Give some examples of evern8o7dq0f3j k+q.sq:c o q f+sdyday vibrating objects. Which exhibit SHM, at least apprd+dq3 oo7fcj0s+nkq :s qf8. qoximately?

Is the acceleration of a simple harmonic oscilla,(tpwlb8w d (nfn9dtnt10e j-tor ever zero? If so, where?

Explain why the motion of a piston in an automobile engine: 4y w g6y8u6fabhit(e is approximately simple harmonic.f8 (tyi6g6buwy :4 aeh

Real springs have mass. Will the true period and frequency be larger or smalleny igq,2i/d8j wcq((m r than given by the cw8 j ,qn/(igi q2dm(yequations for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the ma1kr:1dr (ypbgximum speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring sobvm0x1 .ia,p2u -spe cale, and then is released. Describe the scale reading as a fun s10vou- p .x,pbea2imction of time.

If a pendulum clock is accurate at sea level, will it gh8 xs/ixg8aul e8o n8;cm;w( fain or lose time when taken to high altitude? W8ixfac h8glx8ue;n/;(8 wmsohy?

A tire swing hanging from a branch reaches nearly to the grofrs ey.re(8fue:w- 1wund (Fig. 11–48). How could you estimate the heyr.:e sf 1e re-(fw8uwight of the branch using only a stopwatch?

Why can you make watn,nsx.6+wi j qls.5 rder slosh back and forth in a pan only if you shake the pan at a certain frequi s,s6nn..lxqw+5d r jency?

Give several everyday examples of reson.gaj+ws1gkd (av :8rgmm*)u tance.

Is a rattle in a caroc*(+rk4,u5tqlzr l xo57yfl ever a resonance phenomenon? Explain.

Is the frequency of a simple periodic wave equal to the frequency offp5+ko28v bpo its source? Why or why npbpo52ko+8 vf ot?

Explain the difference between the speed ot)mct3elc* iz, mp49h4 qj:nef a transverse wave traveling down a cord and the speed of a tinti,eje 39*cth:p n4 mm zl4)qcy piece of the cord.

Why do the strings used for the lowest-frequency notes on a piano nor.zkak-i2tufup4c5 h 2mally have wire wrapped arouni t24zaf2u.u5kh k-pcd them?

What kind of waves do you think will travel downe n-t64zbs2 mj a horizontal metal rod if you strikesj -nzt4b26em its end (a) vertically from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increq6x9 1j6hku yqase in temperature, but the bulk modulus B is nearly indep1hq6y6 xuk qj9endent of temperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why cirylcjrrb v68d 4e0x1oox3(id :8laf 9fcular water waves decrease in amplitude as they travel away frx 9lfdb6 jixoc3rf o08v ar48l:1(edyom the source.

Two linear waves have the same amplitude and speed, and otherwise a/ak 3lfi)fi.bh7-ki-uk *h+x .l vnwpre identical, except one has half the lhkvlfanb )3.h/ fx+.7-p k*iiuk- i wwavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two se(z 2,rr5at dztctions of cord as in Fig. 11–33, the frequency does n,zta(zt5 rd r2ot change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there any places rtlhv q9s8* s0n5 yi*ayou could touch it with a knife blade without disturbing the*tss ql 98a0y*ivrnh5 motion?

When a standing wave exists on a string, the vibrations of incib sb2pu6u: x5qn. ;fnc(n fi5kdent and reflected waves x6f.u ;bnqbu:(kin fs 25cn5pcancel at the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one place to ano 64;hek1/ kd x*:zhz vf*zcexdther, how might we determine whether the energy was being carried by particles (material bodd/xdef* vczzkx kh 6h14z;e*: ies) or by waves?

  If a particle undergoes SHM with amplitude 0.10wa :ezldmxe9i 6h9f7 (dv6u bsp *8vn8 m, what is the total distance it travels in one persdz9l h9:d(68 uwm6i7ebve f*x0pn aviod?    m

  An elastic cord is 65 cm long when a1jcyoc tg z /i9l*n6rna*m8 z( weight of 75 N hangs from it but is 85 cm long when a weio/nyat( z*8 jzi69*mclncr g 1ght of 180 N hangs from it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car com34vu :xfk xj)mpress 5.0 mm when its 68-kg driver gets into the driver’s seaumvj 4x3x)f k:t. If the car goes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangts*;j p4o 0 vor:cy*f f)*wnans from it. (a) What is thejft s* pv0c4r;fn:wo on**)ya 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 frequ+cjlc ,8yurvv/6 p uz wqk;4+oency of 3.0 Hz when a mass of 0.60 kg is hung fy48kruvupc6 z w+oq, ;c/ v+jlrom it. What is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. 11–2 at times t1szfmgwbg2 w*6 qul.2 gmbfqwsw21 6 uz* l.2g= 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 caughtul +e iz5ibs.mt9:fp;)a g ;vx in a spider’s web. The web vibrates predominaaiiemvl5+:s9;tg zp f x .b;)utely with a frequency 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 wi 2kcqs.y6g qlthn.h )-th a frequency of 0.88 Hz. When an additional 680hgql. -ns6t k).cqy2h -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 d3t-pyzq4aeo65 wi0etimes per second with an amplitude of 0.13 m. De zeda60-et 4p3wy5oqitermine
(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 the maximum vd 2 /gxk cp9m+e+/c/qx 7 /xp,aoxzzjvalue?g9+/p/xm z7poe/d x2,xzk cxjvqc+a/$\approx$    A

A mass attached to the end of a spring is stretched a distance s2-) qea(xvx rki ;e-j$x_0$ 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 is stjg/u8hfbu /q4retcheqj/ uughfb8/4d an additional 0.130 m and released, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with sprin6lpb-gpogl use 56 73qg stiffness constant k = 280 N/m and is executing simple harmonic motion7l6p65go-eq gups l3b. 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 mhp e3aa6wup )2k6n: ib to “load” a 0.180-kg ball. W)a ph:6n23 wk6bipaue ith what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to one 2k5kfv-j +teiend of av- t f+5ejikk2 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 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 au9hu t 1j4h .thx vn/f+f7l6uyccording to the equation x = 0.45cos6.4t where x is in meters and txfhlnu6 u. vju/hf 47ht +1yt9 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 from equilibrium is the mw r/uft2 d1),gz wp1kenergy of a SHO half KE and half PE?k),1rdug2fwp / wm1tz ±    A

  If one vibration has 7.0 times the energy of a second, but their frequencies a2v zdii :l;-bxm0. kpnnd masses are p k.0bi;dnmv-:iz2lx the same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillau v)w9hny s72vtes from a vertically hanging light spring once every 0. wvyvnu)s27 9h65 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 tx9q;dqoi / d 8c0lpj(ewo identical parallel vertical springs, each with spring stiffness constant k (Fig. 11–49). Whatqjd8lx9/ ; opqid 0ce( will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t where x is in s1 pm4gxxgob5az-p*yt0+zz wt75e2 qmeters and tpg az 5 tz 0742tq1xb-pmzx+y*wgos5e 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 examplnp qp13 3ut.pi* nbp+mes 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 horizonivwykfr:4agj,.:h y+8p,jh.q ue9d h tal spring (k = 124 N/m) is struck by a hammer, which gives the mass ank 4pij:y.+,gw,r9qhej dh yh8f ua.:v 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 vibrates with gapth4s-7:ct an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point (x=gph7sctt:-4 a 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 stiffne4b7m z)nw jm.yq1hyt1 ss constants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes a 0.600-kg block attachvzene+1 zq*r(9jin j8luk ,.k+(wcoged to a fixed horizontal spring whose spring stoc9eke+,iq j+vj(8zzrn 1*nu(wlgk.iffness constant is $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with mass 65.0 kg jumps f/l r6cfn-p epe1ll 5so3xuo20slg(u+ rom 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 th6 po2lgrs5 x1c l sne/(+plefu0 -lou3e unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrations inklouo,g881 v6pl*f tw exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if ye 6 b60lkg2kxit is to make exactly one swing per second? (That is, one complete vibration takes exactly 2.0y 66exklb2 0gk s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its pn)f)ebk6w m.f2net fufj2a 36eriod on Mars, where the acceleration of gravity is about 0.37 th) ej6b e6n2)u n2kma fff.tf3wat on Earth?    s

  What is the period of a simple pendulum 802ye, qw fa1sf 9q1iy1mwkf8c. 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 cgps5bj7bv2;a5a d7v7wck y, mass of 365 grams, and it is relda5 2syp7vk 7v c,bw57aj cgb;eased 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 clock lolf*egxi1+k6 ez,nz 7z9v4vyu ses half a minutee+i94 x gnk7*vye6vz1 fz,zlu per day, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the mn z5rg/ w 75bm6lngd2daximum 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 oscillawpy.)a0x itl 8tes at a frequency of 2.5 Hz. At it is released from rest starting a8.)0wapy ixltt 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 h z8t* v:o/bcjb ;snxy9is anchored boat every 3.0 s. He meas*jboxys 8 n9 bzc:/v;tures 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 and travels with a speed of 343 m/+zigel)exsz a(0 b4o8l-f4 bms How far a4m i8o )z4sbl-0g( ezeal+fxbpart are the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 5506 1/0ndzpt pu/nk 25 goiwd*dp kHz and 1600 kHz (kilohertz) and travz 20dptd/w5p6*/nio1 p nugkdel 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 longitudinal on lmkkt(o8;yj6):; vcikzl9 waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have tp8t//fsimgyn7l z1l7he same elastic modulus, but one is twice as dense as the other. In which rod will sy7it8g z17n pl /l/fmthe speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apart. If the-2yvl1 gf4h z4balr/l tension in the cord is 150 N, how long will it take a pulse to travel from one support to the otblglzf vya 21/-lhr 44her?    s

  A ski gondola is connected to the top of a hill by )o64,ujzh ynw 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 sends a wave pulse along the cable. It is observed o znhu6)y, wj4that it took 16 s for the pulse to return.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

  A sailor strikes the side of his ship just below the surface of the sea.4+,ft+(zta xnhgla b 6 He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is the ocean at +6hlfgt4zxa+at ,nb (this point?    m

  P and S waves from an earthgfl4i0y q1o kd k8u7w,quake travel at different speeds, and this difference helps in locating the earthquake “epic y0d1fkkugilw 87 oq4,enter” (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 sinusoidalvrb-fxk ej1abv8rt 4 ;x162fk transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixturetxej 1x 6fr-1r kv42 avbf;8kb 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 ew ho 0b w6hbzp7a(y9fzap5q65arthquake P wave passing through the a 0z hzf5a66p9w5(h pwbyob7qEarth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an ea;: 4szrcj jm rxzd yp3.+5vh5 4rite:prthquake wave passing through the Earth is measured to be ps:hrzitj; v5z43rmjd+r.ye45 : xpc$ 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 52+(napff qllfrequency travel through the same portion of the Earth, but one is carrying twice the energy. What is the ratio of the amplitudes of the two wavesn(aq fll2 +pf5?   

  Two waves traveling along a strek lzjj2ki/b:yl 1;ib 9tched string have the same frequency, but one transports three times the power of the other. What is the ratio of the amplitudes of the tw bk92 :ilkblji z/y1;jo waves?   

  A bug on the surface of a pond is observed to move up and down a to*)tz5f641vnoje w s bital 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 whain fs)6ezwjt4 5 ov*1bt factor does the bug’s maximum KE change?   

The two pulses shown in Fig.d ; w-::svs8vw;kpkes 11–52 are moving toward each other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments later. s:dv8k wss pw;-kv ;:e(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 atj va k6,j89 h(dciy3os 440 Hz as its fundamental frequency, what are the frequencies of the first four harmo ,o9j kay(h6jd3s8 vcinics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what freqigaq,g d9( z:2q*r9v l8jcqrzuency will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of the string vibrates as a standing wave.) 98 ql ijgdqa 2qz9 *grvcr,z(:   Hz

  A particular string resonates in four loops at a frequency of 280p;9 e pi0vpbjp1ysjcl8f :z1+ Hz. Name at least three other frequencie:zl;9bv p+pes cjji py081p1f s at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the frequency of standi 8j0 ;put-mvj1 g7ojwcng waves is 4jo c 0m-g uj8t;17vpwj75 Hz, how far apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and to 0vod8z a. hrdg7iihr7+q 1.350 Hz, what is the frequency of the fun+r7i v 8.d0iq1o hgta.7rzho ddamental?    Hz

  A guitar string is 90 -7c20u4p cvgjmcm :jbu, pd0ccm long and has a mass of 3.6 g. The distance from the bridge to the support post is L = 62cm and the string is under a tens:p ,ugv4cjj 7p0m-mbccc0u2 dion of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string i88qm a1 9a 1r vx:vq6j :pkuo8ilakox9s supposed to vibrate at 200 Hz, but it is measured to vibrat k1rm:v u81qoa8 x i9ova9p6jkxq8a:le 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 measuref3y m:)vx 4ksar/khy 6omr1b +d to vibrate at 205 Hm /a6 kh1ox syy4)rkvbfmr3: +z. By what percent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-amplitude mechi32pfe 7wkile y6 :7rg9 eg-gganical 60-Hz vibrator. li-f 9726:kg7yepge gwg3rei 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 moviizb( w+ty..hgldu gk 8j0.(eu ng the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave pat.b zg(8eg +jl( 0.uwhi k.duytterns 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 righ/j+-,9utscfevq z c(9z2km fe t frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the speed kvc 2cf,e z9m /es-t9fz +qu(jof the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundary within the Earth bo . qljn02m)utwoz )s-etween t su2jmtow oznl0)q).-wo kinds of material. If it approaches the boundary at an incident angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “shelf” where the vel8ezl/5etj ycoh.1 .uu ocity changes from 2.8 m/s to 2.1 m/s If theeeu..1/h cyj8lz5tou 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 aew/ (lepb qbzx9/ ;wcjk.j9 -+oj nqb3i qm38air. If the -wbjeq.k/i/n;cmbq9 l ep+3qaz x9 ojb(wj3 8 sound wave 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 str7fku5 w3 h2 p30 9epn1pxevk,ju1 xunnikes a boundary between two types of rock at a 38 2ek1 p3x9wu1npnku3 fuj 05nxhe v,p7$^{\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. Accordaq9u qbh6 i5n7h; c .c-3 lr8omanisp3ing to the user’s manual, the dish has to i .qcqb9hcos38-6am75a n;inhr3 upl be pointed in the direction of the satellite, but an error of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 250 km and velocity 750 km/h travels across the Pacific : uku1hs +5g5fb7g9 sxylvx:uOcean. As it approaches Hawaii, people observe an unusualuxgyku51 5 sxb: uv9s+f7g:hl 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 stpz 3 *sgcry0+a1m,q w djy2apijl9/v3iffness 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 (appl+i2qc1 v0,/wp* yra jd3z 9psg 3ajymroximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fir uwd8 cbje,4 rh:u3m6ge net 18 m below, which stretches the net 1.1 m. Assume that the net behaves lm3ej 4,cwh8br:g6u d uike 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 ( gv)f.r /wpehspring. The mass then falls 33 cm before it stops hrf( g/).e vpwand begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge springi nm, /nhf0nhoj*(o+7xj9g sa at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is th/*xah9fniho g,(m js+ n n0oj7e 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 right pace of a n 4 x8 -n26m4iz.*h7,gkooygnafpfsnbout 1 step per se8oofgm kyi xf72nznhg -*p n 4s6a4.,ncond, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the9ol mp 2cv4lw) center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequency of the sound emitt9lcwpm 42lvo )ed?    Hz

  A 2.00-kg mass vibrates according to the equat4 uuo3x:ou wk1ion x=0.650cos7.40t where x is in meters o3k:ou41 uwux and t in seconds. Determine
(a) the amplitude,    m
(b) the frequency,(round to two decimal place)$\approx$    Hz
(c) the total energy,(round to one decimal place)$\approx$    J
(d) the kinetic energy and potential energy when x=0.260 m.(round to one decimal place) PE$\approx$    J KE =    J

  A simple pendulum oscillates with frequency f. What is its frequency ik a dilvigcc,0 wb+16*f it accelerates at 0.50g (a) upward,c* ici+1vwb k g,ld06a    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on kzgoj56,y1ck vc4nl *0.r htn the raft, it sinks 4.0 cm deeper intojn ycloknt4. 1vcz6 k*rh,50 g the water. When he steps off, the raft vibrates for a while.
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a musical instrument are tuned t4jo 0l s(oveohhhfj(*p 6wq+- o play at 392 Hz (G) and 440 Hz (o*h4o h jeqjl(+-(w0h ps of6vA).
(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 twb i :dkj2g,wea09r)gt o-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier sectiongjtk bw9 d)g:,2ia0 re of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the tip of each pron.kz:br tsp+4t:du)tu g moves 1.8 mm to either side 4utb dpk) :.ts+:z turof center. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscill:0h)7 ewnmads ates with simple 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 wihs nd07)w:m eath the board during the oscillation?

A string can have a “free” end if that end is attached to a ring that can slide lmblp1 *vq4o1 *a w3nswithout friction on a vertical pole (Fig. 11–57). Determiwan11o3l*lb*sm vp q4ne the wavelengths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum habyh b y)3k5u0hb1gs+qd -a) ohs a period of exactly 2.000 s — each one-way swing takes 1gk3buyds +yab -)0 hb) hoqh51.000 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 swk7k9 x muj7v h72k8olk, vj2gaing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period of the v,2kk 8 vmau v7k7l7hgj2ko 9jxertical oscillations or the period of the horizontal swings, and by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

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

  A 10.0-m-long wire of masyyo7w7 z g)2c u/88 e p+vxow(m,ew3o7dt juevs 123 g is stretched under a tension of 255 N. A pulse is generated at one end, and 20.0 yy7u(dev3wv 8cp/moxwjez 2oeuto7+ 7,)g8 wms later a second pulse is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spring with spring steqskz9q5 vd n32 1m1cmiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillations that will allow the penny to just st21qmmz3 s 5v9ndcq1ek ay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car aw9-akqx 5.mgn t the junkyard. The steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. What is the period of themq.5k9- nwagx bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown i7:o( *62 byfc gt)bgtakq j4vxm0xn8kn 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, estqxkkj80bnabt 2y :x7 g(*c v)o tm4f6gimate 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