Give some examples of evea.ca 1i)d 2q*ew ;hpnmryday vibrating objects. Which exhibit SHM, at least approxhcd qwm*ain.2pe;a)1 imately?

Is the acceleration of a simple harmonic oscillatlezz 7fvd +m: ta:w +/y hr07j.+ohvcts9l1efor ever zero? If so, where?

Explain why the motion of a piston in an automobile engine is approximately sifhuqq3hgz;8*glj2)8 r f3 5 v.amtnuzmple h5za )2*t.8 h3 j nmrugv;uzfqfhg lq38armonic.

Real springs have mass. Will the true period and frequency b6 fwaui 12m:o*78eflw twqc+ ne larger or smaller than given by the equations for a mass oscillating on the end of an idealized massless spring? feww 67 n aum1 owftiq*c2:+8lExplain.

How could you double the maximum speed of a simple harmonic oscillator (S3 rxcs, l3hpg,kj 14mwHO)?

A 5.0-kg trout is attached to the hook of a vertical sprk3:2lhz*c lqp: hjr uh8(m+yh ing scale, and then is rhh:z2+ lr qpjkc (8:mhyh*lu3 eleased. Describe the scale reading as a function of time.

If a pendulum clock bpqs4/y*;8u prc 1ffyis accurate at sea level, will it gain or lose time when taken to high/ s8 rf1cqpfub;*p 4yy altitude? Why?

A tire swing hanging from a bran s/lz z9zatm3;vhj( k/ch reaches nearly to the ground (Fig. 11–48). How could you estimate the height of the branch using vzl;/a9zs 3jt/kmzh (only a stopwatch?

Why can you make water slosh back and forth in a pan onlyy ix )ky(zzf8q -dfg+5 if you shake the pan at a certain frequeny x8d-5 (gi fzzq+fk)ycy?

Give several everyday examplesaely414c + xnd-sn8 ga of resonance.

Is a rattle in a car ever a resonance phenomenon? Explain8m *oneabaj +:.

Is the frequency of a simple periodic wave equal to the fro0t:oh 0p4 e r05vamriequency of its source? :ra 5oir00ov0 he4t mpWhy or why not?

Explain the difference betwenqpyhue 5 3q6a*fbzt2n+-a 1uen the speed of a transverse wave traveling down a cord andutbn1 yz u-qq ah25n p6+3*fea the speed of a tiny piece of the cord.

Why do the strings used for the lowest-frequency notes on a piano zjd8x/ py:/y9 tpym0dnormally have wire wrapped aroundm y8p/:xy/pyz jtd90 d them?

What kind of waves do you p25sfmots/v9v m /t4igi))a i think will travel down a horizontal metal rod if you strike go if)smp/v 9tis 4t/va52im)its end (a) vertically from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase ixo) ljl:fp pg13 x;5nun temperature, but the bulk modulus B is nearly independent of temperature, how wo)g;jop3u x x:lnlp 15fuld you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in ampli0kyr1 5mf5zjj(8/36gpxh cfa xhbe. dtude as they travel away from the sourm hj 5f1z e3/5gx.0hrpfkax6cy8(dbj ce.

Two linear waves have the same amplitude and speed, and otherwise are *u9ofm b w+c.widentical, except one has half the wavelength of u +c9wbf.m wo*the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary rf*7whdrxcb/i wut*g o+3* o:between two sections of cord as in Ff3iu+ /7x *owdw r*hrb:*goct ig. 11–33, the frequency does not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there anl9:w ugw :etnlo*hj9n6mq1wa: obc;v(fn.7y y places you could touch it with a knife blade without disturn n9wumvy c gln*bowl:( :ht6e1oqa9;f 7jw:.bing the motion?

When a standing wave exists on a string, the vibrations of incident and* w+qzfe: bw x08dvo3e reflecte3oebqxww+ 0dv*8 zfe :d waves cancel at the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one place to another, how mig7g.hs ;-e8 fjlb vyw/ght we determine whether the energy was being carried by particles (material boj;ebv ggw8/hslf7 .-ydies) or by waves?

  If a particle undergoes SHM with amplitude 0.1onkg u;h),j7w8 m, what is the total distance it travelsk hu,j n7wo)g; in one period?    m

  An elastic cord is 65 cm long when a weig cn.9uso( d-kwlyyz u( +p0j2zht of 75 N hangs from it but is 85 cm long when a weight of 180 N hangs fr. 2dy k(sz o-0lnypuuj9(cz+wom it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compres;28lwzwi ( .s;y uafirs 5.0 mm when its 68-kg driver gets into the driver’s seat. If the car goes over a bum is y(i;wr2 l;wu.az8fp, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2. sb 0 p9:exeh2xuorxcv-4u4-w z(rl p5df.d+f7-kg fish hangs from it. (a) What is the pseff4x-4e:xo +5xv(rlz 9d-u dc0.w ubrhp 2spring stiffness constant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a frequency of 3.0 Hza:6 ,atw:y2 (zqccd na when a mass of 0.60 kg is hung from (2 6cacy,zaq:t wa d:nit. What is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table ind r:ttqnuaz7; -icating the position x of the mass in Fig. 11–2 at times t = zr :tq ;tnua-70,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 caught in a spider’sk/:ldde60-47;.r /physvja rnc,xi os ti zc 3 web. The web vibrates predominately with a freque3rct4rj7.ssozhki :vxy/6np dlia d,c/ 0; -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 vibrates with a frequency of 0.88 Hz. When an uqxsf2ht)bv ;msoch- / u4v :-additional 680-g mass is added to m,uvv shm4c)u t-xhqof2/;: b-s the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at thi2gngh5- tz, g(m h2lee end of a spring vibrates 3.0 times per second with an amplitude of 0.13 m. Determine h ,hg ( lg2ngtzm2-ie5
(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 hal+wya jfph//y;8 m:ggnf the maximum valgaj/hy +ng yw 8/:p;fmue?$\approx$    A

A mass attached to the end of a spring is stretched a dio; /pk4e) 1 rdsy7nglfstance $x_0$ 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 lwdan0t).9*cfl3*lejms a;a the spring is stretched an additional 0.130 m and released, how long does it take to reach the (new) equilibrium posiane0;9 wa * lfsljm3 lct)a*.dtion again?    s

  An object with mass 3.0 k-n5dji6crpc s4h1p t qajx0.qdg *12sg is attached to a spring with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is moving with a speed of 4-gshs.ta p15xpdcj d61qiqr*cj n02 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 compredqs7ee+2 ) ogbss the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed w 2o) degq7bse+ill the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionlesstv)i0r g5y (qu surface is attached to one end of a spring; the other end is fixed to a wall. 3.0 J ofti5gv()r 0uqy work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, the mass experiences a maximum acceleration of 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.eyn3adls o*q pqf: f3d srv3*;nq59 k+45cos6.4t where x is in meters and t is i3ndf*5l3* +:yase3 fsd qo ;qqn9krpvn 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 enej j/ka;v -7bk / 1uxhsetyey(u8h-z +crgy of a SHO half KE and half PE? ±ke c1u(hjeh-8sy a/;k7v bx+zjyt - u/    A

  If one vibration has 7.0 times the energy of a sec lyoh. enz+0*n)2ps( uliahx,ond, but their frequencies and masses are the same, what is the ratio of their ampl.p20 *ae)nlu, xnis+ohz yh(litudes?   

  A 2.00-kg pumpkin oscillates from az 0 n8e;dme6jy4hixq: vertically hanging light spring once every 0.65 s:0j6nihdzyx e; 4qe 8m.
(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, 1u56)h zroyxi each with spring stiffness constant k (Fig. 11–49). What will be the frequzo 6xhi1uy5)rency of vibration?

  A 300-g mass vibrates according to the equationsp ph5:f;c,8,bo2pmls gyf5d x = 0.38sin6.5t where x is in meters and t is in secso ;2: 8f,b pflgmydh, s5pp5conds. 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 v j 4mr1z0 ,u65yi8omn,zc va5byqh)a/ s x6ujof 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 m4)mhroosrnlh5 -*(ion the end of a horizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass amhm )l4rnro(s h *o5i-n 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 stif pae5 9m6mx/hgbo1gp 7fness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) with positive veloci1gmmp5 hbopg 7/eax 96ty 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 n l7ot.6a9 pyohr v0qzms 6c32to two springs, with spring stiffness constants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes a 0.600-kg block attached to a fixed horizonuaz,9 8jd:yu jtal spring whose spring stj u,8jduay z9:iffness 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 high bridge. After rea5ohg 4nj8+g1ec) w6d nfqkl2mching his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the uj5 nw)n+ lmg2d1oehk 86 gc4qfnstretched 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 a**sdr elo +kvitc8:+u)c2bt 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simplo i,+3gcekvs vg2-8mve pendulum be if it is to make exactly one swing per second? (That is, one complete vibration tas2 vovk3v - +c,meigg8kes exactly 2.0 s.)    m

  A pendulum has a period .pcn* /homxd 9s6s/n5cv/tupkl-by( of 0.80 s on Earth. What is its period on Mars, where the acceleration of gravitpb/hcv p yn.-/6c5t oun(k l* sxsdm9/y is about 0.37 that on Earth?    s

  What is the period of a simple pendulum 80 cm longwbv0u44(4tayuyxpdf ox 7;)h
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 m, the pendulum bob k*bhwy :n6pzw *-t-he has a mass of 365 grams, and it is released at an angle of 12h*nwtbw : hepk*z- -y6.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’s pendulum has a length of 0.9930 m. If thq(5s *5rpelmc ;ijh) he clock loses half a5hi)hm s*ercj ql 5;(p minute per day, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximu(yc2j nwa9d , n1+nfy1 ifs.pkm speed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at a frequency of 2.5 Hz. At it i6vjhgf ugi7s 9(,js3is released from rest starting at anisju,s 39vgf 7( gihj6 angle of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests pass the bow of his anchorea/chcq i 9,ans8* ro 34) kmbll6ephz;d boat every 3.0 s. He measures thel*i r4mch9kno/s; a ,z 3blchq)6ap 8e distance between two crests 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 q-cjz2nt(h )mn 5x--z sxwu,6p xpu9 jof 343 m/s How far apart are the wave crests (c-j,-mxt(hs9 62czujz5)nu q -p pwxxn ompressions)?    m

  (a) AM radio signals have frequl4 ir3kl1wv,tp5p; xnencies between 550 kHz and 1600 kHz (kilohertz) and travel with a spee4ilpprv, l w1x5t3 ;knd 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 o o s(h(q bit/6.g7ot2wbme9bi f longitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one is twice:.ayhx4uq cx z-j: m /j26otj3wo: fgkbe*/ab as dense as the other. In which rod will the speed of longitudinal waves be3-zatb:ouj.w:f cgx4mx /q*k /6 e2hoja: byj greater, and by what factor?   

  A cord of mass 0.65 kg i tn,y4/nux, wws stretched between two supports 28 m apart. If the tension in the cord is 150 N, how long will it ttnynwu/w 4,x,ake a pulse to travel from one support to the other?    s

  A ski gondola is connected to the to1cd .-;qjwp(l/cgj hgp of a hill by a steel cable of length 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the c/1gwqlg-cjh. (p dj ;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 sea. j sip:ra,:cv/r6n-f: 4ipvicHe hears the echo of the wave reflected from the ocean floor directl p 4ircn6ci: pvfj::,/avr-siy below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an ear6ftt o 2za8f53cv vi+ethquake travel at different speeds, and this difference helps in locating the earthquake “epicenter” (where fzvoatc 35v ife682+tthe 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 q*v5 qh1d(ejm sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakvd* ( eqmj5qh1es, 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 intenyt6h -i ,.aqqmsities, and (b) the amplitudes, of an earthquake P wave passing through thy, h-q. tqa6mie Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing throu rm-rfmugh(i w1h2+6vgh the Earth is measured to be gv(h-w mrrm2if h+u16$ 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 portion z)l-y. hv.n r ki0eynl*:rl0x of the Earthr0n lz)nxkhrv. . l e*y0ly:i-, but one is carrying twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same frequency, b-b 9foi)fbnfz e;q7 -jut one transports three times the power of the other. What is the ratio of the amplitudes of the two waves? bff-fb z jq;nei-97) o  

  A bug on the surface of a pond is : 88pz y(6dqdqk7ee jpobserved to move up and down a total vertical distance of 6.0 cm, from the l p8kjd7e (qp:z6y d8qeowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward i+e s-ypmn8)lmvxvmol8/) -jeach other. (a) Sketch the shape oo) e i m)+x-v8svny8pmll/jm-f 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 happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as itdetz7 t83h2xd wz+l ecq84 en*s fundamental frequency, what are the frequencie cdx47*qw z 2 elhd8e8tn3ezt+s of the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hzlwufhr8+0-j xw/3u y p when unfingered. At what frequency will it vibrate if it is fingered one-third of the way down from the end? (That is, only t 0y xuru/+hp -83wwjflwo-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frkkwu3vb 7nf1j 52 7bhcequency of 280 Hz. Name at least three other frequejbk72v1bhcn wf75ku3 ncies at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string i v sfk /0hh1mzmcno4gn+ 8vs(.s 92m/s If the frequency of standing waves is 1 08 h(v/m4n gc.zfsokhn+vsm475 Hz, how far apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hzzud; -o36m ehhq6 vpe2 2t, ca;0pmqly and 350 Hz, what is the frequency of the fundamental?ldm-mh aq e6y;p,2zqp0o hv3u2t6;c e    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. Thel )oyq/e5,mlyu l q2(8s hr3jf distance from the bridge to the support post is L = 62cm and the string is under a tension of 5l3lsorj28qu5y() qhlyem, /f20 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 -g/y wtzz/)rm Hz, but it is measured to vibrate at 205 Hz. By what percent should the t/) zy tgmw/zr-ension 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, b l/oe-u b) 2h:1mn,jhmk+gax yut it is measured to vibrate at 205 Hz. By what percent shou/nge+1:bomm ujhyx, -lh )a2k ld the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-ampl*.z utkthkugaa5.jh h5rp*6ras / 6f,itude mechanical 60-Hz vibratz hfhkg aks6ptt ru/5*.*5a. jr6ahu ,or. 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 sgi/ h8t5+glpb k9qc8b tring may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different stand59ltp kcbgi/8h 8+b gqing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at justw5 0:7ame/e9cfj twu9n ut, a: cnv2nu the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-, 92 eu vwt mw5juut0n7nf:ne9cca:/awide 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 withgf6l vp 79nrha 0c0kl-in the Earth between two kinds of material. If it approaches the br0l - 9nkgv60lchpaf 7oundary 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 u4jz.p;6vh 7flm 10c3tubym:o3kdv hhnderwater “shelf” where the velocity changes from 2.8 m/s to 2.1 m/s If the incident w0;yz4t m hhjmckhvp1ou3vl 76.db3 :fave 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 air. 9t-s.owg6b ufw9+ ;hkst tp:q If the sound wave hits the cold air interface at hsk6s;w: bowq.-tg+9pt u f9t an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave strikes a boundary between two types of ronuh00ica4 wqrjx+9y 7ck at ac + xu9ja4iq70h yw0nr 38 $^{\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’sa+ibvox;s n. 3 manual, the dish has to be pointed in the direction of the satev;n oax3b.+si llite, 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 a, gy dbp2e8a3y ; mll*:7u4pi0ayuemz nd velocity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people obs840uda273,am; :y yli zmpele*pbyugerve 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 consk c*:vis1o g /dbii1bn/2*cqdqy0n 8htant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collides with d 0okhi*i1 ycbc*8/2bq nn:vq 1ids/ga 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 tox)nk :ky2 b4h 2-vmyr ihs)j+*lpiqn0 a fire net 18 m below, which stretches the net 1.1 m. Assume that the net behaves likep))2j k2k xlrshhvyi0+* y: qb-4im nn 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 fr:-8t c*sstve aeely hanging spring. The mass then falls 33 cm before t*:8 vaets -scit stops and 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. 1w7;z 5y yla9as1–54), compressing the spring 5.0 m. (a) W 7s5wy9aal ;yzhat 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 cof/q95vmfkaz 12 xfzr9bfee (diameter 8 cm) at just the right pace of about 1 zb 95qf xkrz12a9/vmfstep per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm frolyspoj9 6k) 0im the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will piy0l j 9ko6s)be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t wheruz ,zpvh6qp t-t* xx1or8m51 fe x is in meters and t in second xqxt8r1* uz-p1z pohmtv f6,5s. 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 frequencylk *gp(vr* 1y+ fpc96 oueql0 q;koy.s if it accelerates at cl.r ouyyl0fk(p qp+qoe 19*sg*v 6;k0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on the ra/kl: jun6ej19ok *km kft, it sinks 4.0 cm deeper into n6 j/ekojk91m* kuk l:the water. When he steps off, the raft vibrates for a while.
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a musical instrument are tuned to play at 392 Hz (G) and ) mllzgmz6 gz;w;4 o+d440 Hz (A). ;z gm zod4m;6)+zwgll
(a) What are the frequencies of the first two overtones for each string? G : $f_2$=    Hz $f_3$=    Hz A : $f_2$=    Hz $f_3$=    Hz
(b) If the two strings have the same length and are under the same tension, what is the ratio of their masses ($m_{\mathrm{G}}/m_{\mathrm{A}}$)   
(c) If the strings instead have the same mass per unit length and are under the same tension, what is the ratio of their lengths($L_{\mathrm{G}}/L_{\mathrm{A}}$)   
(d) If their masses and lengths are the same, what must be the ratio of the tensions in the two strings?   

Consider a sine wave traveling down the stretched two-u,uloa-x* pt95 ai 8cppart 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 waveleng,aul8 icp tpo *5uxa9-th greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency ofua su h26h4k60 vsg,mo 264 Hz, and the tip of each prong moves 1.8 mm to either side of ceno4hu,6 vguahkm0 s2s 6ter. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillatesda /ornqk a 8kx w;fms+r/s(-- with simple harmonic motion of frequency 1.5 cycles per second. What is the 8 kax;s ( n-r//mrkod awsfq+-maximum amplitude with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that end is attached(b tltja68n:h to a ring that can slide without friction on a verticajln(a8:ht 6 tbl pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulumtp 9)m ve;hnp: has a period of exactly 2.000 s — each one-way swing takes 1m ;np te9pvh):.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 oscillbzxhm2omzpgm- 02xgwhh7 gle/9ij8rc51 z( 6ate 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 of the vertical oscillations or the period of the hoh pm 8/olzeh65m x7122hxwb-9i(0 rmgggz jc zrizontal 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 stretchzp 8 vhx.mpmv v9pxw07:hc:7ued under a tension of 255 N. A pulse is generated at one end, and 20.0 mh8vh97: 0v .up:v wzcxmpxmp7s 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 stmvt t36x*gpt y2;ru (biffness constant k. A penny of mass m is place tg t3yvp(m6urbx;* t2d 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 120;hi, 2 bq 5o .8noqlw1awlculh gqc*1,0-kg car at the junkyard. The steel crane cable 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 is the period of thww qqa2,; gb1.qcu, nihohl8 l5o*l c1e bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plaf nmk4:7x lb+nte as 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, given+mx:l4f7k nn b that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz