Give some examples of everyday vibrating objects. Which(;y :if8 /va s0jqyd0pns7dui exhibit SHM, at least appra q / :ydpv8jui70 ;s(ysfn0idoximately?

Is the acceleration of a simple harmonic oscillenclv,: xww,c1lqs8r 4 ,es+sator ever zero? If so, where?

Explain why the motion of a piston in an automobile engine is approximatqdwfe3 3))gg n. enaa.7jx1zvi7s 7ssely simp7 s3e73i xwv7ssg.a)afn .ge1d)qznjle harmonic.

Real springs have mass. Will the true peno ; ;)i -wiaaayf:cb hs*y-i5xy-j o+lvs7b 8riod and frequency be larger or smaller than given by t;7-i:lyxwiasba fhacy o8-*i jn);5o byv s- +he equations for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum 3h4t w6gfml8a speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is atteghx 3*rzfi99 a 84u3wwp qhz8ached to the hook of a vertical spring scale, and then is released. Describe the scale reading as a function of zwh3 ape 4 hq8fuxrz9gi983*wtime.

If a pendulum clock ishzcq l l6p6yd,l-q3 5f accurate at sea level, will it gain or lose time when taken to high afy6 3q5h6 pl-l,ldcq zltitude? Why?

A tire swing hanging from -lyfr + c4ltb.a branch reaches nearly to the ground (Fig. 11–48). How could you estimate the height of the bra-rtl y4c.lf b+nch using only a stopwatch?

Why can you make water szl va,b/l7ddj wj 3l;q-ruj1(losh back and forth in a pan only if you shake the pan at a ce;bz /j17 ul(w,3l dlajvrqdj-rtain frequency?

Give several everydaysa0 o4e9bnf,l examples of resonance.

Is a rattle in a car ever a reteq-j*) lz a w7pr0h4ysonance phenomenon? Explain.

Is the frequency of a simple periodic wave e 3(-3ut-gx,ru jw eubpzjfo-3 qual to the frequency of its source? Why or why n 3g-j-z,wxt b3frj- ep3(uuuo ot?

Explain the difference between the speed of a transverse waw/myby5 si(z +2o zkgfz*/y 0eve traveling down a cord and the speed of a tiny piece of thek0 2s*(bgz//wi 5yzmyf+oz ey cord.

Why do the strings used for the lowest-frequenr,fxr1 h; m*nt:ce3o ycy notes on a piano normally have wire wrappeft :1*;hnxc,yrmr3oe d around them?

What kind of waves do you tb2u g4a2f/ s e-vq(riohink will travel down a horizontal metal rod if you strike its end (a) verticall-/a24rg e(vq2iofsbu y from above and (b) horizontally parallel to its length?

Since the density of air decreasebad98m5wgk 2uk,*hv b s with an increase in temperature, but the bulk modulus B is nearly independent of teu d* am k2bgb,85wkh9vmperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in amplitude as they travel a/ca,4 72cbmwo4i fo xtway from the scatw/2 oi4xco7mb f,4 ource.

Two linear waves have the same amplitude and spez, egjvg.sm/ih5)q ;fed, and otherwise are identical, except one s.h;i /emgzf v,5qg) jhas half the wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the (84 0zut( .kd e3oxw4eifpdjfboundary between two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and v0zw8(.(4efxo djt4kuf 3i e dpelocity do change). Explain why.

If a string is vibrating in three segments, arepc*p :.ivc2nrm42l k t there any places you could touch it with 4k.nit 2c ppvc*rm2:la knife blade without disturbing the motion?

When a standing wave exists on a str s: 8 /ggm2y42ycrkaaiing, the vibrations of incident and reflected waves cancel at the nodes. Does this mean that energy was destroyed? Explramis:ggc82y4 k /y2a ain.

If we knew that energy was being tra by t9t:h s5h;buxosz14n/k8z;u jml0nsmitted from one place to another, how might we determine whether the energy was be1x 8s5lkb94zhtmu yo;sjb u0 n:h/; zting carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 qu, mxd w:-.gw,2oktl,pey7vm, what is the total distance it travels in one peypul.mge2w7w-vqd:t,x,, k oriod?    m

  An elastic cord is 65 cm long when a weight /( b u8 dsy8s04yrezhvof 75 N hangs from it but is 85 cm long when a weight of 180 N hangs from it. What is thb/0hys 8usd vyze(8r4e “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg dri :tghlcfo;2t5q;jd-l1 s wde)ver gets into the driver’s seat. If the car goes over a bump, what will be the freq :;-h wdcqfle25d)g lo j1t;tsuency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs from it. (a)b q;nd;tf+,q d What qq;tbfnd+d ;,is 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 fred 1j+z*a.se bvnyrs,u*rvtkx **2z8vquency of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency if onlzv.by,j21avz *tss*r +v*udn x re*k8y 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x q-k,jrbfy8d ot4x44 jof the mass in Fig. 11–2 at times t k4foxq,t4dr j 4y8 -jb= 0,t = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

  A small fly of mass 0.25 g is caught in a spid,xoopw,zs 5 vhnqm *43er’s web. The web vibrates predominately with a frequency o,nwxph4 zq*sv o5m ,3of 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 freque3id;b xgn5zcs1w82id fm6i1 nncy of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is fd1bc2sng6nz8w5id3 x 1;iim 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per sec4qnh .;kjez7 :62dk-okdrxydond with an amplitude of 0.13 m.:dd q47 jker;yok.znd 62-x hk 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-zxs*0 tpqp5b equilibrium is the speed of a SHO half the maximum valp s0p- xqb5t*zue?$\approx$    A

A mass attached to the end of a spring is stretched a dis6k.s :1hgfczl tance $x_0$ 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 the spring is2x blh goty9v25+syb2 stretched an additional 0.130 m and released, how long doelb2 2 xv y2+bh59ystgos it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring l yx;:i9vk lnbau7 9o5yr7qdg2j,w w2with spring stiffness constant k = 280 N/m and is ejx;o 7,v 52:qgbw7lilyd a rn92yk9wuxecuting 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 spring of a toy popgun 0.200 m empq g9/; f -dcia7ei9to “load” a 0.180-kg ball. With what speed w df/e 9i7-cpeq;g9i maill the ball leave the gun?    m/s

  A mass sitting on a hv1r ducl10 z7+y+sb jlorizontal, frictionless surface is attached to one end of a spring; the other1+scu bl 0z71l+r dvjy end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, the mass experiences a maximum 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 accordn7 uu .rmof;b3ing to the equation x = 0.45cos6.4t where x is in meters and fnu.b muo3;r7t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement frhx9n/b pw,uz+ )9slfoom equilibrium is the energy of a SHO half KE and half PE? ± + z h9sp/ f9ux,wnolb)   A

  If one vibration has 7.0 times the energy of a second, but t7o/- u hpie- ji*.yayzheir frequencies and masses are the same, what is the ratio of their amplit/iai-yj eu*y- .oh 7zpudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light spring q7/e)y thges /once every 0.65e )/e7y/ thsqg 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 suppoj w(r,q;ss svvbgxny6/9x.e()jsvj3 rted by two identical parallel vertical springs, each with spring stiffness constant k (Fig. 11–49). Whatv3jqxgevyss.nbvx(,w r js9)s6;/ j ( will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t wherek2, u3yll+z vv x is in meters2l,3yzl kvv+ u and t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows two e3g;(olv0d47 elcjo:rcrv-0 y sxqkz. xamples of SHM, labeled A and B. For each, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on the end of a horizontal spring (k = 124 N/m) is st45 sjd.q rw*,sl- l 3dirvan:aruck by a hammer, ir:r w. n*ds5javq ,sld4l-3a 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/m vi:5d3e he5y e;(zjxfcy brates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium poiyc;yx3f :e5(e5 hjedz nt (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 eaxc5k pexqf. n4g93)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 bloy jrdzec xq::0laq440ck attached to a fixed horizontal spring whosec4jzx :q0qd4r0 ealy: spring stiffness constant is $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with mass 65.0 kg jumps fro5ic)wny ;)m+x lokh;w 6w hai9m a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the unstretched length of the bungee cordih+wonlha9mx; w5;wi6k c)) y.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrations in exactly 60 s. What is its e-a wte:z5kb2 -y 8c8pmlya8f
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum b,9/deawnj(sghoi3y1m8w q5 t e if it is to make exactly one swing per second? (That is,9esj/d (1t3hni ym8qwg 5oaw , one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its pj9r ope9-h:izeriod on Mars, where the accelerati 9 jzprh:oi9e-on of gravity is about 0.37 that on Earth?    s

  What is the period of a sylg jswl0lit69-i ;v3imple pendulum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 m, the pendulum bob has a mass ot3c4 e3ai+;kjl1 txpvf 365 grams, and it is released at an angle of 12.0 i3 cv ax+lpkt3et4;j1$^{\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 r9kk0jdb/ n0u. If the clock loses half a minute per day, how should you adjust the length of the kdjkn0 bu9/r 0pendulum? shortened by    mm.

Derive a formula for the maximagv;a00( ; p ozyvgeg9+q6egsum 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 oscil2 tkmsr-d2ebv7bh 7 l ;6)gy3ijz0iovlates at a frequency of 2.5 Hz. At it is released from rest starting 2-hk7 )e3 dryii jv to70 2mlbzgbv;6sat 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 antds0 ( a4my9tcchored boat every 3.0 s. Ht4 t0sy( mcda9e measures the 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 air j2,xr+6drbdq+n /snd travels with a speed of 343 m/s How far apart are the wave crests (compressions)? rj,2x/dq6r sbirn ++d   m

  (a) AM radio signals have frequencies between 550 kHz andac/4w0.k*u7srcukr f 1600 kHz (kilohertz) aw rau.0rsu/c74kk *cfnd travel with a 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 longitpe5rj3j4ri -bc-r9 inudinal 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 as dense:usojhva9 * 00 ejy9po as the other. In which rod will t o9u je0jopv*:9hs0ya he speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretche3nzfezpr1 4k;xg9b ,yd between two supports 28 m apart. If the tension in the cord is 150 N, how long will eyrf4 ;91z3zp,kx bgnit take a pulse to travel from one support to the other?    s

  A ski gondola is connected to the top of a b4d:fx;2*nlh6x yv ykhj0 -5n teqn*w 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 terminal and sendb6*tf2;qnhnj5x- w 0lexdh yyv :k4n *s 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 hi -.gij *w4hlzps ship just below the surface of the sea. He hears the echo of *4w zhg-j.iplthe wave reflected from the ocean floor directly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an ea 59*wzwd1 nptcrthquake travel at different speeds, and this difference helps in locating the earthquake “epicenter5w*nt1c 9z wpd” (where the disturbance took place).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced surface wave can be approximated by a sinuy5i8j avsoqfat:3if/ ;k 50 xysoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Sevixt/ 3 y:fy;85s okai0 qf5ajt the acceleration a>g]    m

  What is the ratio of (a) the intensitie8xoc;dztz nz2 rtq 28 (lplefo 5hm7;.s, and (b) the amplitudes, of an earthquake P wave passing through the Earth and detected at two points 10 km and 20 km from t dqh2to(xc ; zpm7 r;2ze o58z8tlfl.nhe source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is measn be3yih/ae4fi6u x2d(ev q;-ured to be 3qn d-2he a e4fiey/b x(;vui6$ 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 trave9 ut qr kkn/0-nn;.skxl through the same portion of the Earth, but one is carrying twice the energy. What is the ratio of thekx. ntn ;r-sk qu/n09k amplitudes of the two waves?   

  Two waves traveling along a stretched string have r hydf.0pgbrr; 5kt9d ,yz 8m8the same frequency, but one transports thre ,.r kfz885 r;ry 0ybhp9ddmgte 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 tga ,4me:e qmv/o move up and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. Ige me/4 a:mv,qf 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 each other. (a) Sket vp0i 5g6r ohxo-0sqo8ch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight. What so6o 5r08qog0xp h -ivhas happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its 8n r uq r28zv,m+u +wc6eb8eohfundamental frequency, what are the frequencies o+covrzque+w 8,2 re8bu6 hm n8f the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. er4.t1jogy r -0kfr30kte.mb At what frequency will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirgmty3100rk.4e jt bo errf-.kds of the string vibrates as a standing wave.)    Hz

  A particular string resonates ibxdxr9+/ g4: u qi8krxn four loops at a frequency of 280 Hz. Name at least three other frequencies at 8r i +4x/qxdk9brg:xuwhich it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waveskpoe6w4a2s gx(7ge :/ bl qf3f on a string is 92m/s If the frequency of standing waves is 475 Hz, how far ape kag(sl47xo2 e3qpw f /f:6bgart are two adjacent nodes?   m

  If two successive overtonesfn-fnmyo1 uezc o 8 i1ghn3 *u:70tlg8 of a vibrating string are 280 Hz and 350 Hz, what is1fi 1o n8m g:yn-o0h gt78zu3*ec lfnu the frequency of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The 8bk*wall)0 rkdistance 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 fl wk 08*r)lkabirst two overtones?    Hz

  A particular guitar string is supposb6nrl*uu+lmin amk0 oq+ ;49h ed to vibrate at 200 Hz, but it is measured to vibri+ar*mk096 n +ouq4l;unbl mhate 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 supposed to vibrate at 200 Hz, but it is ha1( nhdt2; drmeasured to vibrate at 205 Hz. By what percent should the tension in the strd2hhd;rna 1( ting be changed to correct the frequency? decreased by    %

  One end of a horizont uogo4vpv 9 o tvi0.o+oszk277al string is attached to a small-amplitude mechanical 60-Hz vibrator. The string’s mass pe tosp72g+v497ook0.oz iv uv or 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 0y9it.uqzd3 tstring may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many differetz93t0 y qu.idnt standing 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 just the right f-,qo4029:bldgj3vbqtriey5 i - fmql requency, 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-wide dib50rbl tilv:f9jq42e-o3- m y qgq,tub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling u-kkgw g/n+i2t +)rff*tq)oe lw- e /eat k.0 km/s strikes a boundary within the Earth between two kinds of material. If it approaches the boundary at an incident angle )r*k e -q+w/tg/f ful io2knt+eg)-weof 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 the15j pkq;np19egylft.1n/ t:nl 50mjcs x 0ubh velocity changes from 2.8 m/s to/pnjh 15l5mcn;sklb :0 epg11n.qf9u t yt0jx 2.1 m/s If the incident wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air when it hits a layer of cold, dense t3 y 1ad3: l )sybjsefsuqz,94a(b+znair. If the sound wave hz3)(n4a:9 tyus3s bylsz,b1+fjeqd aits 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 strikva r: 6 yi3hamr d4aoxq+f24o*es a boundary between two types of rock at a 38 3 yi4rqm f 2ah dor4x6+o*aa:v$^{\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 c6x1vf+ hdv )lnl)kq3v 72dev in diameter. According to the user’s manual, the dish has to be pointed in the direction of the satellite, but an hexc v lddvf17 6n2+)q)lkv3verror 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 wavelen9cv *3rs0hr1:uqbi jnc vjeifi4z w32(y ic15gth 250 km and velocity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe a19w3r(:cj32viii 4 qne5u r1f hjcc yi bvsz*0n 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 cifkek 9e2,8) tcs/gxt onstant 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 conservatioe8kgx)2ktsi9c fe t/, n of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m below, which str 4k7 9zs g) se0phcrjau51mq.petches the net 1.1 m. Assume that the net behaves li4sg5 q9hme7kz.c01) prj s upake 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. Thm2 xhihs2f 01xe mass then falls 33 cm before it0f hmx 22shi1x stops and begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a hun5q 4svymx rzp5 g 9:*ja7; a*etqc4jzge spring at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the5sy 7ezc*g5mrap4 ; 4:nq9qjx *jv atz spring stiffness constant of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of coffee (diameter 8 cm) at just the rk)qa+rqrl/ 8 gight pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the speed of waves in the coff)aqrg8q lr/+kee.    cm/s

  The ripples in a certain groove 10.8 cm froelfhm,drx2bq+*;ipr3;xl 9te v /ezp,( f7bqm the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What wi7x;*d ,(+3 q2 mevf,rhqep ;rbtzibpl9/ef lxll be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cwki2n jyk ci07h16f(,wdt v (qos7.40t where x is in meters and t in seco7cj,i0h 6i qt1k wvkw(2fydn (nds. 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 fr,txo7xp( )huvjjri -h (4mqu 3b3u,lzequency if it accelerates at 0.50g (a) upward,b,o ,)x3qh3 (x(pzvlu htu-7i 4j rmuj    f
(b) downward?    f

  A 220-kg wooden raft float5rci/ wng) ap1. 8qklos on a lake. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he ste.n18 w /)kq a5pcolgrips 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 3letwucc yg0 5ws)p3i8(gmv um56 ke7,92 Hz (G) and 440 Hz (A)5 uel7mt i, pswevu()8 c0mg563kcwyg .
(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-part n4d8(u .xg: )j5jny yzirm8p zcord 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 wavelength greater in thu8ni)djjxz8 .mgzy4r 5(yp:ne heavier section of cord or the lighter?

  A tuning fork vibrates at a frequenj:keko-c)hg -bkc57u cy of 264 Hz, and the tip of each prong moves 1.8 mm to either side of cen:5)kccue k--gkj 7bhoter. 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 rdwtr *9w8t ld+9cm,aharmonic 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 the board duri9 ,rdcwtt 8d*ra9 w+lmng the oscillation?

A string can have a “free” end if that end is attached to a ring that can slidc il kqm )6y0 m,:xfh9t+rdoo;z)hp-je without frmdo 0fh)k x+m ;hclrozi -jpt, 6y)q:9iction 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 sw,bp)a1 41s:mqemyl zaing takes 1a 1m1saypb4) ze,:qlm.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 vertical direction or can swin w yfakd.)6y 0v,e (vyj (u99p1r;rkhtojw1fq g 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 by whaf0 prky uaot ywvhje qj1(6v;9(w 1d k,9y).frt 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 stryyad hopd1kv 2 0-ar.j6/6 a v ;9huojxoxtz8/etched under a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is z/0o h ;6j2vyh8u ajo o9aydrxt-ap.6dkv1/x 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 stiffnesq-6b 8o0nuf07pq scl es constant k. A penny of mass m6u be fpsqc0nq0l-7 o8 is placed on top of the block. What is the maximum amplitude of oscillations that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steelv 68fs.s(xgux q0 at, :gzv3ag crane cable is 22 m long 8.fg6gx ,0aavu(g:zs 3qsvt x 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 the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fi mj88m( 4syfxcg. 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 f(c8 s8my xmj4on 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