Give some examples of everyday vibrating objects. rsp op4i2oasc29 .jq,Which exhibit SHM, at least approa2c. p24ij, s9orsqopximately?

Is the acceleration of a simple harmonic oscillat)-4foeolkaq1lll)m 8- di:gior ever zero? If so, where?

Explain why the motion of a piston*4a m ;5lnh 9kd-s -yrde*wtkc in an automobile engine is approximately simple ha5ka9*rdd -nk-lwy 4t;s*emhc rmonic.

Real springs have mass. Will the true period and frequency be larg9: utvpec)6umz9yd4d) vo8o ger or smaller than gdmc8uo:zo dpt))y evv6949g uiven by the equations for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum s quch1q4 5t;2 hng,8qc(f clbspeed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the jcq+ 0qulj g6f )v4(fb:7l9gzmxhj)o hook of a vertical spring scale, and then is released. Describe theg7zx+ :j)09 jlcl fbfqh4ug(qm v jo6) scale reading as a function of time.

If a pendulum clock is j7 :9dl e+oz/ jjf/28akox c ck/4iyxiaccurate at sea level, will it gain or lose time when taken to high altitude? 9ci e/fkj+/8l/oxjx cai4 yk2:jdzo 7Why?

A tire swing hanging from a branch cwbk69kr 4/(pu+a rhx reaches nearly to the ground (Fig. 11–48). How could you estimate the height of the branch using only a st ruk/+wp64kx9brhc(a opwatch?

Why can you make water slosh back and forth in a pan only if ydzwcoeun -iu0b2 ,* (zrfy3g/ ou shake the pan at a certain frequency?-byf u( 0giuz3,2*/eoc drzw n

Give several everyday examples of resonanceboudz d8u2a1 sr 1,r4v.

Is a rattle in a car ever a vda w4vnq 8 *2ayet0,e*;sm w-ga6duyresonance phenomenon? Explain.

Is the frequency of a simple periodic i6zd2 dmg nrg4;b ni5/wave equal to the frequency of its source? Why or why no in56gid / rn4zbgd;2mt?

Explain the difference between the speed of a i awi aclcs3 ja. xhiup-q*04v7f-i23transverse wave traveling down a cord and the speed of a tiny piece of thew fiaa3ui- p*s-x 7.av3 q 4ih20jcilc cord.

Why do the strings used fo nd ehrx/i,i3 rg7qslfqo a48o 805)ddr the lowest-frequency notes on a piano normally have nxqf,rqd8rs aodi g/57le)0 h43d o 8iwire wrapped around them?

What kind of waves do you think w)dqg4ejtbv/0vw8xe,0 nz zc v u)z86qill travel down a horizontal metal rod if you strike its end (a) vertically from above and (b) hot4zenexv/g zc6bj8)0wu)z q8v0v,d qrizontally parallel to its length?

Since the density of air fg,i ;wj6y*,a iinukrl3yv.j w),w( 2as e*ozdecreases with an increase in temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound wa2iy.g6aaifusr; )wln (w,,*v*e,wzj j 3i kyo ves in air to vary with temperature?

Give two reasons why circular water waves decreau u(:(nb6mlrpr k9x8nse in amplitude as they travel away from the s( pk:rrx6l 8 (bnumu9nource.

Two linear waves have the same amplitude and speed, and otherwise are idenkccqx z,zv8( y *8g8gitical, except one has half the wavelength of 888q ycz xi,(gczk* vgthe other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundarv c) 2bsqv idgxo6hq3jq:-*6 yy between two sections of cord as in Fig. 11–33, the frequency does not change (altq: c i6vd2b3 hjv*)-q 6gxsyoqhough the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are the821)r fbh. ,5wwsc iee* +jgr bcdna/jre any places you could touch it with a knife blad)ji wg8hre1+ ebb,d5f .an2cjrs*w/ce without disturbing the motion?

When a standing wave exists on a string, the vibrations o/ual7qbsno sqc6n +.*f incident and reflected waves cancel at the nodes. Does this mean that enes+nqoalscb.7 *u/6n qrgy was destroyed? Explain.

If we knew that energy was being transmitted from one place to another, ho2t ):enmraj 5nw might we determine whether the energy was being carried by parenj5)rtmn a:2 ticles (material bodies) or by waves?

  If a particle undergoes SHM with ampl mna.4ow6u5z jr thj1-itude 0.18 m, what is the total distance it tr5m-r4uhat n .61wjojz avels in one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs ym( 0nbi*, 6riq t)t pzzh8ww-from it but is 85 cm long when a weight of zwzti6 mwnb*q, i(0h tryp)8-180 N hangs from it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg7p3 b6:gvh zsh driver gets into the driver’s seat. If the car goes over a bb szh 6p37v:ghump, 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 2z8m u2s2jmfbit. (a) What is the springu2 2f8bj2m zsm stiffness constant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a frequency of 3.0 Hz when a mass of -nz5ir25tbz p0.60 kg is hungniz 5rzpb-25 t from it. What is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. 1 chh2 s61,l+o qdd uo/lui)0qu1–2 at times t = 0,t =q d21 qiu+)coulshdu6/o,0 hl $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 j 95ty(c+xjyd(g. l hlis caught in a spider’s web. The web vibrates predomin .+lx5t(j9cy(g hljdyately with a frequency of 4.0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a spring vh d.u; gy6pu6dibrates with a frequency of 0.88 Hz. When an additional 680-g mass is added to m, the freug6u 6pd;h yd.quency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end 4iwa0b cln/s/ of a spring vibrates 3.0 times per second with an amplitude 0inbw c4a//sl of 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 displacement fk47 q 9 ;mqkrz*hw0ba1yj tpl)rom equilibrium is the speed of a SHO half the maximum value ) ;1twqr04q9zp7jk*ykmbh la?$\approx$    A

A mass attached to the end of a spring i ( --w41l8tk q7qdgm vk.c/vrk* nd 0j(nmhzjes 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 s 4,:fh ld8/ lbjqbmodt4+ct5zpring 0.315 m. If the spring is stretched an additional 0.130 m and released, hjt,lh m/ clz4b4+8otq: dbf5d ow 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 stiffn 2.ejfmf,if7h ess constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it iif ,f7 f.2jmehs 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 compre5d) phxj04 p ;(dlgrwxv(lw.4s 0bkwlss the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what )0pw ;glx4p.h(v5 r( b w4lw0kdjdsxlspeed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionle dx 9/k(qq khksn:mc6:g-n;l7tbpx7vss surface is attached 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 1nkq :xcxd m7 (hnp klq/ 7k;ts-6v:gb95 $m/s^2$ 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 where x is e2tyt e4d6*.ovc)b n/0hcezv in meters and t is in seconds. Determi0obc.)dtvhe6etznc/y ve 4 2*ne
(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 3zofttl dn:;r 5- c, eft)-cs8hb8nyma SHO half KE and half PE? ± t8-8,snlof -ccfn)rd;te: hy ztb3 m5    A

