 “shaunt8rax l9d;4ij /4nelf” where the velocity changes from 2.8 m/s to 2.1 m/s Ifidln;j494na/r8 a xut the incident wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air whe2z0( b5vhqti on it hits a layer of cold, dense air. If the sound wave hits the cold air interfacbq2 0hvi5( ztoe 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 boundary betwee 954q+z s mkcy+s0uu)om7gwnpn two types of rock at a 38)q5yz pkm4ou+gm 79 cus0wn+s $^{\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 t hc,4/ adq(nw6dmd /wb8yz tw-he user’s manual, the dish has to be pointed in the direction d qtwb4/n(ddma6z8-yw h/ c,wof 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 25ku .qr7n:6mju31 5 ac:ync fvq0 km and velocity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died3:r7mu un.na fc jkqv15y: c6q during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumpe ux +xjb(vbsc9a g),238jqegj r has a spring stiffness constant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approximately 8ge+q v( a)jbcgx9jsx j, b23u5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m beloc/ktjqdz p0wp ejby0; :57u)ow, which stretches the py5kcj :w)j0u07beo dpq;/z tnet 1.1 m. Assume that the net behaves like a simple spring, and
(a) calculate how much it would stretch if the same person were lying in it.    m
(b) How much would it stretch if the person jumped from 35 m?    m

  A mass m is gently placed on the end of a freely hanging spring. The c vbfxm 0rj vinl;1ga22,.n,pmass then falls 33 cm before it stops and beg1vfv2b , clxngpijn,m.02ar; ins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring q h*-g3r,uyp n .wy:tvat a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What isqyn-tv r. pg,:uyw3h* 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 n-mrm9egj+gci/ur/. ylsts / v c p4yf5 t/,6ecoffee (diameter 8 cm) at just the right pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the speed o c/.y/vr rm,5 cel9etsy6s4-igmn/tg/jp +f u f waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the center of a 33-rpm phonogre9tknc)v )hjpq/ 4owlx9e;ymj 5z,:vaph record have a wavelength of 1.70 mm. What will be the frequency of the sou;jlv9yqome k)t )pzcjwe,x:94n /5hvnd emitted?    Hz

  A 2.00-kg mass vibrates according to the equ;8o(lp.u9bixb, g.g+ zoer i, a p/tzbation x=0.650cos7.40t where x is in meters a;,.izu9pbb(ge b tz/lo ,xr8go p.+aind 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 f0q4n y rytkit*gaa4 +2spm7-trequency if it accelerates at 0.50g (a) 0n-7rymapt 4iakgt+ qy*24st upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stny 6rwic- 8mp.wn5 ic4zuv1,aands on the raft, it sinks 4.0 cm deepumcww 4cz n8i,y1v- 5rp .ina6er into the water. When he steps off, the raft vibrates for a while.
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a musical instrt+g ofd9gq70z ument are tuned to play at 392 Hz (G) and 440 Hz (At9g0dgqzf+ o 7).
(a) What are the frequencies of the first two overtones for each string? G : $f_2$=    Hz $f_3$=    Hz A : $f_2$=    Hz $f_3$=    Hz
(b) If the two strings have the same length and are under the same tension, what is the ratio of their masses ($m_{\mathrm{G}}/m_{\mathrm{A}}$)   
(c) If the strings instead have the same mass per unit length and are under the same tension, what is the ratio of their lengths($L_{\mathrm{G}}/L_{\mathrm{A}}$)   
(d) If their masses and lengths are the same, what must be the ratio of the tensions in the two strings?   

Consider a sine wave traveling down the stg1u;) pacw-3ae c7u hkretched 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) -ka c gw1pe)73u;ahucfor the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and ;wqrmwnoh3+j2b/cg.m s)m l;rw 0 h,qthe tip of each prong moves 1.8 mm to either 3h +wn s.wo;mqhqlcgm/m wrb,);02jr side of center. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simple harmonic motion of frequency 4sfm*e )2 tnfyu/noz31.5 cycles per second. What is the maximum amplitude with whichu4s n 2ffzm3ny/teo) * the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that end is attached to a ring that3zekrm3u ox6 ;2+ 2 awxygynj- can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with one end fixed zu2ng ; 6krmj23+e3y-y woxaxand the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each obo8d c;ul:ldzi;g;.y;bzf;z tf+-tq 62fsfx ne-way swing takes 1.000 s.; gdfs;fl 6x;;zqtl8 :zbdftio cz;. -2buyf+
(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 o .lto-*qbckw:scillate in the vertical direction or can swing as a pendulum of smal.b*wtl - kcq:ol amplitude, 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 stretched under a tension of 25yh-32 jn/l tjg k-o-zl,qmg/o 5 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated2m g/ h-ogo-k,tlq-z/jy lj3n at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by nv.6sw 5 dtur 5lh,x0 6y8ypzmb 46krda spring with spring stiffness constant k. A penny of mass m is placed on top6k d0sv rhb.6rmyx6yz 4, d5 tnp5uwl8 of the block. What is the maximum amplitude of oscillations that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel cra*;,bwuy:rc- pnqm3m ane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the m: wr,pun maqcb*y ;-3cable. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (wh;euoq ri-;+z hich 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 -i; ;+ uhrzqeoto 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