Give some examples of everyday vibrating objects. Which egeqg2 mxq+b nup*(b4jg+35 tc xhibit SHM, at least approximatelce+25tpgjuq+ q gn 43 gxmb(b*y?

Is the acceleration of a simple harmonic4zn +3sfvd3yg oscillator ever zero? If so, where?

Explain why the motion of a piston in an automobile engine is approximatess +ydn2i,c 8ely simple ha scsidy+ne ,28rmonic.

Real springs have mass. Will the true period and frequencyry 8h9p6qn* pzc9ab3 c be larger or smaller than given by the equations for a mass oscillating on the end of *bzpca3q 6rn h98 pc9yan idealized massless spring? Explain.

How could you double the maximum speed of t::qstl6tp 6in2 lw m:a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vesbv7ul dnj;fkwxg,-y7g+ y)/rtical spring scale, and then is released. Describe u w 7;s/dgbfvj-x, )+yyngl7k the scale reading as a function of time.

If a pendulum clock is accurate at sea legqtrn5l 1 nn 1r/)f.uv8sk7ndvel, will it gain or lose time when taken to higskrn/f7vu5 )n g1r 1.tn dnql8h altitude? Why?

A tire swing hanging from a branch reaches nearly to the grqj/t (g e3p2rpound (Fig. 11–48). How could yej 3r(gpqpt 2/ou estimate the height of the branch using only a stopwatch?

Why can you make water slosh back and forth inubz;51/p b qdy a pan only if you shake the pan at a certain frequ1z; db5yupbq/ ency?

Give several everyday gvr arveq5 5/a 2jz m1zui1y(.examples of resonance.

Is a rattle in a car ever a resonance phenomenon?g6gwd5cn z*8v rv1d 5q Explain.

Is the frequency of a simple periodic wave equal to the frequency od /k/e (pfzrez*(2wn6d x v7)jsrd uh/f its source? Wh/2r)uvpdwkd zf eszj/nd(6e /(7* rhxy or why not?

Explain the difference between the speed ofy lua b5v8 7 r,d63s:kfcpuyiyj)4k 6o a transverse wave traveling down a cord and the speed of a tu67ay vu8 :dsrb6 l45ikj,okyy fp )c3iny piece of the cord.

Why do the strings used for the lowest-frequency notdq pr3ndzu )*x oi)w:t)xl85 ves on a piano normally have wirtwvq5r izn )d*ol)x)u3dxp 8 :e wrapped around them?

What kind of waves do you think wil9rmlwh:7 a9+elsebh ,l travel down a horizontal metal rod if you strike its end (a) vertically from above and (b) horizontally paralhwm sh 9l7,eb+ra9e :llel to its length?

Since the density of sv v0+m z1vnh(.bun*sair decreases with an increase in temperature, but the bulk modulus B is nearly independent of temperature, hown (zns1s*0vuvb h.m v+ 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 e94yuq u*e: r6:caam xaway fromr e 9equ4axc y*m6u::a the source.

Two linear waves have the same amplitude and,a/o. cx,epkd8 + h7wstq2say speed, and otherwise are identical, except one has hal q, wh sa,8sp7a+t kxc2do/ey.f the wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary je;*yh1b e18y v vt9y p2k3qtwbetween two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocity do chan9wy8*1 k bjv1yye23qte hvp;tge). Explain why.

If a string is vibrating in threezn9 gq *1 rsh.4fid0kz segments, are there any places you could touch it with a knife blade without disturbing the mot*khifnsd. zr1z 4qg90 ion?

When a standing wave exists on a string, the vibrati9ko .wonv0) zwons of incident and reflected waves cancel at the nv9 )w0woozk.n odes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one place am 6ru uuqp y31pn2h,+to another, how might we determine whether thehp mpr+a3n2y q61,uuu energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amp8p3erfub7b s*txa*d/ litude 0.18 m, what is the total distance it tre3tdub*r p8 b xfsa/*7avels in one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it but*f 7o)e.ulcq jvi5f 5s is 85 cm long wh .esi5lq f57f*)ovjucen a weight of 180 N hangs from it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kda g8 amdlo bz5+qm8t9;b w,*ng car compress 5.0 mm when its 68-kg driver gets into the driver’s seat. If the car goes over a bump, whaqzawnm*o btdb9,8g58 l;d+amt will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cz,a *p 0p 1uw xtu-4bcubq*9hym when a 2.7-kg fish hangs from it. (a) What is the spring stiffnespha10tc9,-u*pyz b bu4 qw*xus constant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a frequency of 3.0 Hz when a mass of rv uh+add6/b/u2z el )0.60 kg is hung from it. What2/uehv/ ) adulr+zb6 d is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass i8 w23ezoq/ rgl ej45-ubzfzr r:s x2m2n Fig. 11–2 at times t = 0,t = zmrg/2x ro:2u423 8 -zzeqrlf5jswb e$\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

