Give some examples of everyday vibrating objects. Which exhibit SHM, at qo, ng52 6k b3mhb1hozleast approxih,q2kg b 3o5hm 61nzbomately?

Is the acceleration of a simple harmonic oe2*x(3pij 76 escbhay scillator ever zero? If so, where?

Explain why the motion of a piston in 2d1ij pro7l(4qfvlkm* o-3 nqan automobile engine is approximately simple harmoni -1i*vm3rdl oqqn kljf4o72 (pc.

Real springs have mass. Will the gx5tnp-zkl2c93bx i7true period and frequency be larger or smaller than gz9 xx g25l-k37ptncbiiven by the equations for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple harmonic oscidulr(9a/h2ap;3y k e/tyx a0 lllator (SHO)?

A 5.0-kg trout is at6vfoa 5;jk h(;gxe6 vuwa1h4 ntached to the hook of a vertical spring scale, and then is released. Describe the scale reading as a fuw4a5e( ; hjugx ;1n6havfkov6nction of time.

If a pendulum clock is accurate ao r 3ic.sbhuxt75-+pet sea level, will it gain or lose time when taken to high oe5ph 7 cts -.b+rux3ialtitude? Why?

A tire swing hanging fr tg fp8 p2n,jkg9nyx.9om a branch reaches nearly to the ground (Fig. 11–48). How could you estimate the height of the branch using only a stopw8k 9n,. pfytj9xg n2pgatch?

Why can you make water slosh back and forth in a pan only if you shake the pan a,: 6h)wst mtzhmqb-mr 7k*9ew;yhg3br o5ad 4 t a c5bo4w ky tzr7gw9;t:6 m,*ame qsrhdhh)b 3m -ertain frequency?

Give several everyday ev-7 *z fgm u5yqckjw;lz +-b/4we3ifqxamples of resonance.

Is a rattle in a car ever a resonance p5d- n.zjkie xj7j 5/a9 drn7-zsi)iiqhenomenon? Explain.

Is the frequency of a simple periodic wave equh6m8/axg6xj u al to the frequency of its source? Why or why noa8um6gh /6 xxjt?

Explain the difference becxh+*2 )wsvjctween the speed of a transverse wave traveling down a cord and the speed of a tiny piece of the cordx* wcj+shc2v).

Why do the strings used for the lowest-frequency notes on a piano noru2:a mo0dm.ec7 vpbo 3+w;jk vmally have wire wrapped around the+;7 dpa0: o2m3.bemjcvo u kvwm?

What kind of waves do ym7gf ku2 qfgleg6. 9v:ou think will travel down a horizontal metal rod if you strike its end (a) vertically from above a fql7kg e umg:fv29g.6nd (b) horizontally parallel to its length?

Since the density of air d *odm p,p;mbxpoabtk/y(3 v7- yg (o.cecreases with an increase in temperature, but the bulk moduop x ba mm p .(7*g,;kbdty(vopo/3cy-lus 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 decre3 vq2v n 8xkgbeqpsi)oeq:d/z071pz0ase in amplitude as they travel away from the source.knzsqq 1p:x7/pzbee 2vogv 0 i d3q80)

Two linear waves have the same amplitude and-h)e (yos,aw- 4zoani speed, and otherwise are identical, except one has half the wavelength of the otheh ,oa yow-za4ins( )-er. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sections of cord avrlw rsmonzkx( 39w( 7x3 01kxe2*k qps in Fig. 11–33, the frequency does not change (although th*3vq9wr 2xnw0 7ke(3p lsmxkz1r ( xoke wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there anymgfn0 /dy t0e dnbdkr3()d7/s places you could touch it with a knife blade without disturbing the motion/end/dr30g) s b kmyd(f t70dn?

When a standing wave exists on a string, the vibrations ofai7r d s :-vpea))jt-e incident and reflected waves cancel at the nodes. Does this mean that energy was destro) 7pvi :t -)a-aerdsejyed? Explain.

If we knew that energy was being transmitted from one place to anothern61j+jfthfrh d1 *w00g;wujj9m+h-n s5 qekl , how might we determine whether the energy was being carried by particles (material bodies) oht*0j +wj6 s+-kj1nhdl5fu;mjg nrwh1 9qef 0r by waves?

  If a particle undergoes SHM u4n-(k+ns ubi z4go .awith amplitude 0.18 m, what is the total distance it travels in one pe .kuo-n i44uagzs (bn+riod?    m

  An elastic cord is 65 cm long when a wei trq*u nqnaa+u g0yu/b/4q* n)ght of 75 N hangs from it but is 85 cm lonnun0au *bqn* g+ua)/yq qr4/ tg when a weight of 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-kg driver gets into4:n/he ,5vx .zossyksn)8 ia adw.2gk the driver’s seat. If the car goes over a bump, what will be the frequss4h )x8.kvnk,az d.n/agyw:es oi25 ency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs:4y,jm p1/4ru htjaxf tekc95 from it. (a) What is the spring stiffnesstt9ceyuja:44pm5 ,rkxh1/ j f 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 Hzv vz98)y:y1rpj 2ifcl when a mass of 0.60 kg is hung from it. What is its freque2j:lfvyi9rc8y 1p )v zncy if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. 11–2 at qb/g2c j4x ,x*,m /lz ygf*tl-tr.kvl times t = 0,j./v q f *m /ty rl4x,,c2*bxg-lzkltgt = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 web vibrates pred )mp3f jzd f)xds dum7 ,0y.l)q)fdlt)ominately with a frequx0d)qdl )dzp 3)m,f tjy)mf)7sf ldu .ency 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 vibraw: :n+nvux(p g1txnsb9-+m o*j 7b3a lbt1diktes with a frequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 Hz. What++b * japs lt9(1:7 nbuknow-3 1xvgdx:btmni is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per second with an ampl z y-a omohw,8iuvvqac sac. 4wx x39.3*gf9y:itude of 0.13 m. Deioyw94swx xa 3uf.*y9 g qz,cv3a omc:-va8h.termine
(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 thetnl4rw8,t j.h ;y0mcg 91frl)gl e+ za speed of a SHO half the maximum value? a9clgr1jt,.mnrf wz8 t0+h)e lyl 4;g$\approx$    A

A mass attached to the end of a sprin lz8t.yb)4vv564lcpck+tlq y ,0hpc w /4zbga g is stretched a distance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stre(8l mdt)(.vj*fkuq b ntches a vertical spring 0.315 m. If the spring is stretched an additional 0.130 nmbf t).q( *8 j(dkvulm and released, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with15::au fr 6h wmop-,6wqxyzzw spring stiffness constant k = 280 N/m and is executing simple harmonic xpwf5 :oa-qyuh,w mz:6r1z6w 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 o 7n1ipy-i0mdl(fuqr- ) cl /s5v*yyfcompress the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will the balld(7 s 0uplry-*yn1oi/ 5 vqyimcf-)fl leave the gun?    m/s

  A mass sitting on a horizontal, frictn.d8 r0 w2euvyfk:q h/ionless 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 spriueyrfd/ .:hkq208vwn ng by 0.12 m. If the mass is released from rest with the spring compressed, the mass experiences a maximum acceleration of 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrat: ig85z :yyd/bzql.cs es according to the equation x = 0.45cos6.4t where x is in meters anddl.ziyg5c:s :8yzb /q 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 fjhmz r 7xbmt+n-s;l72xs t9g eua;v02rom equilibrium is the energy of a SHO half KE and half PE?m2 m;2e7zn-+ bxv0rg9;j tuxss h7atl ±    A

  If one vibration has 7.0 times the energy of a second,tdl.o,t1hz2 y but their frequencies and masses ary1,d.lt oth2ze the same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light sprin *9 t*kv jjgu9wsrj9- (q:8f+ozuqyysg once every 0.65 s. kfuty:s9qu(8-vs9q *yoj w +*g9zr jj
(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 suppxa5e9jb5u t rpca7f+ -orted by two identical parallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What will be thcf xjaue7ba95p- +rt5e frequency of vibration?

  A 300-g mass vibrates accord.s.fq67ibs vfing to the equation x = 0.38sin6.5t where x is in meters and t is i if6fqv7b.s s.n 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;ty-h b-d : bqgx.h5sulkv- d7 of SHM, labeled A 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 (kt za3ac /hw0q/ lcyl-6 = 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.96m/s Det0/wc36l h tcaaq/-ylz ermine
(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 y*um f+t/foh,N/m vibrates with an amplitude of 28.0 cm when 0.26/,* ffuyhm+to 0 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, with spring stiffness ci4 e ewj4qug0*tvl* f/onstants $k_1$ 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 fixm:pgg2*kng*sv+,r/ da3 o vdted horizontal spring whose sprindtsgg: p3*dk, v* van+gom2r/g 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 from a higc x9m6po/5sjdns.j.7x+kmt xh bridge. After reaching his lowest point, he oscillates up and down, hitting a low d/9om xj7x 5sj+pnx. mktsc6. 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 in exactly 60 s. What is itsq2+ jb1uh2wevmn9.qxl9h zg* qqh) s(
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum bewj/6vkw73)wki s uei3 if it is to make exactly one swing per second?/vkiwww s3 3k67j)iu e (That is, one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on .u1he ,8v4;s afl *2t2ualjmte-g himo(dh2o Earth. What is its period on Mars, where the acceler 8et2jm4dvhsgloa,1 2ouih-t2h .;*f ( mauleation of gravity is about 0.37 that on Earth?    s

  What is the period of a simple pe )5mfg7hpjw l)ndulum 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 pend* 0;jvg4pzx etulum bob has a mass of 365 grams, and it is released at an angleptvg40 e*;xzj 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 hassqvks d6 0t5+q a length of 0.9930 m. If the clock loses half a minute per day, how should you adjust the length of the pendulum? shortdtq skq6 5+0vsened by    mm.

Derive a formula for the maximum sg sb kl*vcx58q/7qlx0peed $v_{max}$ 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 iwj +hg fkxqv+ i:27a.t+.p qdks released from rest starting at an angle ov kigad27 xkp.q+t+j .qfhw+:f 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests pass the bow of his anchoo3i1:w ng+ px3ulhe)cred boat every 3.0 s. He measures the distance between two crests to be 6.5 m. How fast are the wavn gx)h 3 eo1+picu:w3les traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and9n m+*jonu; 1wob:mfh travels with a speed of 343 m/s How far apart are the wave crests m;+w:ubhnmoof*1 9n j(compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (kisf,bsg:tmt8sf-s -5k lohertz) and travel with as:8 k-msf,5gstf-t sb 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 waves inu qv* g0k1xldj7i2t)t
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the s;)q h qzg ;kh3p(9c7*vbaw oraame elastic modulus, but one is twice as dense as the other. In which rod will the speed of longitudinal waves be greater, and by whaog*zvpw q 9;h(cq7a;b ) ar3kht factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 msnh0 dj kw4, buk:;pdw 7xp z.hm)u*x4 apart. If the tension in the cord is 150 n,4dzxj07uxhu p:;hm* .)k wpdsk wb4N, how long will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to the to b fe*si0m-mc6p of a hill by a steel cable of length 620 m and diameter 1.5 cm. As0 e-6fi cms*bm 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 the seav00tijku1ky2.no3(f jpgdy; . He hears the echo of the wave reflected from the2f itk0.kjy(d 3j1npvuy0 g;o 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(zhwzi g 0(yp2y aa)hm/ :omi/ at different speeds, and this difference helps in locating the earthquake “epicenter” (where the dg/mh iwy(:/ ha0mzpoa)y2i z (isturbance 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 cp t8tk ; 6vjg 6n,w1w;229btzfvyxv qsurface wave can be approximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture ox9 vywq62jvf8tkng;1vc 2,;tp tb 6w zf 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) the amplitudes, of an earth/zmtt-4mrj r:, 0bkwb quake P wave passing through the Earth and detected at two points 10 km and 20 km from the souzkmw0bt : - m/r,4bjtrrce?(a)    (b)   

  The intensity of an earth1ctjw1 ,irlg 2;ijzv 1quake wave passing through the Earth is measured to be ;1r cwzv1jl2i gt,1ij$ 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 travel through the same portio,ywkb5a9sx/t8.fw y0 wid7x :e2b1itx q v z;wn of the Earth, but one is carrying twice the energy. What is the rat 2w978.vwxekttxia/w 01syx;qzw fb5,b d: iy io of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same fe o0ox4hb7( 3+e 6c-dch dnlffrequency, but one transports three times the power of the other. What is the ratio of the6oddf7f30cobnex+-e hlc( 4 h amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move up and dowjxank;0; 4ug ziz06 pfn a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decreak 0;0 ug ;xnfz4jzp6aise to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown i3iy bpeqi 8p9gb* isu2om rj:657e5osn Fig. 11–52 are moving toward each other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments later8 iob3rp5:5s9 py6eo2 ubgiji qs7*e m. (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 fundamental frequencyi+hqx h+4w- :ds)a biy 0pcbz,, what are the frequencies of the first fcza),y0 +ipw:bbxqsi hd -4+ hour harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what frequency will i 7yevqen8dk(e +rl24mt vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of the string vibrates as e2(m ekv ql+ ryd7e48na standing wave.)    Hz

  A particular string resonates in four loopsf2 qohs g*s2i6 at a frequency of 280 Hz. Name at least three 2h o*6isgs2fqother frequencies at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a st (vqktn;-wmu + ;u-j(kge fun9ring is 92m/s If the frequency of standing waves is 475 Hz, how far apart are tmu+wv jt-(nqg; ku( u9f-n;kewo adjacent nodes?   m

  If two successive overtones of a vibratp 473nm; dvqe cql-/eting string are 280 Hz and 350 Hz, what is the frequency of the fu3q ndclp- e/7tem qv4;ndamental?    Hz

  A guitar string is 90 cm long and has a mass of azvhb 7f4c4 .j3.6 g. The distance from the bridge to the support zfv4jba7.hc 4post is L = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vvc; tj;d g,ukx3n0x:i/z3ax oibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed toj 0xv/ xx:,tkd;3uza gcn3i;o correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrat3. eq9oqvwq .g;/ bpese at 200 Hz, but it is measured to vibrate at 205 ebose3v.p.;gw/q9 qq 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 attachx4vyu 7o*zfnd,)t(ko8uc6ilkcm f ./ed to a small-amplitude mechanical 60-Hz vib, )kl ci(vnfkf 7*6xyou4mt /zcou.d8 rator. The string’s mass per unit length is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of the stri.o2z lhnh., .f+m33zgoajhwcng 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 blg nmh.zc,.+ hzw.h32faj oo3 etween 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at just the right frequency, thi c7g lw he 7xoutg-do5:zw7-+e water alternately ris zgghco77wi :d7we5 ol-t+-uxes 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 tub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundary within the :,z stzbmx2n( Earth between two kinds of mz mn t2,zs(xb:aterial. 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 “f* wu2i tkjl (nqtco4d(1/o (zshelf” where the velocity changes from 2.8 m/s to 2.1 m/s If the incident wave crests make a o dun ktofc/(i*jt q21lwz(( 434$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air when it;g((r:mt no zb lzym:, hits a layer of cold, dense air. If the sound wave hits the cold air interface at a zyr t,;lgmbzo::m( (nn 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 strikean9y8l 8xln/zto *, xc9ief xb34 gpi.s a boundary between two types of rock at a c4.bz9xnlxf ii, e3/xyt 8glp9*ona838 $^{\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’sfrb4 ;n)r9yy f39caeo manual, the dish has to be por4 oyfy 3a9nb c9)erf;inted 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 750 km/h travels acrosk: njf kj-+fb3vmf/m* s the Pacific Ocean. As it approaches-+kmfb*k /j:fn fvmj 3 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-a45he5mr)gd dgmp j4 bumper has a spring stiffness constant of 550 kN/m Find the maximuam d) 4jed5-rm5g 4hgpm compression of the bumper if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m below, we1jlc-c( m)xnq6t wmv +t4vk 5hich stretches the net 1.1 m. Assume that the net behaves like a simplev() +t em-c65kvj4x ltcnwmq1 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 efv +s ,hb()ummue86r spring. The mass then falls 33 cm beb+v),e mu r( 68fshumefore it stops and begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a sfi(j96 jcx.bs ,:oc8b ncfq+wpeed of 22 m/s (Fig. 11–54), compressing the springcwsnfcfi9bo(j+8: cq.j ,6bx 5.0 m. (a) What 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) at just the rightcmx1 x.qkbe7yv2j 1+,g0 gic9 l/r xrpu4 s1ox pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the qk0isxlxv1gxb9,c 4u7gpr1mr/1. o+x cy 2jetop (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the ce+y6e207 f5z-oz uikmazp kw,t nter of a 33-rpm phonograph record have a wavefa62- ,u0zzkit75k + owmep yzlength of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to t(l sk0c-7r qbm ),w: bz 0jpyg.wwe)wthe equation x=0.650cos7.40t where x is in meters andslt) .0b7w0(yqcwprwz-e kj:m wgb ), t in seconds. Determine
(a) the amplitude,    m
(b) the frequency,(round to two decimal place)$\approx$    Hz
(c) the total energy,(round to one decimal place)$\approx$    J
(d) the kinetic energy and potential energy when x=0.260 m.(round to one decimal place) PE$\approx$    J KE =    J

  A simple pendulum oscillates with frequency f. What is its frequency y g ,uvgl1uur8kc/rp/l bs*;; if it accelep,8c;g1s/y u g*klr;/uv bulrrates at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a la7d.fo w). v6l0cx(rqap+ofbb ke. 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+bbp(xr.7al6)d vff0 o wqo.c 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 toq;lh ur4dhv3 3;p kx:t play at 392 Hz (G) and 440 Hz (A). huvt3qh x4r : ;d3pl;k
(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 strtmjqc3ogk9r4;c- f k,etched two-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the mgc4 q;9f,cjkrko-3twavelengths 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 tip of e78 qre:jtpx9h ach prong moves 1.8 mm to pe h7j8tx9: rqeither side of center. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simple harmonic motion o5(ce-zwb 1lxcf 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 placeb-e wxcz1l c(5d 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 attacp x5oiubr+:r0 j3t0mlhed 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 sbixpt3:r l u50m jr0o+tring with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each one-way swing);ivoni 1 ba:u takes 1.000i:a b iuo;1n)v s.
(a) What is the length of a seconds pendulum in Austin, Texas, where $g=9.793\mathrm{m/s}^{2}$    m
(b) If the pendulum is moved to Paris, where $g=9.809\mathrm{m/s}^{2}$ by how many millimeters must we lengthen the pendulum?    mm
(c) What would be the length of a seconds pendulum on the Moon, where $g=1.62\mathrm{m/s}^{2}$    m

A mass hanging from a spring can oscillate in the vertical dire;-3 ,s5lx3j0wwor fpjs g+mi qction or can swing as a pendulum of small amplitude, but not bo +s5 3rpslqmf0ijwwj3;ogx,- th 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 undhq90+tq;8dll b o8 qdnbhr- k:er a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at the opposite end. Where will the 80 tql;nh ddk9- qbb o:+qlr8htwo pulses first meet?    m

A block of mass M is suspended from a ceiling by a spring with g git,l, aj453gydx6 rspring 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 penny to just stay on top of the block? (Assuld5 4g 3yga,xrg,6t jime $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel crane cablf81k*f:b cww be+ bs2re is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. What iw:1 ewbsc8k*r bbf +2fs 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 givw d.lx.in;8fz -ubq,ues the dimensions of the block). You push it s,qbzn. 8ul duw i;fx.-ideways 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