Give some examples of everyday vibra 6 xqnm.)-:powu3*d5ezufwrcting objects. Which exhibit SHM, at least approximateu wzcnm r6ufd*qw)o3.:-5 x pely?

Is the acceleration of a simple harmonic oscillator q6rk(;9sjg1vvsof3 m ever zero? If so, where?

Explain why the motion of a piston in an automobile engsr w j4 k zvwd;o8nic4i,tuxn9rc96 ;+ine is approximately simpr jxc v;i84 k9t;r,dus4wo +i6c n9wznle harmonic.

Real springs have mass. Will the true period and frequency be larger or s1e3:hejr1v5fgrp o tpql 1:9 kmaller than given by the equations for a mass513 9k1rf l pt:vegjqepr1o: h oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum spwfa. y17 0cli .siaa/leed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to thn+ vlvwo1k z4,e hook of a vertical spring scale, and then is released. Describe the scale readi,4won l vvz1+kng as a function of time.

If a pendulum clock is accurate at sea level, will it ga;n b esig12ia g+ye7;ain or lose time when taken to high altitude? Wh1nag 2i;e;sie a gy7+by?

A tire swing hanging from a branch re1 pl (p2dxp0lzz7vv8 raches nearly to the ground (Fig. 11–48). How could you estimate the height of the brancp z7( xpz 1p8dl02vlvrh using only a stopwatch?

Why can you make water slosh back and forth in a pan only if you shake theyuae3x;bj g yb 9+x+m f;2snu5 pan at a certaify+b; ba;xsm3n ue+u 9j 52ygxn frequency?

Give several everyday examples o.v .3ph(a c0fo5d:jkqikc p+of resonance.

Is a rattle in a car ever a resonance phenomeno0e2y*aruo,hbz p) - din? Explain.

Is the frequency of a simple periodic wave equal to the frequency of:96 )dqg* pzmi/gm9/ye damb6ut6w fr its source? Why p qmme *b9a/y)d6 6g i 6fg:m/zdwru9tor why not?

Explain the difference between the speed of a transverse wave traveling down a cnx s az7noh11y)v4qhc04 hc6dord and the speed of a dq01 47h y1 xoz4hcvan)s6nchtiny piece of the cord.

Why do the strings used for the lowest-freq)4gipzt3r 9/984uzuh nkh xuv4qvo 0uuency notes on a piano normally have wire w ruq/9 up v4z84knt94uox0hg)uhzi3vrapped around them?

What kind of waves do y ye5gpn4xp :pkj0*)smou think will travel down a horizontal metal rod if you strike its end ()e:0 sg5xnpkypm* 4 jpa) vertically from above and (b) horizontally parallel to its length?

Since the density of air decreases wkbr 6f:; wsdhk, ah/v5ith an increase in temperature, but the bulkkhbskfh5 6,/a w:v rd; modulus B is nearly independent of temperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in amplitudewn.wp69rs+3h dgkmo , as they travel aw,3spr6kd+ wn 9mohg. way from the source.

Two linear waves have the same ampln4i7 lv :o3z3jqp r3xe;(d.slb 9ve neitude and speed, and otherwise are identical, except one has half the wavelength of the other. Which transms r:ponn belev9dx; jv3z(7 3ql.ei 43its more energy? By what factor?

When a sinusoidal wave crosses eq: hzx jg3v0x3f-g:su2d*rw the boundary between two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and veux srg3 :w qj2-:3gzvfdx *0ehlocity do change). Explain why.

If a string is vibrating in three segments, are there any places you coulxinr (7oc)2l o2e8xfod5y e:ld touch id eyo8 e 7xxic foor2:2n)5ll(t with a knife blade without disturbing the motion?

When a standing wave exists on a string, the vibrationsi83xmk(l q e:a of incident and reflected waves cancel at thq a(38k :elixme nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one ppwuhk p68khes7.7k4s;bt:frvz f n92lace to another, how might we determine whether the energ ;2.f8spk477v zkhf:9 tbwk6 epshnu ry was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the total99y lg)lg0nk j distance it travels in one perio gn0j9g9lk l)yd?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it but isqxw(/p2xo- k22zgy ny 85 cm long when a weight of 180 N hangs from it. What is the “spring” constant k of thisqwop(n-y zg2kxyx2/2 elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg driv3bjm tc065gcmag.: al) jaih(u n1/oyer gets into the driver’s seat. If the car goes over a bump, what will mngg:cu6 j)aoh 103a ybtjl 5ca m(/.ibe the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hqeif*s ooq1ev) wu/.9angs from it. (a) What is the spring stiffnes9ef/e *s.iuwvo1 qoq)s constant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a frequency of ls*w0a/3p,0;rb6fx0w s8vxnufevlo 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequenl3a*rvf e6bsop;wxf0s0v ul8n0x/w, cy if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the positionzu5ygh an i.;4 q(ytv* x of the mass in Fig. 11–2 at times t = 0,t = z;*.ayg 5hy t(4 qvinu$\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

  A small fly of mass 0.25 g is caught in a spider’s web. The wiz h*tc+2ui) ;nj ugw.eb vibrates predominawit 2c ;ngu)zhi.ju+ *tely 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 vibrates wi4hbymw5ts w kt+fs586th a frequency of 0.88 Hz. When an additional 680-g mass is added to m, the fre tyk6fw+st 4wb sh855mquency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring viw.(o14- jo1ubg ,3y bvoikugobrates 3.0 times per second with an amplitude of 0.13 m. Dety bu(og ouo3j.-owbv 14,ki 1germine
(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 x kckhj gqzgk3-p5jgn./ )*2yspeed of a SHO half the maximum valueg32-jk5.jk kx/p) gyhcg*nq z?$\approx$    A

A mass attached to the end of a spring is stretwhlaw(o,m.f08s.pdi .z 8 dzzched 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 sp7q,m w1 eicl:5q 5ruaaring is stretched an additional 0.130 m and released, how long does it take to reach the (new) equil1rc,75 mweq ui5qla: aibrium position again?    s

  An object with mass 3.0 kg is attached to a spring8iy.xn1xk 8. 1jfwbois:sf9 x with spring stiffness constant k = 280 N/m and is executing simple harmonic n :k 1.xs 8 x1iijsofxf89bwy.motion. When the object is 0.020 m from its equilibrium position, it is moving with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compress th6tc ibhnedv r8y81 8c0e spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will the ball leave trnvh0ed 6b18c itc 8y8he gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to one m6g7:wlgv .j ,uk97mu smks,)cz fd6yz5m6u hend 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 experiencf 6 udm6 6wgvzu smhm9s7g.y,kuk,j57zm:)cles 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 t7hg-6 )yzl:b zrs bv u*g6jbh.o the equation x = 0.45cos6.4t where x is in meters and t is i*zg7h6:bsbz.- r)u vyh6g jlbn seconds. Determine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equilibrium is the energy of a SHO half K(z-ad :+z hw1 yleb fmmqr5wjhx,j q0:9)kg( iE and half PE? ± (yk imj)lm1ehd+ ,f azxq90bh(rq:w:g - zwj5   A

  If one vibration has 7.0 times the energy of a second, but their fr8r+qla1p7c i gequencies and masses are the same, what is the ratio of their amplitudes?p i 81gr+a7qlc   

  A 2.00-kg pumpkin oscillates from a verticals :hk8w:o x))i-un esijj:7erly hanging light spring once every 0.6:)8ejrkse7ih ouiw n:j s:)x-5 s.
(a) Write down the equation giving the pumpkin’s position y (+ upward) as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. y = (   m)cos($\frac{2\pi t}{0.65s}$)
(b) How long will it take to get to the equilibrium position for the first time?    s
(c) What will be the pumpkin’s maximum speed?    m/s
(d) What will be its maximum acceleration, and where will that first be attained?   $m/s^2 $

A block of mass m is supported by two identical parallel vertical . f,wftm1j+clg+ /m5o70 ow9fhlj nwq springs, each with spring stij+gwfhnj. m w7f , c5t9ol olw/f+01mqffness constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t where x is iu)blp sstk9 *3n meters and t is in seconds. Determine lksps 9 t3*ub)
(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 a,lo /5fiokg/ ynd B. For each, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on the enjq0qoi 9n/-m wd of a horizontal spring (k = 124 N/m) is struck b o90-/jqnwmqiy a hammer, which gives the mass an initial speed of 2.96m/s Determine
(a) the period and frequency of the motion,    s    Hz
(b) the amplitude,    m
(c) the maximum acceleration,    $m/s^2$
(d) the position as a function of time, x = (    m)sin(4.08$\pi$t)
(e) the total energy.    J

A vertical spring with spring stiffness constant 305 N/h g13502qlxk upmh1 smm vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. T01 2u5qkmsh1h 3plgx mhe mass passes through the equilibrium point (x=0) with positive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two springs, with spring stiffness jm cizq ;n2phi o)v-*al-x9a/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 attygf h q r ls722hob8f+mm7cx,cdx r*1;ached to a fixed horizontal spring whose spring stiffness cosgm8 c7cox f,2yfl rhd 1xqbr 2*7m;+hnstant 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 6 9g:qaxcrb.. c5.0 kg jumps from a high bridge. After reaching his lowest point, he oscillates up and down, hittb .qr9xg: acc.ing 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 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 4 ypf+hf8(r7 uwpi)spj cc1e9in exactly 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 second( uu;jgv*u ri7 z7lif+w lmg8,? (That is, one complete vibrationugm +f,7wl8 gurijv; lz*i u7( takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is ih5m-b7mk) x5iukt5h u ts period on Mars, where the acceleration of gravity is about 0. -k75)km5xi 5muuthhb37 that on Earth?    s

  What is the period of a simple pendulum 80 cm lojwgh g0;( f2;o6 y/mow -1wahltvjx 9wng
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 8zn2qbra/2; zl,u xweq;z6 vu0.760 m, the pendulum bob has a mass of 365 grams, and it is reqb uw/rz ;,l8z22q vnuaz e6;xleased 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(-ut.e5f +z rp *hsjqn m. If the clock loses half a minute per day, how shouldj. zfnh* 5pstuq(+r- e you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the u2hzutqp,8 :by ,h pe.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 xpm dz4h(-lo/. At it is released from rest starting at an a /hl4zo(xdpm- ngle 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 cresfgjwy 10d n.3pm gp*f az f:j0jt0w56dts pass the bow of his anchored boat every 3.0 s. He measures the distance between two crests twg6yp.01j: mg j03dfpnt* dj50ffza wo be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequenccig)f0 zc; 1+lku y9koy of 262 Hz and travels with a speed of 343 m/s How far apart are the wave crests (compressions)fic ol+9c k;uz01gky )?    m

  (a) AM radio signals have frequencies between 550 kHz a n8qpjai nl5t,m:c spf0ng27)nd 1600 kHz (kilohertz) and travels2tcl gp m)n0,qaf7i: 5nnp j8 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 longitudinal waveytg;o;-p6czez rw;(m s in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the samev sl.satw;b8) elastic modulus, but one is twice as dense as the other. In which rod will the speed of longitudinal wavbaw ;)vss.l t8es be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apgb257b q *kjzdu kn(5oart. If the tension inkg j7bk5n2 (*5qbzuo d the cord 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 cable of lengthwm-rft na)l2/ 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and sends ) 2nalwr/fm-t a wave pulse along the cable. It is observed that it took 16 s for the pulse to return.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

  A sailor strikes the side of his ship just below the surface of the scpo8s1 s.npb./6otfv ea. He hears the echo of the wave reflsnbc.8vt p/p 6. f1osoected 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 different speeds, and this dif tci0kizax a3b+)+f 7xs79bjcference helps in lock0ba++7 scx tj9i b 7iaz3cxf)ating the earthquake “epicenter” (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 surface wave can be approxim ro.j-j+l a1qjokswq+o* d 36kated by a sinusoidal transverse wave. Assumk3 jq+w k*j1ro .q+o j6as-doling 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 a>g]    m

  What is the ratio of (a) the intensities, and (b) ta d-efeq2 e1d*he amplitudes, of an earthquake P wave passing through the Eaafed2dqe e*-1 rth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earth- evet 201 lsza 88qr4iz)7 kcexcgz;pquake wave passing through the Earth is measured to be 7sei qk;cga4 x)z1lcv2re-8tez08 z p$ 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 travab+haujl w tm77 dvshr+: g5blpq6.,5el through the same portion of the Earth, but one is carrying twice the energy. What is the ratio of the amplitudeqhg bd.ls6,7 :vpjar5t7+mbuhwl5 + as of the two waves?   

  Two waves traveling along a stretched string have tlci 0ndt /lp3)ed( .brhe same frequency, but one transports three times the power of the other. What is the ratio of the(dn0)3lcbi/ rp.lt d e amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move up and down at(khfzfiq/3b, aa y1 + total vertical distance of 6.0 cm, from the lowest to the highea b+ y/fzt( 3qfah,ki1st 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 moving toward each othshu 36jz dv :(u)bki-vt52* wc1blk h6qaey-qer. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sket d lactv*h:5uyujq 3)s1bki 2hz 6vb-6 (eq-wkch 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 440 Hz as its fundap+ 9y8rccsq;sqisscx bl m2;g48 hu1m49 fmu9mental frequency, what are the frequencies of the first um1sbc+qcmc9y 9ihgsfs9 4r;8plq s48u2;m xfour harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfinge;6ybkbl.t ecr07kah1a(1m2 :e wd jksred. At what frequency will it vibrate if it is fingered one-third of the way down from thk61.w7k; :k eb1rj20ha b(elcastdm ye end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four looppr3zq5 +q dww.d2isp* s at a frequency of 280 Hz. Name at least three otrqp qds 3 p+.dzi5*ww2her 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 ok3b k6 kwx)e2diuk.0at1at- of standing waves is 475 Hz, how far apart a)kwt63 1eadkk2b-k0x.tiu ao re two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 350 Hz2yg-:l svk .qa, what is the fre.kq yl2a -gvs:quency of the fundamental?    Hz

  A guitar string is 90 cm long and h:q- *ww jjw- 0vanoxdy8npf:/as 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 520 N. What are the frequencies of the fundamental and first two ov0ndjwnp-x-ww*:vq :8a y o/jfertones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, htt4 fwu712lm 5gi ha:but it is measured to vibrate at 205 Hz. By what thl 4f m:thu2igw157apercent should the tension in the string be changed to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hz, but it is measuredxn;oqlim 8+, sji -r;q to vqq-;,xi;ro m l+jn8is ibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a smal1jt*uokq/+ wtqcmu)j 1y, x+jl-amplitude mechanical 60-Hz vibrator. The *tk t uj o/,c+w1+uqyq)1mjxjstring’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 string may be adju5j69e ohx8 ipyk dcr,*sted by moving the pulley. If 6xrpikeod *cy 5j8 ,h9the hanging mass 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 water back and forth inv:gkvus-p.-s/v ir t. 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/ .v-pv-:grv ukit .ss a 65-cm-wide tub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave tj 2n6pwl.cuu:0 hhng+4ss v2xraveling at k.0 km/s strikes a boundary within the Earth betw6: w4 ls+ug20xphnu csj2v. nheen two kinds of material. If it approaches the boundary at an incident angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “shelf” where the velocity changes f-yuj fum ;lmz:k:bo -t663o1vaj z9oqrom 2.8 m/s to 2.1 m/s Iu tz- m: vuq13kjojb ;oyo66flm:z -9af 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 wh2zhcq -,8itp wo(gz9 qen it hits a layer of cold, dense air. If the soz2q-(9hcpi, q w8otg zund wave hits the cold air interface at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave strikes a bounyqior ( :8zs5jqch 5z*dary between two types of rock at a 3qzy8 izqj5s:* (or hc58 $^{\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 manul0 8c2lcx2mz3wwg v49*nmznk al, the dish has to be pointed in the direction of the satellite, but an error3ck8 2m*nnw zlm4cw zl2xv9g0 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 waveleniv6fz ci1jr0 .gth 250 km and velocity 750 km/h travels across the Pacific Ocean. As it appr.fizr vj60ci1oaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness qa 4 ;j*hu5 o (2insm,9iu6;fdhmggto constant of 550 kN/m Find the maximum compression of 5fstgm u* iomod69 gha,i 2qh;n4(ju;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: Use conservation of energy.]    m

  A 65-kg person jumps from a /5ba-o2k nmfnkn z6*zwindow to a fire net 18 m below, which stretches the net 1.1 m. Assume that the net beho6/f2knm5a nzn -kzb*aves 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 freelwy1mv v k-j5l+ zyu4mvf3b8z.y hanging spring. The mass then falls 33vkbw zv1fyvz+.l-mu3 8 y5mj 4 cm before it stops and begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at ngyb5 m:k5 -86k rq(w1xhfmqz a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the sprin1f myk kx568zqb:(w5r hmn -gqg 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*d3.pmki7z hqd;2o wc cm) at just the right pace of about 1 step per second, the coffee sloshes more and more until eventually iz72 od; kmwdqh*.ci3pt 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 cmcfic56mc2v /n x.uwo; from the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequency of the sound emitteccfn w6vcui/xom .;2 5d?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650a wdbuu/xu j,6 p*l3cf1-m u3ucos7.40t where x is in meters and t in seconds. Determu,31jufpcw 6/l3mdauu-xbu *ine
(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 isz3 5wqn y*cd wdmj9v: c geiir/26,qm6 its frequency if it accelerates at 0.50g (a) upwi2cg:qq9*53v c ny6 rzdwd wi ,m6mej/ard,    f
(b) downward?    f

  A 220-kg wooden raft floats on a e *4yng nnuc1;lake. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the raft vibrates for a while4u*e ny;cn n1g.
(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 music y+-pct)1 dbo1nmp7;vfb mkxu8 /n4zdal instrument are tuned to play at 392 Hz (G) and 440 Hz (A). ncz7pmyx4d1b1+b- p8 f / )m;nt voduk
(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 tw0n .ekgn 6la5jo-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greanl5an 06 ke.jgter in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and theqxcea ;.,-2h xmy e7 z1djz.xl tip of each prong moves 1.8 mm to either side of center. C y7lmz2dx ex.j;,.ea-zc1xqh alculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simple harmonic motion of frequency 1.5 cycles prhu-:s xiw*3r /q ayoud *h-i*er second. What is the maximum amplitude with which the end of the board can vibrate i:huri3 r*s/*-w-xd uhy *q aoin 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 :p abpm.-zcb;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 s-:apb m.pb;zctring with one end fixed and the other free.

  A “seconds” pendulum has ap8ba5aq(u ug wsf )+p0 -,rdrj period of exactly 2.000 s — each one-way swing takes d+- q8ruabpj fag,)rw 50(u ps1.000 s.
(a) What is the length of a seconds pendulum in Austin, Texas, where $g=9.793\mathrm{m/s}^{2}$    m
(b) If the pendulum is moved to Paris, where $g=9.809\mathrm{m/s}^{2}$ by how many millimeters must we lengthen the pendulum?    mm
(c) What would be the length of a seconds pendulum on the Moon, where $g=1.62\mathrm{m/s}^{2}$    m

A mass hanging from a spring can 18rb w(s9,xpxice0 xposcillate in the vertical direction or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period r(i,wsxp8 cpx1 e9x0bof 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 255 N. A pulse mpw8(:w z+ p1p kwo94b slg4 gbg4v0ajik+ z1:wp goggb9lsp8w4m4 (vjw4bp a0s generated 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 by a spring with spring stiffnesn) 7 k1obg fcj::ee)w) gbn1xzs constant k. A penny of mass m is placed on top1ge1znkbc7j e))nb wo::x g)f 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 junkp( d2): xftv)wspp ib(yard. The steel crane cable is 22 m long and has a diameter o)vwb(p p(idxt: ps2f )f 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. 11–58 (which also gives the y2 taj +45s:o tctogs/o wy02bdimensions of the block). Yc soys0 t4+2oy /ato52btg:wjou 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 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