  A small fly of mass 0.25 g is caught in a spider’s web. The web vibrateqvx kj0:e8oa l4/ funps/tp+ /s predominately with a frequency of 4.0 k0fsxp/tq4 je:8/ovn +p/ luaHz.
(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 d/hl)5m b-q j0pg2rop with a frequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 Hz. What is the/q 5-ol j 2hdrpb0p)mg value of m?    kg

  A 0.60-kg mass at the end of yn+p/n*tf9k qk7h6n n a spring vibrates 3.0 times per second with an amplitude of 0.13 m. Determinenk hnftn79+qny k *p/6
(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 maximuns0dox .op- 9am valuoxnpod.a0 9-s e?$\approx$    A

A mass attached to the end of a spring f w0* 7gv c-zot1w cmir -s5khd81kp3xis 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. If the sb 5lc :r/pdfy.pring is stretched an additional 0.130 m and released, how long does it take to reach the (new) equilibrium pos 5by.rd:f plc/ition again?    s

  An object with mass 3.0 kg is attached to a spring wj5s3 aws dxhl ,yd+ckz* mi02*sb.+wbith spring stiffness constant k = 280 N/m and is executings 0 wmzs b*,hxcw +y+a 2b5kjli*s3dd. 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 0.20+3 p8y:f mfqane5 mi*q0 m to “load” a 0.180-kg ball. With what spe3 if +q:ya*mmq5np8fe ed will the ball leave the gun?    m/s

  A mass sitting on a horiwskv/p mw7i(ku1/bw) zontal, frictionless surface is attached to one end of a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring c mbwwk7/)sw/( ki1puvompressed, 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 ail;+trq2g( a) gy*jwp ccording to the equation x = 0.45cos6.4t where x is in meters andj2w* ip yga+);lrq g(t t 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 u x5ct;dtl;8oaz66 jlis the energy of a SHO half KE and half PElzdl 8co6j6 t ;x;t5au? ±    A

  If one vibration has 7.b . rt,hhia .vp.m5r8t0 times the energy of a second, but their frequencies and masses are the same, what i bhma., vitp..8rrh 5ts the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a verticallytqaj.p )v3rs4aqtj (5 hanging light spring once every 0.65 s. j(5s )ta4t3.jvpaqrq
(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 cwvd4)d(;irs /aqp;ktwo identical parallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What will be the frequency of vibration?kda)dp/ c4;qi; (wsr v

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t where x is in 16bzsa xowieq0)(org /a vc.3meters and t is in seconds. Determinga0 )se(wrxai.ocv36 1/zoqbe
(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 exu9..x6r p: l5eunjgmzamples 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 1s 2mpgby * 9d- bypineg78-l(iznto0rest on the end of a horizontal spring (k = 124 N/m) is struck b2b1smi-*t 0 yg(zyopg 9i -dnlpne7b8y a hammer, which gives the mass an initial speed of 2.96m/s Determine
(a) the period and frequency of the motion,    s    Hz
(b) the amplitude,    m
(c) the maximum acceleration,    $m/s^2$
(d) the position as a function of time, x = (    m)sin(4.08$\pi$t)
(e) the total energy.    J

A vertical spring with spring stiffness constant 305 N/m vibrates with anskuza; /2h:nc b76gma amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) with positive velockzga2b;6 sn chuma7/ :ity 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, withyoq n)-boe0 px; 6e,jr spring stiffness constants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes a 0.600-kg block attxq 6*qsrd)t( tached to a fixed horizontal spring whose spring stiffness constant 6qt)*xtq r( sdis $ 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. A6d tjm fe238grfter 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 l8jdmgtr6 e3f 2evel of the bridge. Calculate the spring stiffness constant and the unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vjf*b88qu:mz4cl 5ktm;bag;82z pr geibrations in exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly one swing per p( qifp) u9x*gsecond? (That is, pi9)fx*q(upg one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What04p 8tb-* f- xj7bemo:tgymnd is its period on Mars, where the acceleration d8ytx *0n-g bfebmt4o j:7 p-mof gravity is about 0.37 that on Earth?    s

  What is the period of a simple pendula67fam/hdug8m j5 iv6j 4elulx )kl5/ um 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simplw41gvix (j+ah e pendulum is 0.760 m, the pendulum bob has a mass of 365 grams, and it is released xa1vh4j +iw (gat 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 lengtlow )j e. 4gf-k zrb+gmk)ho78h of 0.9930 m. If the clock loses half a minute per day, how should you adjust thewobzm)l e.7j r4gfkkg8)-+ ho length of the pendulum? shortened by    mm.

Derive a formula for the maximumq- -/5tp:krudbi/afb speed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at o74zf;q/ oqjnl sbply..rsdfm,4 / o+ a frequency of 2.5 Hz. At it is released from rest starting at an angle of 154 ,ln/q/ofb o fdl.j.o4sq;yzm7s+p r $^{\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 iv+yiuc ptxmtm 66rj6.n:4*n wave crests pass the bow of his anchored boat every 3.0 s. He measure6* + 4nvcui jt.x ytmi:nr66pms 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 wiknjwcby(uozc8 h0 ;+ 2th a speed of 343 m/s How far hc28(0uc yn;o bjzw+kapart are the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 16f;t cno h5p)64(sjjy k00 kHz (kilohertz) and travel with a o)sy 4jcpf(; h kjnt65speed 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 longitud .6z*w3*yi18loxp dw d jwo(ouinal 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 dey f)x.ir;7,cy bxzwy0nse as the other. In which rod will the speed of longitudinal waves be greater, and by what fa,iy.cfyb );w z r0xyx7ctor?   

  A cord of mass 0.65 kg is stretched between twousx ),z wajlopp8 u, s63k0,nw supports 28 m apart. If the tension in the cord is 150 ozk0,,,us3lu) 8jp6a wswn xp N, how long will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected tu;0n3 axz3rxpo the top of a hill by a steel cable of length 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and sends a wave pulse along the cable. It is observed that it took 16 s for the pzp3r30 ;a xxnuulse 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 surfa ,em83yy v0nkuce of the sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is the ocean at this my k e8uy30,vnpoint?    m

  P and S waves from a)bp1xyce 8 a pww5syfd0in4 fmp5(i--n earthquake travel at different speeds, and this difference helps in locating the earthquake “epicenter” (where the dis4-b8 iscfp5dp(1i-yw5fpa mxwye 0)n turbance 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-producl /yddj;w. m06(zp rysed surface wave can be approximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture 0pl s(/y .6dr y;jzmdwof 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, 7 yx1y+a2b jcjok4r b;and (b) the amplitudes, of an earthquake P wave passing through 72 k ;x+roba bcjyjy41the Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is measured to e5+yvsccfnpu8: 0 w7 xbe 8uv f:0c+y5x 7 cnpwes$ 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 trave3d-sijiyv70-v iq*a h l through the same portion of the Earth, but one is carrying twice the eners0 jv3*vh-idiiyqa7- gy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched stripivb zfk5d z ),w6q6(png have the same frequency, but one transports three times the power of the other. Wha wzpi, b5( vz6qpfk6d)t is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is (:8*sg8egnipw wcu y(observed to move up and down a total vertical distance of 6.0 cm, from t*igns yg (wcpe8 (:8uwhe lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each other. (a) Sketcf 6kv n)l/mmc5h the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) Ivn fl5m k/)c6mn 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 atkcw(e(xc 1lwj r/ (i/x 440 Hz as its fundamental frequency, what are the frequencies of the first fkceix j/1lwrw(x(c/(our harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what frequency will it vjfqa 8b7ouc2 )ibrate if it is fingered one-third of the way down from the end? (That o ab2jcu87fq) is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops k m.0ew3c l rp,hayk;7 wji.z/at a frequency of 280 Hz. Name at least three other frhpylwk,j3 m.i;0zae/ cw7.krequencies 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 tn/q j8l.7 ;uhziqh 3sdhe frequency of standing waves is 475 Hz, how far apart are two adjacent 73uzq; 8ldh/j .h siqnnodes?   m

  If two successive overtones of a vibrating string are 280 Hz allaehy7//z+ w2x /uf nnd 350 Hz, what is the frequency /aezxln 2+ y/f/ulw7h of the fundamental?    Hz

  A guitar string is 90 cm long and has a masmdj id jg3x5z(+ ht0a/7sis)x s of 3.6 g. The distance from the bridge to the support post is L = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundamental and first two overtones? id+3s j)sg 5ht/jxzxi0a 7dm(   Hz

  A particular guitar string is supposed to vibrate at 200 Hz, but it e:xm yp19f (a f5hyo8lis measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?So the three frequenciesm(8 eo5yy:x1f p 9alhf are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is sq7-u+- 5aiaujxkx - ulupposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should t-ua kqu 5ua-l- j7ixx+he tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-amplitude mechanicacyz*8+h,sq- ydrd89.xn p6off z*bk ll 60-Hz v,-z *pfh.*yr+ kfbno6 qszyc8ld98 dxibrator. 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 by7fvt dmv yf ;v;*(*qce moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many f ; qyv7e*t;*mc df(vvdifferent 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 fmvwp69ftc/xv :te nn*g)1fg -dm hy;0requency, 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 6tmmhvd;wg0fg: e 1y)pfnn v-9/ xc*t the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundary within 1ml9;+wpa gs)gb e8buthe Earth betwee9 g8 wbpsgla1+bu em);n two 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 velocity changes from 2.y p45j;vqnj(-iy) .inq; sdzld*ib a18 m/;nzyins)bjii4*1yqjdp l.dv- ; q5a ( s to 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 war4zbhb 1ldjiglp:24 :vm air when it hits a layer of cold, dense air. If the sound wave hits the cold air ilp4hvi2 1 z::bg4jd blnterface 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 types810yjt;3z z 7pwvmdgv of rock at a w738g10vjd;zz y mvpt 38 $^{\circ} $ angle. As the wave crosses the boundary, the specific gravity of the rock changes from 3.6 to 2.8. Assuming that the elastic modulus is the same for both types of rock, determine the angle of refraction.    $^{\circ} $

  A satellite dish is about 0.5 m in diameter. According to the user’s+ tex z*a,b6 ,vmpe:ps manual, the dish has to be pointed in the direction of the satellite, but apzvet ,,s: x+*ea6p mbn error of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 250 km a.4lj1yffv9r9 pp2udn nd velocity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual2vpr1 dy up9fl nf.j49 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 bum ddc7 /30+ytcut3putmper 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 ad pu/tcu d3 3ytt7+mc0 wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m below, wf/xje5/ioiy: seu, 4p hich stretches the net 1.1 m.f /y5,pse/j:uoi x 4ie Assume that the net behaves like a simple spring, and
(a) calculate how much it would stretch if the same person were lying in it.    m
(b) How much would it stretch if the person jumped from 35 m?    m

  A mass m is gently placed on the end of a4 gq ,lvbvb6v: freely hanging spring. The mass then falls 33 cm before it stops and begins to rise. What is the frequency of the oscillavg6vqv 4:lb ,btion?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 11–54), comprew k6p6c n+phai)6blh+ssing the spring 5.0 m. (a) What is the sprink 66l6iph +pnb hw+c)ag 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 a9ty.c.gyf6 )opqp,oi cup of coffee (diameter 8 cm) at just the right pace of about 1 step per second, the coffee sloshes more and mq .ft.p6yg i )yo,9ocpore 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 grlg* k ofs7ak:6oove 10.8 cm from the center of a 33-rpm phonograph record hask6:akgl7of *ve a wavelength of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650c pl7vk8 *dt;/qsk1d w 3xn/impos7.40t where x is in meters and t in seconds. Determine xm3/pt kq;pslk7 /8*v d1n iwd
(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 oscillate* (ixqg:.lum2vt3- g fvax +lbs with frequency f. What is its frequency if it accelerates at 0.50g (a) upward, il v*:btax gf 2+(qm3u -g.lxv    f
(b) downward?    f

  A 220-kg wooden raft floa5.o r+h,xx bkats on a lake. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off+5,xrhx.o akb , 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 plaldjl a*/z0,n cy at 392 Hz (G) and 440 Hz (A0j/llc*d az, n).
(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 cord of Fig. 11–3el(g w 2btw+e-3. 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 bot lwtw+ e-gb2(eh sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at ph bynkb0e7l k:gw9e f36td14a frequency of 264 Hz, and the tip of each prong moves 1.8 mm to either s yl1kb3wn:6 t74de g0k9hpfe bide of 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 simple harmonic motion of frequency 1n*6r2hucc: j y ni(kv:.5 cycles per second. What is the maximum amplitude with which t:y u2j6nn( khcic:v*r he end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that end is attached to a ring that can slide 2dhar+k /3xvbwithout fr /b3+adx2hk vriction 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-wa a ea;vqp2c g9,0easv*y swing takes 1. gp9 ;*,qv02easava ec000 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 tojfrrgvt.,ro;ad3k n )1/,fg 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 peri jrn/frd.ar ,;k3,g)ototvf 1od 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 mass 123 g is stretched under a tenswlzjw3o w 9x8-(y 7mslm01rk sion of 255 N. A pulse is generated at one end, and 20.0 ms ow7ml( wsxk y j9lr30szw18m-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 sti4pfy vsn2xu lh;zau2 do+rx*h/o +z6 5ffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitudhh/ y 2 5fou2+v6nx dx;poslz+*rauz4 e 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 steel :.utv 4o urm0ks eg,vhov71jk 69txm4 crane cable is 22 m long and has a dirmsk06ej v o t7.u oh4k1vvt4,9mgu :xameter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (w1aigb1 yj k4ayco*qyw (jjf drk)(t6c69b2r*hich also gives the dimensions of the block). You push it sideways as shown, and then you let go. The jello sj1oga 6q6fkbcywb219rir dy k(a*ty4(j *cj ) prings back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this vibration, given that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz