Give some examples of everyday vibrating objects. Which exhibit SHM, at least gt -6h,gak2 kk1znhqqnwu,- ( i* sd0dapprothkznhqd-20w-,g q,kkdg1na s*( ui 6ximately?

Is the acceleration of a simple jt m -1c q-2l2twbn/dhharmonic oscillator ever zero? If so, where?

Explain why the motion of a piston in an automobile engine is approximately si exc01el:p dxidm*- 62vrq7elmple harmoniv -2:6mdeex*ql i1 0ecdpl r7xc.

Real springs have mass. Will the true period and frequency be z4)o6gsc -lu ylarger or smaller than given by the equatioucl -so 4yg6z)ns for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maxq 1evk +8d/s1.xvurymimum speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spri ml9c3f-lxqspx+r 261 a erzu4ng scale, and then is released. Describe the s l6mzx+q 19c ul2x3afepr4r-scale reading as a function of time.

If a pendulum clock is accurate atkz,2*l*.b dw iog2y ;k0ghl rdb3eje* sea level, will it gain or lose time when taken to hib*l w b. ozrgg 2*,3ke ;2lkhj*dyd0iegh altitude? Why?

A tire swing hanging from a branch ln,h)lyolhr) t z+4q5 reaches nearly to the ground (Fig. 11–48). How could you erzh lht)yln , 4o5q+l)stimate the height of the branch using only a stopwatch?

Why can you make water slosh back and fort g9ji23(ptgpr0eeg 1wh in a pan only if you shake the pan at a certain frequenirw93pg peg (10tg2j ecy?

Give several everyday examples of reso0lotx5r8; ey8tc. h/ujo5 v oq c:m0agnance.

Is a rattle in a car ever a resonance phenomrx5 veoy ( tew+:+q:u1tom-u genon? Explain.

Is the frequency of a simple periodic wave equal to the fr.sd7 (0 ll:thh 1fu hojn2pqz7equency of its source? Why o7:1n70. l u(lhfh2 tjhqpzodsr why not?

Explain the difference6x17wkp ,2+cx k6bti p7w:kf xbb dg0r between the speed of a transverse wave traveling down a cord and tbxbkx k17b pfx6iw2trw+kc,7 p:g6d0he speed of a tiny piece of the cord.

Why do the strings used for e-bn6pq kx86w;* bfifthe lowest-frequency notes on a piano normally have wire wrax8b; k ifeb6-6 q*fwpnpped around them?

What kind of waves do you think will travelu5wzl6y 1d*f;wxh s4u down a horizontal metal rod if you strike its end (a) vertical xdu4 s1;*yul zw56hwfly from above and (b) horizontally parallel to its length?

Since the density of air decreasesx/f k )3)zvrl:ak(rio with an increase in temperature, but the bulk modulus B is nearly independent of temperature, how would kaxi(v )kz o/f)r:lr 3you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water wav .7jtvfly tgf22h48pj es decrease in amplitude as they travel away from the sourc.tjglj28t 4 pyf f7vh2e.

Two linear waves have the same amplitude and speed, and otherwise are t wjvbs(:n85 shri-j,identical, except one has half the wavelength of the other. Which transmits more energy?(:htjnv-bs i8,s w5rj By what factor?

When a sinusoidal wave crosses the boundary between two sections g02l nwzrj1h, of cord as in Fig. 11–33, the frequency does not change (althourghzj,2wl0 n1 gh the wavelength and velocity do change). Explain why.

If a string is vibrating in thro 1m gdf)syo 0o7q:*sqee segments, are there any places you could touch it with a knife blade witho qmyo: *so gqodf7)1s0ut disturbing the motion?

When a standing wave exists on g ;1:oafa/spla string, the vibrations of incident and reflected waves cancel at the nodes. Does this mean ta1l/p f:g so;ahat energy was destroyed? Explain.

If we knew that energy was beinl3.-:o q/mt;8ll cxts gr2clig transmitted from one place to another, how might we determine whether the energy was being car2tsil r8c lcg -l /xtq;m3l:o.ried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, whagf5fy3i* wlgim 5w.-fgmud . 5t is the total distance it travels in on5l.i3* mguw mf-f5.5wigfyg d e period?    m

  An elastic cord is 65 cm long when a weigu15 tphy ,f/agjn.dc (xzqy +*ht of 75 N hangs from it but is 85 cm long when a weight of 180 N hangs from qz/*n(,+jdx ya.u y ptc5fgh1 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-kg driver gets into 5 ,l;g4nq lebithe driver’s seat. If the b4ie,lgnql5; car goes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs from it. (a)es 1/gf.w 2t aimwx3/y What is the spring stiffnesfwm/w3eyix a.g s/t12s 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 H;h rdru grp2j-fq(lg o:f .z63z when a mass of 0.60 kg is hung from it. What is its frequency if only 0.38 kg hangs from irjdhfrgruf:p6qog2 (3;l -z. t?    Hz

Construct a Table indicating the position x of the mass in Fig. 11–97c5d /aod03 d fvt/4bfp dhrd2 at times t dfrbo fc79dad3ph0//dd54 v t= 0,t = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

  A small fly of mass 0.25 g is cadj mzm16wzk-tnqr8,: yn,0 k*v8p) bxh ii1av ught in a spider’s web. The web vibrates predominately witr80x kavk, mh,z)q-in :18tv 1 pij *dm6ywnbzh 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 with a frequency of 0.88 Hz. Wh2 :v+so: (h9,x2jbn baqpxevcen an additional 680-g massp qvbe2 2:(vb9xaxc,+hnso:j is added to m, the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 tqmfef 6;swv3a7t2 bt+ imes per second with an ampli;aq7sbm w +6 3tftf2evtude 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 from equilibrium is the speed of a SHO half the maximb.w2ugoh tz06t;ux tyx(d 3w-um value?g(u. 3wu td z0;6whx-ytxbto2 $\approx$    A

A mass attached to the end of a spring is : 8k p:w7vvbwystretched 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 vmn+hi0zk2p (+.hvbgzr(nh-.y q;zaaertical spring 0.315 m. If the spring is stretched an additional 0.130 m and released, how long does it take to reac g2(0a;+pb.r+ yzhhvnqmik.zazn- (h h the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with spring stiffnes cr*o7k l 9 pu6t0ke.ozha.ndr.t2ibe l-d-.z s constant k = 280 N/m and is executing simple harmoni29k l*67-eitrpzoo z t-l r.0hdcnabde.k.u. c 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 the spring of ai t b+alj..wafw,;fm7 toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will tjf.wb7aa.,m+ fwl ;tihe ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surfqc+fnq20 v0w ,p:o mwnace 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 acce,qpwwv+n0 nfc 0m2o:q leration 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 wka/2 v *7dgaod ,i2ysshere x is in meters asi sak2ygo2d7,va/* dnd t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equilibrium is the energy of a SHO+ 0kq-a0.mjnq yv d3t-r4ghi w half KE and half PE? qm 0.yj4-k+w0h 3rnqvtd-gai±    A

  If one vibration has 7.0 times the energy of a seconvoevady0l:a;f +j w dz 7zk47;d, but their frequencies and masses are the s4 7 0jav+yk zlv;7ezw: fdod;aame, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light spring once evs:x14:v q7o-* fgkgk-f9frmj sftq j+ery 0.fk- xvm+9s*tofqs4fj:k7fg jq:g-1 r65 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 springs, ew(s x5wzm)5azwl h10 tach with spring stiffness constant k (Fig. 11–49). What will be the frequency of vibration? hx(05)z5waw wlszmt1

  A 300-g mass vibrates accordinh/ ;ki3vzh9ro (r1ivsp;czwz3ge53v g to the equation x = 0.38sin6.5t where x is in meters and /k io9vg3;h5zv 3epihw1csz;v3( zr r t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows two examples of SHM, labeled A- /b5aqam xew*3we3f d 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 on the end of a horizontal spring (k = 124 bq8( t,9 wzpn 3h0agbaN/m) is struck by a hammerq b0z(n8,ahatb g39wp, 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 s( tw4ro09-ke 9tt zz.9lpbyavkl1 i0ptiffness constant 305 N/m vibrates with an amplitudep 0ot14azeil99b.yv 9k p(kl-zt0rw t of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) with positive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two springs, with2 y3 k9xtz 0kj0eptpy5*v.lzv 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 attached to a fixed horizontt4;g: *khv jplg2vnp 2al spring whos :2 vk4pgjlgvtp h;2*ne spring 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 mass 65.0 kg jumps fo/t9;9p - ,jmrx(gc.ln dkc/ scxrf*trom 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/ ,mscjp-dtk.nf9rc* tg/9; or(xlc x comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrations in e79i8rzaps2 1ro s9 ;vqj1 esidxactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exa s8po.cgsx3o4 ctly one swing per second? (That is, one complete vibration takes exactly 2.0 sgs4xc.o p8o3 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on Mars,og( a1k5j)m;t+a yi3s zfax0 7nkdpk/ where the acceleration of gravity is about 0.37 that on da1k/tzag ymfk) o ;i 7(s+kpj53x0 anEarth?    s

  What is the period of a simple pendulum1m5wqg; xpp2x 8gwf z) 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum ia ,d;u8ya1coyzmb 49 ts 0.760 m, the pendulum bob has a mass of 365 grams, and it is released at an angle of9t4u;boadc1y ,ya mz 8 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 e,,m 63 rop jwb)-nktypendulum has a length of 0.9930 m. If the clock loses half a minute per day, how shou 6,b e3wyk-)nrjmpt ,old you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximum speesqi 4-ow,er qd)zz+a/ d $v_{max}$ 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 released f,v( -ta5cbljnrp6ri 2rom rest starting at an angle of 15 ba l5r2p -jvr6,n(ic t$^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests pass the bow of his anchored boat xvli0-e6czop2 7- n reevery 3.0 s. He measures the distance between two crestseexi-c 0-rz nl76p2v o to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with a speed l+igul13oj x+m:vj .z j 87pvqof 343 m/s How far apart are the wave cresjjj.g:+li1 7muvz 3 ql+8pox vts (compressions)?    m

  (a) AM radio signals hokq:lpoh z5+ hb6)jn/ ave frequencies between 550 kHz and 1600 kHz (kilohertz) and travel with a spee hbonh)lp+5 j oqz:k6/d of $ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

  Calculate the speed of longitudinal waves in ck*a7t3;m do03jamca5; qqevnzoxn8 ::, giw
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same 3m/-nfc ,iamh elastic modulus, but one is twice as dense as the otnha3 -m f/cim,her. In which rod will the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is : fu*l,q3nw .t xixy-dstretched between two supports 28 m apart. If the tension in the cord is 150 N,y.t,q xu: -xl*dwnif3 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 length 620 mz gi 2 -wy4n1du llifbd2b:q:5 and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and senq wydbu5bl: gi:2l n4i 2fzd1-ds 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 sid+1asv .tv.dw:zf n0i7c5pao ke of his ship just below the surface of the sea. He hears the echo of the wave reflected from the ocean floor directly below 3 .t0vnpafc51+kizvo7.dsw :a .0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at different speee t3y0t() tktmds, and this difference helps in loc(k0)tettt3 y mating 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 approximated by a sinusoidal tlec ,eo;:s.yhxcc;uq0o *5c7y7 z*;dvgyi fw ransverse 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 a>g] ;zq o:c*ywcyc iu v o 57y*cdslh0 7exeg;.;f,   m

  What is the ratio of (a) the intensities, and (b) the amplitudes, oferc ak2v8yqh)k7l6 4 c5;asxa an earthquake P wave passing through the Earth and detected ata5 c8vs;kkqy 2rhe6l 4ax7a)c two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is measured to bi ub7zlt5h/w /6avi:n e 5/ /lz:viniwbut67 ah$ 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 samis 1t.6yax6a1gm/ s(hjb*n0o8dp mw he frequency travel through the same portion of the Earth, but one is carrying twice the energy. What im 1o8/p.6 *ga(0bx1jhmsdnwah y6 ts is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string kuuvv 8,t inp7 0jj,a3zgc3c 0have the same frequency, but one transports three times the pokai70nz0uc 3cvg 8v t ,ujp3,jwer of the other. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed tokrw/,ps8ty9 )j zr9 r9 -rk-pa hqcc3g move up and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease to hkpg 8 y,c9j p9-at3 z)rrk/-r9csw rq4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving 1 8ro/wf0:1ez rohgo6tq .wmrtoward 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 each other, the string is straight. What has happqrozf611 .oomt0:gh8wr / rweened to the energy at this moment?

  If a violin string vibrates at 440njddm/; e.0ikc r) e-,wfxsd9 Hz as its fundamental frequency, what are the frequencies of the first four he.ier)/s ckfdw,-nj;x9m0d d armonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what frequency will o;43 1ii:y08 sj tjvo8cpnbpoit vibrate if it is fingered one-third of the way down from the end? (That is, onlp4vij n:ib0o8 jp13oy ts c8;oy two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonf 41s zt h8 :wih;ld*ssu4tmz-ates in four loops at a frequency of 280 Hz. Name at least three other frequencies at which it will r8 tsf; h4u-m*sd:si ltzzwh41esonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a/n:9rw 2cbtfyqp,zx ,c 1 7mfa string is 92m/s If the frequency of standing waves is 475 Hz,f/wqfr b2yt9cp:n z1,x7c am , how far apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 2802j* smynj,(b.1lor,w. lk5.lb a regv Hz and 350 Hz, what is the frequency of the fundamejv bl,yr (k5,jo. w*l galnb.1.2rmsental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. Thegxcp /q-z+*4)pxhoy+ *2qt54 jtjjanoz/ r t q distance from the bridge to the support post is L = 62cm r /jtjo4p2ah* ) p+t/tco* jnzx+z5 xyg4qqq- 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 Hz, but iots-vru ;6fv/) za7 o*m6el s*ubh54y lkvnj/t is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to corrr*67vj )/ asvekuh4szl -;l mn5f /6oyuv*tobect the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibr u7.pc z3fchg/ate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frc.z/ 7cf3 pghuequency? decreased by    %

  One end of a horizontal string is attached to)t6tz1m )y (,sb tquera:.ojo a small-amplitude mechanical 60-Hz vibrator. The string’s mazt1yo.tu:)q , r)ebtmo 6ja(sss 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 strin ; hxq4wgy r**u+pzmy9g may be adjusted 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 and xyw*ymr9h4 q* uz;pg+1.5 m?   

  When you slosh the water back and for* cjjhb *ajl6;t/ 9yrzth in a tub at just the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose thyhrjbaz*;/ l9j6*ctj e 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 waves6a c( dpqzdm6uki m-ovi9);, traveling at k.0 km/s strikes a boundary within the Earth betwk,-9d6c o piq6m izva)d(;m sueen 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 ul lm3wg (2fv,ero 2-jthe velocity changes from 2.8 m/s to 2.1j g(u2wll f3-2emr,o v m/s If 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 cold, dense a0/; 0doy+zie9gqb hp w/:wy ojir. If the soue+zq0hgj:o pw ;i ow//yd9b0ynd 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 sttzm1g gab;. 5rrikes a boundary between two types of rock at a r;gm1.bzga 5t38 $^{\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 manz20k2vur1b+tz qcffqx gk; /8ual, the dish haszfb tk2kq 2c0g/ x;rvqz+u1f8 to be pointed in the direction of the satellite, but an error of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 250 km and velocity 0/m5dv52qau5pgw c ti 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 died during tsunicwmqda/vg 2 5t p5u50amis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness constant of 5a sbm :x uy5a0;v/if-klml+2s50 kN/m Find the maximum compression of the bumper if the car, wialsm/0amk; -buv+2:is fly5 xth 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 window to a f t4 e9z;jt oiek-h2d*u8at9l+kp b+osire net 18 m below, which stretches the net 1.1 m. Assume that the net behaves li -okuzh+ps * +9a8 e42ti;kltteboj 9dke 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 s b2y whm/*5ozbpring. The mass then falls 33 cm before it stops h2bm*yw5zo/band begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 11–54), co8v o1 sqbb.n5v2 vds h0l+y4pompressing the spring 5.0 m. (a) What is the spring stiffness constant of thenvl.v84 hob10 2ysb5od +sv pq 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) atj,d8u* ia b ptsgb0.e3 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 spee8,*bt sp.eb3g a 0djuid of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm 4o :qa2cjd/ rofrom the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What wil:j2 4qo ac/rodl be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0 : zzjrqu(+m2q.650cos7.40t where x is in meters and t inu+z2qqmj z:r( 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 wuudh y/, uu0c7,gh k* e1imxr1ith frequency f. What is its frequency if it accelerates at 0.50g (a) upwa ruhc1 /*xh dmu,gk0ui yu,71erd,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg xh( ozclrddf80)6c -s man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the raft vibrd -c f0(s8l6doc rhx)zates 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 playu 3 o -z6sdcee1bm+tifs1(qo : at 392 Hz (G) and 440 Hz (A). 3zsb6 to +imefs1c o-d:(1equ
(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 down7. 0 +mvnd k-rouvdpdx12 a/kc the stretched two-part cord of Fig. 11–33. Determine a formula (a) for the r7 0mnac.r/pk2dv-ukd1 xod v+atio 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 greater in the heavier section of cord or the lighter?

  A tuning fork vibrates atxxj ocfq)0:7v a frequency of 264 Hz, and the tip of each prong moves 1.8 mm to either sidefxo : xcj)qv07 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/avvqys /7 d(k harmonic motion of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56v/(s/yv7 qd ka) will not lose contact with the board during the oscillation?

A string can have a “freexres35;oz w 9k” end if that end is attached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with one erw ezoxk9;s53nd fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — ;pu;qax k e:f/g)xf1 ktlw /v+i9wx3weach one-way swing takes 1.000l wqa f+:p9k 1wt;u;kwi/fxx)xv/3g e 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 sdcw -opwse:c .8d1 f7ypring can oscillate in the vertical direction or can swing as a pendulum of small amplitude, but not boy1 :.cw8wd fs-7cdpoeth 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 255 p::fcd7(rh w nN. A pulse is generated at one end, and 20.0 ms later a seco: ncpr(hf7w:d nd 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 wi 1/hqerp nq7r0th spring stiffness constant k. A penny of mass m is pla1hq7e r0qrp /nced on top 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 crane cable isfj:nn0 xr :c qn2i7(hpvfc/ y1d 5ais. 22 m long and has a diameter of 6.4 mm. :xr 2(pnfy jdi: 0vs/nqh 7na1ci5.cfA 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 as4u- xv1k.uyd(ile- xh shown in Fig. 11–58 (which also gives the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this vibration, givehevkd4-u ux i(x.1-yln that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz