Give some examples of everyday rxp:v bhm6w9)wl38ubvibrating objects. Which exhibit SHM, at least approxil w3hb6:)b v8uxp w9rmmately?

Is the acceleration b8rbn0j98.bamkr8m- yuja1eof a simple harmonic oscillator ever zero? If so, where?

Explain why the motion of a pidm,rn73) rcw3nq9kvqa l h;p(ston in an automobile engine is approximately simple harmonicw,pcqrn ndak7 v( hrm3)3l 9;q.

Real springs have mass. Will the true period and freque c 6:k6 vxjwj(*djgvx2ncy be larger or smaller than given by the egjd jvxxjw6c k(2:* v6quations for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double c8pyofi1a .; v- -moxmthe maximum speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hookv5yjcb5et86ozdo (hag1 zp.a3/. u v j of a vertical spring scale, and then is released. Describe the gcb58oa uvod3 /zhj j1t.va65pez.y( scale reading as a function of time.

If a pendulum clock is accuzyi ab7n-) f;vrate at sea level, will it gain or lose time when taken to hn-if7;) vba yzigh altitude? Why?

A tire swing hanging from a branch reaches nearly to the ground (Fig. 11–48). Hfy)j: 5*oxr0 hxygg 3uow could you estimate:3gyohy *j0f)xugxr5 the height of the branch using only a stopwatch?

Why can you make water slosh back and forth in a pan only :si4 p+blgwjq djaw-81 a(p-iif you shake the pan at a certain freqlaj1:8 pwwdg-j( -i 4abipsq+uency?

Give several everydac-04j/1du xx wdj,hxwy examples of resonance.

Is a rattle in a car ever a resonance phenomenon? Explain5q5zg68cj upm b(fm 5p.

Is the frequency of a simple periodic wavetdi0 j9(2sf ,y tatj:6zn8fh k equal to the frequency of its source? Why 8:0aj tktn2dzf jh6 ,fsi(yt9or why not?

Explain the difference between the speed of a transverse wave travep q77kr93od ou)8djddling down a cord and the speed of a tiny piece of the cord.r38ko 7d)o 9ud dq7pjd

Why do the strings used for the lowest-freq7yi r6ocfmz )+uency notes on a piano normally have )zc7r+myoif 6 wire wrapped around them?

What kind of waves do you think will travel down a horizontal met lzz/-vt,b da:hpi2m vs2( w/ual rod if you strike its end (a) vertically from above and (b) horizontally paralleldib/z:wsv (-/m zlh, 2vt 2aup to its length?

Since the density of air decrea8cd7,3awck 7atuj3d nses with an increase in temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves in air to vary with temperature? 3c8a j,t3k7wuddna7c

Give two reasons why circular water waves decrcl3 zs)si p(r:ease in amplitude as they travel away from l(p )3 sscrz:ithe source.

Two linear waves have the same amplitude and speed, and o hbrf)eut1mu .o47 j8mt lrt35therwise are identical, except one has half the wavelen5f ) t.tur e8t7hmor1ul4jm 3bgth of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between tgp 64h6 atdqb-wo sections of cord as in Fig. 11–33, the freqg -t4qbp6dh6 auency does not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three sn qy37gvps;k0c*c c d*egments, are there any places you could touch it with a knife blade without disturbin*03vg*; c7yqkdc sncpg the motion?

When a standing wave exists on a string, the vibrau4s gc/ xro0 q))(qqgxtions of incident and reflected waves cancel at the nodes. Does this mean that energy was dc xgugq0(q/))q r4soxestroyed? Explain.

If we knew that energy was)9ex+oujt 3 mg.t2nlx being transmitted from one place to another, how might we determineg3ottl ju)+mn . 2exx9 whether the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, wo8qbzrc+r2jcr 1 / ge1hat is the total distance it trr qcrjcz ge/ob8211+ravels in one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs frp z,8e m- cl(5lolyv4 csebtys/k052bom it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” constant k of this elas0 s5o-tlb ycbepczs vlymlk4(2 5 /,8etic cord?    N/m

  The springs of a 1500-kg car compress 5y i7r bg/5h8v/ ,psxzw.0 mm when its 68-kg driver gets into the driver’s seat. If the car goes over a bump, what will be the frequency of vibrations? zyghx5 w8 pbi/,7v/rs$\approx$    Hz

  A fisherman’s scale stretchesn(ap262og ada kfh fo*e5,mohf2a* n) 3.6 cm when a 2.7-kg fish hangs from it. (a) What is the spring stiffness consonfn2k ehao af*6fm(h*o2pd 25aga ,)tant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a frequency of 3.0 Hz when a mass of 0.60 jh)k.)*q/o yvh+f/u tlzdfa/q6l )yw kg is hung from it. What is its frequeq.df6a)/zu)v hq jyl hy)towfl /+ /k*ncy if only 0.38 kg hangs from it?    Hz

Construct a Table indicaa tar. h) i/h,tl-mrr6j(fip6 ting the position x of the mass in Fig. 11–2 at times t = 0a.p -m j 6,a(/hrtrrfli)t hi6,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’s web. The webg6ri* mbswh/. vibrates predominately with a frequew * ghir/6smb.ncy 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 rz8b*c 36/l 6qaj+zh h+*hriou*sgz n0.88 Hz. When an additional 680uhl j8+ znh6rgaozc*r *+ hi3q*zs6/b-g mass 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 timesd . fnbz2ty3gy.hvus s5(u;-c j:lud) per second with an amplitude of 0.13 m. Determd3y; gfsh:yb snju)u(cu 5.vt .z-2d line
(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 t7k5o) dt1mxv:z d 1-zn)gogqi he maximum value? ikdq)5gxt z1)no gm 1z:v-o7d$\approx$    A

A mass attached to the end of a spring is stretched a distance z 2+2hpto0apk $x_0$ 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 stg;r/42 l h hzuxe4af-dretches a vertical spring 0.315 m. If the spring is stretched an additional 0.130 m and released, how long does it take to reach the fzlrhgdu-x/ 2;a 4e4h(new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with spring stinf rqr6b 6w +9jz c2.tu3yqg8tffness constant k = 280 N/m and is executing simple harmonic motion. Whr+ 9rf63.jtgcw t n26 bq8uyzqen 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 v;hvcgg ins75-j)q4kmbs,(t2 mhh 1dto compress the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will the b1 7,hvhd sv-)k qct4 ;hnjb25gm(sgi mall leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attachedz,pnxq5q:*vq, x(sbdz,4 v, fj r8yow 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 experieq,r ,zyvz58,vpx bqdw o,x qs(:j fn*4nces 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 = 0.45cos6.4t whe:y.5nw5f kjsk re x is in meters and t is in seconds. Determ:fw5kjnk5 ys. ine
(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 halfgfd/ 1ch,+b teas dh9ik j4/4z KE and half PE?/b49c14/hih+ fdstda, gejz k ±    A

  If one vibration has 7.0 times the energy of a second8s21sy dx* nyj5 oq dceve g4;+hys8e), but their frequencies and masses are the same, what is the ratioyye1d+)*5nsvg 8y8s2eoj qe4chx sd; of their amplitudes?   

  A 2.00-kg pumpkin oscila)j gr5484ehx rj9ltjlates from a vertically hanging light spring once every 0.65eh) jgx5 r4tjla4 98rj 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 sprissrc:c;y/x4lm,1w5 duip w :ings, each with spring stiffnessp/5cd:wriu: ms1ys,4x li;w c constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0 .py7n/7:g hpyf p.btv.38sin6.5t where x is in meters and t is in sec /gtypn :7pfb7.hvyp .onds. 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 h/);uxdvv 3oz 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 spwc 7f-q.dz)qs a , xeypgu411nring (k = 124 N/m) is struck by afpgq n7 z1-wq1.ecuxy4d)s ,a hammer, which gives the mass an initial speed of 2.96m/s Determine
(a) the period and frequency of the motion,    s    Hz
(b) the amplitude,    m
(c) the maximum acceleration,    $m/s^2$
(d) the position as a function of time, x = (    m)sin(4.08$\pi$t)
(e) the total energy.    J

A vertical spring with spring stiffness constant 305 N/m7+ zrc7t3o b dmth8kg* vibrates with an amplitude of 28.0 cm when 0.rb3d 7t8 k7mhg cto+*z260 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 constants i yf kx9r+jf*i;6vv)w$k_1$ 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:84.6xv kk dwqe ,ytmewc3n-j 0.600-kg block attached to a fixed horizontal spring whose spr.68:wyxejt43 , n cewm-qkvdking 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 high bridge. Aj k9(nnt ,ommr tdwx4x1 hb*./fter reaching his lowest point, he oscillates up and down, hitting a lowrmj, tx*m1k to4/x.hnb9(ndw 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 vib(rjj 2gx8q cq(rations in exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly one swing perdkc*ew q3s7 8s-xt.h i second? (That is, one s*-8ewhdkx7.sq ic 3t complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period e+i;jfqgrm0owyh5),5 kud u0of 0.80 s on Earth. What is its period on Mars, where the acceleration of gravit0kj +yroiheqfumg 50,)wu5d; y is about 0.37 that on Earth?    s

  What is the period of a simple pendulum 80 hzs02:kgj(9p;n fmcz 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 pendulum b,hb8( *e+vw9v tlo 7hc ybdl3eob has a mass of 365 grams, and it is rv t+h lov9dcl,eew ybbh38(*7eleased at an angle of 12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’s pendulum has a length of 0.9930 m. If the clo u3 uoix/ o+mc;yx9l 94cpmht 4q:fq4mck loses half a minute per day, how should you adjust the length of the pendulum? shortened b3;q4chl 4 xou:o4+mymqcumi /t99 xpfy    mm.

Derive a formula for the maximum speed - 9qv8xoh/hlgxm()ab$v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillhi2a dz9xq0dr*v qwar3w 90g- in7u u6ates at a frequency of 2.5 Hz. At it is released from resud93 ndqw7 hrqgwx00z ra-*i9v2aui6t starting at an 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 anchorem w;js6s l8( mpgp/.kak gw18oui 4h9pd boat every 3.0 s. He measures the distance between two crests to be 6wk1j4pap .pg w (mh9ig8kl;6ssomu8/.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of z/1,gxel v;e7 5ut vlf262 Hz and travels with a speed of 343 m/s , lg 7evf1e /5xztvul;How far apart are the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz )q. v)g*oxav yxa9 7goand 1600 kHz (kilohertz) and travel with a s.7g aa9*g)oxvvox y )qpeed 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 longitudinah*:o)vwu*2 bljp1 3e3de kol sl waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic m3 - se-f a i5p.pdly2hp*;tnkfodulus, but one is twice as dense as the other. In which rod win 3 dy-*;.a -phli 2f5kptespfll the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is st 7 qhg:0zq l((f;nv y4or2cxniretched between two supports 28 m apart. If the tension in theqxvcnnlq: f 04y (z(;or7h 2ig cord is 150 N, how long will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to the top of a hill by a s+jh:x: .zoionman;jkd 1a/vcc3a t01teel cable of length 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the tera xo:i3 an.nh0/a;vmtj +:1z1jco k cdminal 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 k.ih osooa2q )99gr (al/frxd3by;j/the sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. Howa fa3boo;r q 9 or2/().9/xhi gsykdlj deep is the ocean at this point?    m

  P and S waves from an 8ao.d6t z +irv;9s ju sh6k0amearthquake travel at different speeds, and this difference helps in locating the earthquake “epicenter” (where the dsdzs9hia j +o 86v;ua0m.rk t6isturbance 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 xkr01gh,mx /o) jrz,p/uu nv8y*f:t q be approximated by a sinusoidal transverse wave. Assuming a fvmxn xyj//:,8) 1rukgpohr 0ft u, qz*requency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplitudes, of an ,f lc.imr ;8guvyhw s y9-/c/vearthquake P wave passing th;v myu/8.s h l vr9/c,fi-cgwyrough the Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing thuu+x3pgodb2c89 f w0arough the Earth is measured to be abgp f+0ud 2c9uoxw38$ 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 throu4 q)p4mv1ok;jejn 3wb. 84xsxmuszn ,gh the same portion of the Earth, but one is carrying twice the energy. What is the ratio of the jxm4ukso81e; j3m n.,bn)vw4 pqsz x4amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same fre rxm(ohgb0m(.p y6k7 fquency, but one transports three times the power of the other. What is the ratio of the amplitudes of the two w. ob p(6x0g7fm(kymh raves?   

  A bug on the surface of a pond is observed to move up and dodroy)bc h +6g8r l63apwn a total vertical distance of 6.0 cm, from the lowest to the highest point,d3 68cp)y aog+rh6rbl 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–:a5vuw 3tg.xyh7kae0r0i ;9 bcnxw;p52 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 later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight.u0yt vxa5p;90 a7:ncrg3b kiw;hx .ew What has happened to the energy at this moment?

  If a violin string vibra qmgboe w )*a *8x(6tdnbe v7kh9g*5kltes at 440 Hz as its fundamental frequency, what are the frequencies of the first four ha a( el9*k6 bkg8exn7bvmw*g)qd5* o thrmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what frequency w+h(me*st . eirill it vibrate if it is fingered one-third of tieh* .s+er(mthe way down from the end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequency of 280 Hz. Name at lek2w;heq 3*idqgk 0vz,ast three other frequencies at which v kw2*keqq3h0z;igd ,it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves o mf, hccj, uvf)/nb 5hsrr+7r-y*(alv n a string is 92m/s If the frequency of standing waves is 475-hcb +,s uff( j crr)nh/ly, rma*7v5v Hz, how far apart are two adjacent nodes?   m

  If two successive overtones of a vibrating sddpf u 3(jrgt07 .jy-atring are 280 Hz and 350 Hz, what is the frequency of the fuy.ar - fjputd(dg j703ndamental?    Hz

  A guitar string is 90 cm long and ha fiv)3ke *ixtax5d1,ts a mass of 3.6 g. The distance from the bridge to the support post is L = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundamental and first two *ttk1vex )di5a,x3 fi overtones?    Hz

  A particular guitar string is supposed to vibrate f7c1cj/xim, m 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 frequency?So the three frequencies are, mfc/7cmx i1,j   Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is suppose ex4sh2s4 7d4f.zwkc j(s,oisd to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency? dec4xsjd hi c(w7efz ks44so,2 s.reased by    %

  One end of a horizontal string is attached to a small-a3 *u r3ramoiu;+*6zm l9pgdlw mplitude mechanical 60-Hz vibra3m wo;69irlgz p* 3mdu+*au lrtor. 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 string may be adjusted by moving the pulley.2hxge21 vc z9. p sg/+kfty,zi5wi5uk If the hanginguv i.tg2e/wpsz,kh y21i fkz 5 +c95xg mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the wagf-3t9y-snmo io 5bl/ter back and forth in a tub at just the right frequency, the water alternately rises andsno 3 i9--omtfb5/gyl 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 Earthvp kiu ac:4i-4vtp )+i between two kinds of material. If it approaches the bok :iv-c i4+v)4 uiatppundary 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 th amz57dsnn+qz-v.y63dz3s(* )k+ yryy lnzv ke velocity changes from 2.8 m/s to 2.1 m/s If the incident wa*kk7+-+a qyzsd3n.z (vn6nmlr 5yys)vz zy3dve crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm aits5 csw +q5f5u).dv dwr when it hits a layer of cold, dense air. If the sound wave hits the cold air interface at vwq t. 5+dsscf5udw5)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 strikei4+w9 )m evrf.mfm- uns a boundary between two types of rock at a 3v 4fr)in. f+9ew-ummm8 $^{\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 abdy3-wx)ghk fhk/ j ;t1out 0.5 m in diameter. According to the user’s manual, the dish has to be pointed in the direction of the satellite, b1w3jf x/tgkd -h) hk;yut 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 velociy2cf k:2i7jxiyw i;r/ty 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusualck fy:i 27wr;j /2xiyi 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 stiffooz + s 59f6jxya-j+x2suiy0s )bc z)mness constant of 550 kN/m Find the maximum 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) + bzjoi2ss 09u-y cxmjx+)s65ayzof energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m below, which stretches(p.whs1u gzm:: ,bd mi the net 1.1 m. Assume t s :1p m,gidz.w(buhm:hat the net behaves like a simple spring, and
(a) calculate how much it would stretch if the same person were lying in it.    m
(b) How much would it stretch if the person jumped from 35 m?    m

  A mass m is gently placed on the end of a freely hanging spring. Tq8bcz kuwfb520yx9lt) l i0(phe mass then falls 33 cm before it stops and begins to rise. What is the frequef(lt2bl qu 9x0i z8)0y5w bckpncy of the oscillation?    Hz

  A 950-kg car strikes a huge spring a /.t*00 enjq7uowvxx18emgv mscz9anl9m :6dt a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffness constant of the x d:e w9q8 7 vzncts/o0em1lungvjx6 *9m. am0spring?    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 right p1erl51 c h:(y5gq3uksq-xle 0ex e4z hace 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 u3e 4qh(qleyhs1k5ce zx :xe5lgr 0- 1the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the trbter6 3 o(4dxu))o e )s,vwwcenter of a 33-rpm phonograph record have a wavelength o t 4rbee6ou)3))vwd rto(xs,w f 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according 9a rg./vz2h1nyawt7 f to the equation x=0.650cos7.40t where x is in meters and t in seconds. Determineyaagz.97 w2/ v1thrnf
(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 g nwbpr8*5y.+1 y,2 h qqgvom)ebi6gv its frequency if it accelerates at 0.50g (a) upward, o+5bg. ) r,y1pye2bwmq* ig8gvvq n6h    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. W e dh+*,apvti.hen a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the ra,de a+ *itvp.hft 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 i mat g(5b(9msm ey:o3to play at 392 Hz (G) and 440 Hz (otm(im5a gm(s 9y3be: A).
(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 q56pb-7cyew e8ymg (btwo-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 7qebc yp6ewy(-b5mg8) 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 ato*del8 gbrnl8)9y 0zu a frequency of 264 Hz, and the tip of each prong moves 1.8 mm to either side of e8 bzul n*g0 doy9lr)8center. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simple harmonic motion of frequency 1.5 cycl mu5w e:a. b 6i,izv3n vnjlvlcy(-.v3es per second. What is the maximum amplitudbi.v6vivj(lcz 3uw :yl-nvma.n ,35 ee 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 ewivatugp5 n, 4 +lw-6-a6k.+e evbbjxse 5w3und is attached to a ring that can slide without friction on a vertpb 3xeba 5t5ni-+.esevl+wkw,gj u aw6v-u 46 ical 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” pendulum has a period of exactly 2.000 s — each one-way swing take4 +:jno dv zl ;*eqush(+ipd+bs 1.000h +j evd+niq+b(dz s:o p;l4u* 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 oscilqbx)* qaa)ubq6ck1 b /late in the vertical direction or can swing as a pendulum of small amplitude, but not both at the same time. Which one iqc*bqaxu)b /) 6a1k qbs 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 oage7x7,;c r+4 6gb7xcmmqkbtlg4 1 lwf mass 123 g is stretched under a tension of 255 N. A pulse is generated at one end, and 20.0 ms l4 gl+bkex ax7;4mm6b w 7qtg7g 1crc,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 spr 0zg vg,q5e3;k+fqt qi7y7skg ing stiffness constant k. A penny of mass m is placed on top of the block. Whk7tfv3yq q+zkg7;gq ,gi e5s0at 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-qvy7f1y gcl1 8kg car at the junkyard. The steel crane cable is 22 m long and has a diameyf18qlyc1gv 7 ter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (which also gives the ds)8gr z*a v n(pom82coimensions 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 viba 8c2ov8mno*rz)(pg s rating 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