Give some examples of everyday vibrating objerx g1y il1x/.uct4 n3d2hwwn0cts. Which exhibit SHM, at least approwyt dx/grnx.031 uc4n2l ih1wximately?

Is the acceleration of a simple harmonic oscillator ever zero? If sg ybwg+8;jb- p,1rcp co, where?

Explain why the motion of a piston in an a/ l u-brm;g-qcutomobile engine is approximately simple harmoni-cl-qb/gr; m uc.

Real springs have mass. Will the true period and freqkpyqeyo t6:t1: m5xk6/f xc*auency be larger or smaller than given by the equations for a mass oscillating onqy16kt a e5p* xc/tofk6:m:xy the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple harmonic otc1; s-pf8kn v3rx)1t .cpdzzscillator (SHO)?

A 5.0-kg trout is attached to the hook of a e.) pg3 k ss/0 0j6mjvt);jlu )qimqscvertical spring scale, and then is released. Describe the sc 3sv 6;mlsmg)jju qp.t00kiq )e)cjs /ale reading as a function of time.

If a pendulum clock is ace( g2ui s,y.vhddxs2-curate at sea level, will it gain or lose time when taken to high altitude? Why?2(v.euisgd, 2 hd-xsy

A tire swing hanging from a branch reaches nearlydwqu 4g+):ah5iz;ym y to the ground (Fig. 11–48). How could you estimate the height of the branch using only a stopwaqy uwyg5ih4:m+z d;)a tch?

Why can you make water slosh back and fortq vog0rh*dh7 3h in a pan only if you shake the pan at agvd7 0hoh3qr* certain frequency?

Give several everyday ex:tdeq+2f yxhyou4f k75r297uvm-tv iamples of resonance.

Is a rattle in a car eve r0y8e2tz 9xxor a resonance phenomenon? Explain.

Is the frequency of a simopr : e8fb)4je.hng8kple periodic wave equal to the frequency of its source? Why or why nnf48 .r)g pjeoeh:k8bot?

Explain the difference between the speed of a iwcg v9ck * di / 4cd.qa6ty80dqx96jwtransverse wave traveling down a cord and the speed of a tiny piece of yviwa6xcc.*dj t d8w94ik96/dgcqq0 the cord.

Why do the strings used for the lowest-frequency notes on a piano bhnw-g mfmhv) o;n2(1normally have wire wrapp -nhh fn1og)b(mvmw;2 ed around them?

What kind of waves do you think will travel down a horizontal metal rod if you8uu217p*yyo w7io xfo strike its end (a) vertically from above and (b) horizontally parallel to its lo8wo7p1f2xoyu*yi 7 uength?

Since the density of air decreases with a x6opd3 b:rbu9n increase in temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves inp: x3r9od6ubb air to vary with temperature?

Give two reasons why circular water waves de3,4 fb;y5 *irdczrzl82degm mcrease in amplitude as they travel away from thm erf2dy g4mr35zl; 8 dc,biz*e source.

Two linear waves have the same amplitude and speed, and otherwiseo lua40yz+ygp a+(sd * are identical, except one has hal o4(sygda+a0 yu*+p lzf the wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sections of cord as./1fws xz 5hvv/q)jl pi00mpe in Fig. 11–33, the frequency does not change (although the /f5wvqpmv0shj/z0.l) i e x1p wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, ea w(2o9) ugkv0v1hgjare there any places you could touch it with a knife blade without d v0)jku hgego29av(1w isturbing the motion?

When a standing wave exists on a string, the vibratioma f xbc)5 rkod5w;s -f(-ocf/ns of incident and reflected waves cancel at the nodes. Does s (5ffc)fo od5;-w a/bxrkm-cthis mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one place to another,vuk61:e n(-2l 8hwmxwmh ca 4y how might we determine whethekwh 1-8( ew:mmc auny42l6xv hr the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the total distance( +jx 6cnu) lk6honf8a it travels in one perif66cho( u kn+)jxla8nod?    m

  An elastic cord is 65 cm long when a weight of 75 N hq))qnc v-c 4gtangs from it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” constant k of this elastc )v )nq-gqc4tic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when: dkj0//zms sb. h3pzt its 68-kg driver gets into the driver’s seat. If the car goes over a bump, what will be the frequency ms://3ps.db0jtzkz h of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm whengrm36 ae lx/qld9xnnud6 /4i6 a 2.7-kg fish hangs from it. (a) What is l3x 4dnd/uil/6ng66xq ea9rm the spring 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 frequenrv idp (ix01b.cy of 3.0 Hz when a mass of 0.60 kg is hung from it. d(p 0viirbx1.What is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the vn0 e/ncj-)famass in Fig. 11–2 at times t = 0,t = -ne0njv a /)cf$\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 sp ;n xe1x ed*3a kpk,iqf.88edgider’s web. The web vibrates predominately with a frek;a.f 3qed8k xx,1de e*p ng8iquency 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 adnf)y4c rdxu61ditional 680-g mass is added to m, the f 1udx) 46fnrycrequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring s,ie+cjt fo+fm0.3nr (yvau0vibrates 3.0 times per second with an amplifs+v.miofj+ace0t(3 u, rn0 ytude of 0.13 m. Determine
(a) the velocity when it passes the equilibrium point,$\approx$    m/s(round to one decimal place)
(b) the velocity when it is 0.10 m from equilibrium, $\approx$ ±    m/s(round to one decimal place)
(c) the total energy of the system,$\approx$    J(round to one decimal place)
(d) the equation describing the motion of the mass, assuming that x was a maximum at x = (0.13π)cos(  πt)

  At what displacement from equilibrium is the speed of a SHO half bzmcbt , r 6/*.5xa4af vu(jluthe maximum valv6m,t*a4crlua.z 5x(j u/ bbfue?$\approx$    A

A mass attached to tg.3s slkc7vcrb* ;b3rhe end of a spring 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 stretches a vertical spring 0.315 m. Ifzylb:;z d gz :+v+nb)lv-6pl.q: jtbo the spring is stretched an additional 0.130 m and released, how long does it take to reach the (new) equilibrium pjo:bvlty qv6z.-z+b: :)d bp gln+;zlosition again?    s

  An object with mass 3.0 kg is attached to,ut78ik5bq:h r*r:x w4; xf yib 7fv 0slr3bbi a spring with spring stiffness constant k = 280 N/m and is executingl7 t7bw*y4:x ;3:kbu05 rxifrh, 8iqbb vifsr simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is moving with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compress the spriye s0;rh phf2up iol5y;o:j 2)ng of a toy popgun 0.200 m to “load” a 0.180-kg poiurs:h 2fpe)5o0 l ;yhjy2;ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, friftle; anx jho7)ck 5(w;av4w1ctionless surface is attached to one end of a spring; the other end hww(aklt e;7v4 f1a5jx)cn ;ois fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, the mass experiences a maximum 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 acwwrl7g40mc c4xz hi7 )cording to the equation x = 0.45cos6.4t where x is in meters and t is in czx0i) 47l4ghmrwc7w 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 equilibcrag)b*(dtwd7p w9 .scq;h e*rium is the energy of a SHO half KE and half PE?;w twes*rc*d.7 p( 9daghbq )c ±    A

  If one vibration has 7.0 k7m3h2wh0z jdtjyq:77 cq qx-times the energy of a second, but their frequencies and masses are the xmhq7y-j z32:wdk7t0qjcq7 h same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hangin/i*ixjsvnx4 bl 0ups 33m x8z/g light spring once every 0.65 s. xj8ix/ b/suv4z *sn0lx m3pi 3
(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 paralym/ug nu(b5 w(lel vertical springs, each with spring stiffness constant k (Fig. 11–49). What will be the frequency of vibrati b/wguu(ny 5m(on?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t 6: 9k+/kguxn j,9idzsw3lqa s ( dj*jywhere x is in meters and t is in secondsj3z+id/w*sg laujn,(yxs q j9kk9 :6d. 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 andx he99r(the8bp;q :cq 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 osg) pk. e5 xfvyt*t/5an the end of a horizontal spring (k = 124 N/m) is struck by a hammer, which givet fya5. /)x*svk5ptg es 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 constaj qfg0 lvw.z+7nt 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes th.fz+qv7j0 lw grough 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, m+jp(+u9h ej/ch8d h t4dr s7lwith 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 ans hr)3k rzm(* 0.600-kg block attached to a fixed horizontal spring whose sprinmz)h n3rsrk(* 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 high bridge. After reaching hiqby 3,u 4:6g;jsdiumj5no ( uss 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 unstretched length of the bungee cordj:ygsbm5 i3jqun 4u, dsu(6o;.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrations )28wo,gn*ql5 ;jbdgc9 i rsilin exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is 2 uz9p2refznv0w .n.cto make exactly one swing per second? (That is, one complete0 .2znr e.n2cwuv z9pf vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period ogiff6)i+2kogx k3l a :n Mars, where the acceleration of gravity is about 0.37 that on Earflgg3+ fi6iokak :2x)th?    s

  What is the period of a simple pendulum 80 4,c:s tqo,-w -yc:*m*aoyo/ pamyqvy 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 pen c0* fwxcnv0on),x )ktdulum bob has a mass of 365 grams, and it is released at nn,cxt )w)0*0kcov fxan 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 bb9tb y,1hgysc,x 59em. If the clock loses half a minute p15 g beys,9,bt bycx9her day, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the2 ;gs8zjzm-io maximum speed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates t0hsn vzg dyi9 ,a7t( u)8bv7eat a frequency of 2.5 Hz. At it is released from restzhey9) ,7b n vg8aduivtts7(0 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 cdhh1k-p0x*1 kuti y5l/ bi4 gcrests pass the bow of his anchored boat every 3.0 s. He measures the distancexh byu1k4g5-idli0k *t/h1 p c between two crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency oqhhiy1 (-1nwpy -i tryf,r156x w,bhof 262 Hz and travels with a speed of 343 m/s How far atyb,iwfwoin 6q 1-5(hy h1,1phx -yrrpart are the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (kil9mxrg( esu(+4)d us6(mug il wohertz) and travel with a i ( 6u+l9 uem4g(su)r mwxgds(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 wavetefh brgv5:/,s in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, ghjwl7 4*2f okxi06 ,cbiu ay9but one is twice as dense as the other. In which rod will the speed of longiucxlbyi ka2,0j hf4wog* 9i67 tudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is str,6yo(de-1;7mh mlr0jrpq s fl) bcz* wetched between two supports 28 m apart. If the tension in the c 7oqmbdls yjl) 0mfr1(pwh *z e-cr,6;ord is 150 N, how long will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to the top of a hill by a steel cable ox vd fc,p)b,5xf length 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and sends ad, fxcv5,)bx p 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 h5z;/ uk-okqn side of his ship just below the surface of the sea. He hears the echo of the wave reflected from the ocu/zk; q- hokn5ean floor directly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an eartgvfkuvwaamot -3l3 bu0( - z(.cd87eomo)iy0 hquake travel at different speeds, and this difference helps in locating the earthquake “epicenter” (wh iy .dbwz-8k3mug 3e-altv0v 7oof)0(oa uc(mere the disturbance took place).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced surface wave can be approximated by (6 nu;f;f ujs6 jj-edaa sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplituej;f juj;6(n sau -6dfde 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,zr+m zm)0ip7l dii;(f and (b) the amplitudes, of an earthquake P wave pasf;lm0 )z7zr +md(iiip sing through the Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing througgow5 sp4x9y 3fers5i. h the Earth is measured to be yi grf xowp55se39.4s$ 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 of gc* wr hf0l/t:l v:3yrthe Earth, but one is carrying twice the energy. What is the ratio of the amplitudes of the twof wc:* 3l0gv rry/hlt: waves?   

  Two waves traveling along a stretched string have the sameqh u(:vwg*q6pb2ta j4 frequency, but one transports tt j (2wuh6 b:qqvg4*aphree times the power of the other. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to m:;) kpny xejnsf0a06oove up and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm, by what factor does the e6n00 s:a);oy kpfj xnbug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward eactdw lme(;n:0r z44q mzr9)u pbb/(zjkh other. (a) Sketch the shape of the string at the moment they directly overlap. mlujbpe9r: ( (/b ;w4 qdk)4zzn 0mzrt(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 its fundamental frequcy.2v b7tkw; uency, what are the frequencies of the ywcvt72; ubk.first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrate9(-ycav bl,i9+gom ucxg4 o0ns at 294 Hz when unfingered. At what frequency will it vibrate if it is fingered one-third of thegc(+-9l xun g4ov9 0ibmocay , 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 frequency0ua u ns;s6m1tehrb 81 d.vqc2 of 280 Hz. Name at least threeb1uevh mq au0 s;6.28dnsr1ct other frequencies at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves onmqrzx0ytb;68qnhr5sloy +) ( a string is 92m/s If the frequency of standing waves is 475 Hz, how fmyn q qorh stb8;)5x+yl0(6r zar apart are two adjacent nodes?   m

  If two successive overtones of a vibrati6*pi y6a2- +8vpm)tj 50 wugs zmjbc4wnp3blong string are 280 Hz and 350 Hz, what is the frequency of the fundaw-a ) 4n pc6mygu wzjjipb5v3 ptm2 +b0*8osl6mental?    Hz

  A guitar string is 90 cm long and has a mass of 3 q gsj5ja51pp-.6 g. The distance from the bridge to the a-5 p js15gpqjsupport post 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 vibrz6icue p6,ia;5v m2dqate at 200 Hz, but it is measured to vibaqzuve, 26 c5p6m;iid rate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is suppose +sg9pl ,w/kbwd to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what perce/+,kbg lwwsp 9nt should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attacmzzuql s6egyg (;04 1dhed to a small-amplitude mechanical 60-Hz vibrator. The string’s uy ;d e4qggl0ms1 6z(zmass 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 moy/ovph l;7el)ving 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 betwe lvp/7yhl;)e oen 10 cm and 1.5 m?   

  When you slosh the water back and f v(qln,)h uxzp -12-5poc ksnrorth in a tub at just the right frequency, the water alternately rises and falls at each end, remaining relatively c xovcqh1ppuks-lr5z)-2n, n (alm 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 with4 3yrhy,b .x*yk rigxxdu78j/in the Earth between two kinds of material. If it approaches the boundary at an incirx dyxy* bh xgyj38u 4,k/r.i7dent angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “shelf” where the velocity changes from 2.v w/p2 eliz).pdy) p,wv9r9xb 8 m/s to 2.1 m/s)ppi9wv,9b/v d) z.p2er wylx If the incident wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air when it hits a layer oy5+hb(d c1n5tao y+njf cold, dense air. If the sound w5b5( aody n1 cjynt+h+ave hits the cold air interface at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave strikes a boundary between two types of rog /7mq-wiz (gfck at a 3 zgi f(gmw-/q78 $^{\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 us3ociw2dwx0 xyh7;z ca-d8r5ber’s manual, the dish has to be pointed in the direction of the satellite, but a2 r coh7y- b08dzxc;wxawdi35n 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 e x0, v x7lus:jestz5+750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warningv ejx,tz5+0:eus7ls x, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car c b)p1mf h+ (v-re*ovhbumper has a spring stiffness 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 conservatior)bch(epmo-v1hv + f*n of energy.]    m

  A 65-kg person jumps from a window to a fir i7e7xaqco9i cc+b1onx12qa:e net 18 m below, which stretches the net 1.1 m. Assume that the net behaves aiac 19q:c cno2b+x q1o7xi7elike 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 the9a/pzl 5kdgi4 end of a freely hanging spring. The mass then falls 33 cm before it stops and begins to rgla5/dp4 ikz9 ise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes ay*atpxb)7.c6 0med l hqekv7+ huge spring at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffness consta*l xm+ 6d)h7 k0 ee7ayv.cpbtqnt 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 right pace of a:kjr+puo+h nba ;3vq7bout 1 step per second, the coffee sloshes more and more oq:;+bvh+p3kurn7 a juntil 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 from the center of a 33-rp f 2egaco,-:qx ejbz*m3ce; n1m phonograph record have a wavelength of 1.70 mm. What will be the frequency of thg2ee,c*m n bc :axq 1zefo;j-3e sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cs/n:expyko2s.n2h k*ahagy -5- fmp4os7.40t where x is in meters and t ingnsn:-ay -2e4 h2spokxk5.y*/ pm fh a 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 if 4u83ac 7xweet it accelerates at 0.50g (a) upwau384taeec7 w xrd,    f
(b) downward?    f

  A 220-kg wooden raft floats on a9,kw eq 7rn uwx/*mko(t7.bis lake. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps of r.ut,w ikm bk7enw/(x79so* qf, 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) aneo a.yv zz+8l(/dzbfh(w4d;ed 440 Hz (A)..8d;w zl / o d4ab+vzy(z(efeh
(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 travelinkf3t cm)q m0fh3;3yaqqz1 o 6mg down the stretched 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 section3o)q0h3mtcqf k 1qymfza6;m 3, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at ayrd9gc p,xx e6wpo 7gg+.x ;4b frequency of 264 Hz, and the tip of each prong moves 1.8 mm to either side od,x 6 ycbg+7r;ox.ge4pxg9 pwf 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 simp*(x-btzs n7hzle harmonic motion of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with th t-ns (*7hbxzze board during the oscillation?

A string can have a “free” end1(;swi azs,vi9q)a ub if that end is attached to a ring that can slide wi s( bq;iazw,u1a9is v)thout friction on a vertical 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 tay.m3 +ynbxgzu62e)hr kes +3 bmh2.)ygxunzr6ye 1.000 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 oscillate in the w((pd;pg h34s3 nd qf)8e tyqfvertical 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 horizontal swings, and by3gh4; ) qq( fs3d8 pye(tpfdwn what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

  A block with mass $M=5.0\mathrm{kg}$ rests on a frictionless table and is attached by a horizontal spring $\begin{pmatrix}k=130\mathrm{N/m}\end{pmatrix}$ to a wall. A second block, of mass $m=1.25\mathrm{kg}$ rests on top of M. The coefficient of static friction between the two blocks is 0.30. What is the maximum possible amplitude of oscillation such that m will not slip off M?    m

  A 10.0-m-long wire of mass 123 g is stretched under a tension of 255 N. o. )3-s3ivddlnzw 8 koA pulse is generated at one end, and 20.0 ms later a second pulse is gz.l8o d) vnsw3 k3i-doenerated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a 6e77nkvg m 6(syahau4i5c:b kspring with spring stiffness constant k. A penny of mass m is placede aik vc4ha: 6gkb75my(7su6n on top of the block. What is the maximum amplitude of oscillations that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg s +s:x ) cts:er;q0digcar at the junkyard. The steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts theqrx +:0gt;d sci:ses) 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 platea4q +rnzm,d ;g 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 frequenn4 q,azrg d+m;cy 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