  If one vibration has 7.0 7h7u,mfp rmf*)irn,/cs3jl v times the energy of a second, but their frequencies and masses are the same, w,)h ,rn 7/cs m*ljv i7p3mfufrhat is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light spring onc9.q )gf) vrwpn*uwy: we every 0.65 s. yn fw:gww*.9v)qp )ru
(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 identicx28w 9z8j *1wt 2qrao yx tvr0d:kl0tfal parallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What:y9t0t0 8d8flota2 qj1wv2x r x*rkzw will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t where x is in me0 ammskbivv*8a.j 9r4ters .riv8m a ma*j40kb9vsand 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 Acr mkar :tu9/; and 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 o-(tbvh htdak+-qyt+ h -(zo;tn the end of a horizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial s+;b-( hdztoyh ta+ t --kvt(hqpeed 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 vibrates with an ampl f -c7covk7iy. e8q:znitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equil-:zcekq.o n8c vify77ibrium 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 spring ev; +fq3z(ac/ie nx5,9esgpts, 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 attachzhnm o:/ 5s3jp 1qi:h 7c(c5pwjli1 sbed to a fixed horizontal spring whose spring stiffness 5 15bi7hh:( zqmiw:pcsspojjc13/l n constant is $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with mass 69 xj3s,hq n6zwi:1gsg5.0 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 s zns,6ggiqx:w93j1 hthe 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 exactl-1rx2 s aelmp7y 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly one swing per secx ioh b+*bs 3(k9dy*uzond? (That is, one complete vibration dx+u( b9szhk3* *oib ytakes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on Mars l.7e0pha /hj5*e roem, where the acceleration of gravity is about 0 7 ee*/p o.l5jrh0hmae.37 that on Earth?    s

  What is the period of a simplvwk-wje6m. 2lonry1 :e pendulum 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 pent5 o u3 a-malq. o57wq5fqig1ddulum bob has a mass of 365 grams,alimgw 5 1u5a7q-.5 odftq3qo and it is 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. If the clock loseswm5k vm ji:b;/ half a minute per day, how should you adjust the length of the pendulum?5vmkmw;bi/ j : shortened by    mm.

Derive a formula for the maximum (gojwkpe.s8 ( rdyfo1h z+g.*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 (i sb,2t,bpq7yuw:lqis released from rest starting at an angle of 1s(:,q wpil y 7but2q,b5 $^{\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 a /,fyh/l qum5onchored boat every 3.0 s. He measures the distance between two crests to be 6.5 m. How fast are thqf / lymohu,5/e waves traveling?    m/s

  A sound wave in air -jhzlct(sk3tb x4,:y has a frequency of 262 Hz and travels with a speed of 343 m/s How far apart are the wave cresl-,t(zk h stjx4y :b3cts (compressions)?    m

  (a) AM radio signals have frequencies betweenfs rze 0a55 x14:uprgf 550 kHz and 1600 kHz (kilohertz) and travzfe54rg:p fsru5 xa10el 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 lonp+x +d8dzc pv(ly;m n;gitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, bux8u)hi ui6)rh,+q.p8s(no 2 5fmhu8mtjsjut t one is twice as dense as the other. In which rod will the speed of longitudinal waves be mu8rths 8)i,8xfh+unjuqijo(p6tus 2 )m .h 5greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apart. If tp,)wg xc62ombxgp .l4 he tension in the cord is 150 N, how long will it take a pulse to travel from one support to the other? 4) moxgp6.2p,xcl gwb    s

  A ski gondola is connected to3vvx u oic-b/) y-5se4g/h.p. kpx i48rwnpmg the top of a hill by a steel cable of length 620 m3kxpmgc4v.ie5/s.bphi4-gu / vop r) 8-yxnw 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 s for the pulse to return.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

  A sailor strikes the side of his ship just below the surface of t.( q(l 2j3uht1k 9(duonggpsthe sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s lgl9( nj((oku 13upqshd .t 2tgater. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at different+5mg)o,lg jz t speeds, and this difference helps in locating the earthquake “epicenter” (where the disturbance tookmg5 jz) tgo+l, 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 8w v+uzka:hc+ 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 accelerau+ :ckza +hw8vtion a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplitudes, of an earth3 kizf8v l0g9je;l1x oaj/)egquake P wave passing through the Earth and detected at two points 10 km and 20 km from the sou1/8ga0 9);fvl ieek3o jjlzxgrce?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is measured u9c hklnpw+ zx+ b:fe.j2 ,isdq+2ax) to be bxwuq2xi kzs+9 n .d2h,fp ac+j:l)+ e$ 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 trav6rm3h zo ,zf3mel through the same portion of the Earth, but one is carrying twice the energy. What is the ratio of the amplitudeszmo r633z,mhf of the two waves?   

  Two waves traveling along a stretched s +l* n/ /esvj0i+zn geq2v:hoktring have the same frequency, but one transports three times the power of thenj kiqs+n0o* g2vz//h l+ :vee other. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move up and down de w2w))u6llr a total vertical distance of 6.0 cm, from the lowest to the highest point, as lduel)w 6rw 2)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 moving toward each othe jnca-i4e2+ kgji- vj.r. (a) Sketch the shape of the string at the momejj+ j42 ai-.iv-cekg nnt 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 happened to the energy at this moment?

  If a violin string vibrates at 44tu 5o(ow1x2dq1ac6l h0 Hz as its fundamental frequency, what are the frequencies of the first four harmoni q2o (o1duh61a wclx5tcs?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfizym8j:l)l tz(ngered. At what frequency will it vibrate if it is fingered one-third of the way down from the end? (That is, only t( yzj:tlmz)l 8wo-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequency of 280h,se p6pq8oj. Hz. Name at least three other frequencies at which it will resonate.j.q ,s 6eo8pph $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a *fn8aqx wz6l 3; om+xrstring is 92m/s If the frequency of standing waves is 475 Hz, how far ao;n*wazx3fmx 8rl+6 q part are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 35:d2 dvvbe*pov. l/ g7yb* uyv;0 Hz, what is the frequenbl. y7 gv/*vd2uv:bp; *yvdeo cy of the fundamental?    Hz

  A guitar string is 90 cm long and has azh qj)/dfvmxd8+1 s w) 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 520 N. What are the frequencies 1dq wj+) 8)/dhzsmfv xof the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200s1iq8lo7al d 4rv4 :8-x1phq m3p pcrv Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequen44pqv1p8l3ir pa s 17c-hq8mvrldxo: cy?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is su+nggf+ )+)q xwemcz -ipposed 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 comz) )+ie-xc +g wn+gfqrrect the frequency? decreased by    %

  One end of a horizontal string is attached to 58rl1zygs5j j a small-amplitude mechanical 60-Hz vibrator. The string’s mass per unit le5jylsrz 81jg 5ngth 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 string may be adjust,z.qxrq .:6 p99vczo suhzwo; ed by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying L between 10 cm anhxz9 qor,qc9z w:;s.zop6 vu.d 1.5 m?   

  When you slosh the watenwc3: r2mo4tm(5:lth+y cvssr back and forth in a tub at 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-wide tr5(o hcst m:42 :lnm+yw3vt csub 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 , in.q++4)up snzfjgoa boundary within the Earth between two kinds of material. If uij) 4o,+sq . +fzngpnit 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 changoplr34+bp/3itu(xq ges from 2.8 m/s to 2.1 m/s Iugp4+(3p/ i3l xbr oqtf 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 when it hits a layer of cl/iwxeg3 s1ek;)gg2,x ut a exuj 079iold, dense air. If the sound wave hits the cold air interface at an angle of 25ee7xwk9ux e g/,u ;t0gil ij3gx2s1a)$^{\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 earthquyztt: ts ;ovb43zk-c 7ake wave strikes a boundary between two types of rock at a 387k otsb-t;y t3cv:z z4 $^{\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’pj f;x4fg-fe* n/g 9bgs manual, the dish has to be pointed inn fge9/-x *ffjgb4g;p 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 750 km/h trav,8 zy-snhp/0eqg 6ibwels across the Pacific Ocean. As it approaches Hawaii, people observeehz 0-i/, 6g8spbyn wq 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 cn-l2bmqi ji,8ho xx-;x7op5x onstant of 550 kN/m Find the maximum compression of the bumper if the car, with ma-onx5l-xqihx ;72op8mj i b, xss 1500 kg, collides 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 lxiy njht w6b- .7b.(jxhx1w + 4*pedg18 m below, which stretches the net 1.1 m. Assume that the net behaves like a simple sp xtpxx 1 lwd. hy4(7n*gwj.i h6bjbe+-ring, 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 ey2k ,boldg u.8 djn:0of a freely hanging spring. The mass then falls 33 cm before it stops andok 0 :l,.ud j82bnedyg begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spr op 3xz/klc87b- ml+pking at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) W p7m kol-+z/lpcb8kx3hat is the spring stiffness constant of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of coffee (diameter 8 cm)xbu8(i8t5 hw l at just the right pace of about 1 step per second, the coffee sloshes more and more until evbhi l 8t(x8wu5entually it starts to spill over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the center of a 33-rwq7phr5owndedp6d 4s*1 n 9v: pm phonograph record have a wavnhvd7*wrpoqwp9 sdn:1de56 4 elength of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates accordifx--s 6;w kq3 (7adf ,hqqaspe.vs*ybng to the equation x=0.650cos7.40t where x is in meters and t in-.v(abf s-,*asy7hf e6kx dq;q pqsw3 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 7+b( h4nsmoux f. What is its frequency if it accelerates at+o(nmb4x 7shu 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft fl7)ctz,;jnx7 qqmueb )oats on a lake. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steq mbecut7xqzn))7 j ;,ps 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 (hx.ygj lfh o/;otdi(o,c4 9 d9G) and 440 Hz (A) 9h,ddj ;(xcyfgh ooiot.9l/4 .
(a) What are the frequencies of the first two overtones for each string? G : $f_2$=    Hz $f_3$=    Hz A : $f_2$=    Hz $f_3$=    Hz
(b) If the two strings have the same length and are under the same tension, what is the ratio of their masses ($m_{\mathrm{G}}/m_{\mathrm{A}}$)   
(c) If the strings instead have the same mass per unit length and are under the same tension, what is the ratio of their lengths($L_{\mathrm{G}}/L_{\mathrm{A}}$)   
(d) If their masses and lengths are the same, what must be the ratio of the tensions in the two strings?   

Consider a sine wave traveling down the stretched two-part cord of)(hpcu5vhg // -ffe:gnaq; 5zspda *r Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the h fzhug5 - pc v*a5gar h:npq(//dse)f;eavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the tif;l pqtqpa1y7s0v ,4ki3 zxj4 p of each prong moves 1.8 mm to either side of centers7 ,;aiftp1pjq 4vx0yz3k 4q l. 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 frequencyg*k qb4f)*do3isdqv5*w ik4b 1.5 cycles per second. What is the maximum amplitudigvq d3k4os)5kb*b*i *w dq f4e with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that end is attached to a r 9spx2 (qi)6j ov8i 1kprwvk.ling that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resovk(pv s6 q1r2pk.ij ox )wi98lnant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of,r 95)f qxq7zl 4 4zicbhzotx5 exactly 2.000 s — each one-way swing takes 1.000 9qr5ql7 z 4x)ozzi bh 54txf,cs.
(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 oscillate9ix0) /yw9jpur n c*mc in the vertical direction or can swing as pr9mnwc0)uy c*i x /9ja pendulum of small amplitude, but not both at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontal 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 /hrt 3z6nsx-5m ddz lj4vd7g3a tension of 255 N. A pulse is generat3ddtlvj64hz7dx35zsmrn -/ ged at one end, and 20.0 ms later a second pulse is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling 6f ryfzi7tly4i515b x 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 pen45i6fzi1by ltyxf7 5rny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The stfnh br2-kiue 1hf*x)0 eel crane cable is 22 m long and has a diameter fb)i 0 k1r2* xfhhnu-eof 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 rests on a plate as shown in Fig. 119jr+r* 5 htk wvpnnn,7–58 (which also gives the dimensions of the block). You pu9 t5nhn,*k+7jprrwnv sh it sideways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this vibration, given that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz