Give some examples of ever;hft* c di57mvyday vibrating objects. Which exhibit SHM, at least approximatelifdh7 5;c mv*ty?

Is the acceleration of a simple harmonic oscillator ever zero? If sos -0 c/97bz iqslyeaj+(3yfhb , where?

Explain why the motion of a piston in an au92(ott.rk zvh 9gx*tw3 jxvz;tomobile engine is approximately simple harmonic.vrzh2tkxg93* t9(;z xo vwt.j

Real springs have ma)vsm:i- qlc *kss. Will the true period and frequency be larger or smaller than given by the e)*lmkiq :c-vsquations for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double th;v*l5pv mk ei;e maximum speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical sknlicjw f* w5+296wmppring scale, and then is released. Describe the scale reading as a 9i5n6kc 2*lww+jfpmw function of time.

If a pendulum clock is accurate at sea level, will it gain or lose time whzcl w b-o,x49nen taken to high x4wn,b9colz- altitude? Why?

A tire swing hanging from 9p1y6in5 +o)8mtqkyql aby vfm,ef62 a branch reaches nearly to the ground (Fig. 11–48). How could you estimate the height of thel1yvfy f tb8e,oa qy+m26pnk95m)i6q branch using only a stopwatch?

Why can you make water slosh back and forth int3)4pzbr5rge:. u r pn a pan only if you shake the pan at a certa bgzrp.t53p4u)e rr:nin frequency?

Give several everyday examples of resonance.cr80qjz1 qk hx2h,jc4fa1 i9a.gf xpnn 1 g*4g

Is a rattle in a car everqaab*y 8 )dd tuoobn,g0)l5 (k a resonance phenomenon? Explain.

Is the frequency of a simple periodic uz9/vp qs7z6i wave equal to the frequency of its source? Whyz6 9u7/pizv sq or why not?

Explain the difference between the speed of a transverse wave traveling do4/i 5mi*4iz /7wfxwkl. pgnc rwn a cord and the speed of a tiny pincpr*m/fw5i ixlw7 k/gz4i. 4ece of the cord.

Why do the strings used for the lowest-frequency notes1yn :c -e9ijia on a piano normally have wire wrapped aae1yn:9i cij-round them?

What kind of waves do you trn6g9lebx ho7 giv y4l)3 .r*khink will travel down a horizontal metal rod if you strike its end (a) vertically from above and (b) horizontally x9).b k ohi6glr* g7y4elnrv3parallel to its length?

Since the density of air d4cyx8. 5 ub6ji/svbn gecreases with an increase in temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves in ac5. bs6ixvjnuy4 8b/ gir to vary with temperature?

Give two reasons why circular water waves decrease in amplitude as they travel a-5*v46/xhvftwi w8d xqfo f.p way from the sout w-ff x/.i6hx58w vfq*o dpv4rce.

Two linear waves have the same amplitude and speed, and otherwise are identical,5l-f*umkmp3.w6r vf b except one has half the wavelength of the other. Which transmits morm* .6fvulwmprk-bf53e energy? By what factor?

When a sinusoidal wave crosses the boundary between two sections of cord as iw rtd,ba9lsodwi(-s4:h j+ 9w n Fig. 11–33, the frequency does not change (although the wavelength and velocity do change). Explain why.l(sh ds9 w-+wj ,rt4: boadi9w

If a string is vibrating in three segments, are therdzsar37jh isq90s 2b+e any places you could touch it ihbs +a9s02s3dqrjz 7with a knife blade without disturbing the motion?

When a standing wave exists on a string, the vibrations of gkkxz (8l)2l(bg hiy0incident and reflected waves cancel at the nodes. Does thk2(ixz g8b (h llky)g0is mean that energy was destroyed? Explain.

If we knew that energy was beingk1 .jkc j zmq/ sxxcjrm97:27m transmitted from one place to another, how might we determine whether the emq1m2ck7jsr 7: jmz/kxx. j c9nergy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the total di s*or4z feb1zv 2a7ghf 6dx6+zstance it travels in one perio7 gs*4 zffb61dar v6+2oh xzezd?    m

  An elastic cord is 65 cm long wheoz(k;h2ffi21 9 bl gmwn a weight of 75 N hangs from it but is 85 cm long when a weight kl2m zbh1 (2 oiw;ff9gof 180 N hangs from it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.,d e ig,zg:.ip0 mm when its 68-kg driver gets into the epi,gg,di z.: driver’s seat. 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-k6o qkeh1a3*fj g fish hangs from it. (a) What is the spring stia*6qkf1hj e 3offness 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 H5ad6 i u)x6fryz when a mass of 0.60 kg is hung from it. What 6ayf d)ui6 r5xis its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass09o(krt7g;2c rbizxi in Fig. 11–2 at times t =bzko9xir72 r (i0;gc t 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 spiz,s/u5wmhtwhy 1+t,s der’s web. The web vibrates predominately with a frequency ofu /w+s,twhy5s,tz 1hm 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 vibra3fdi.+k cvs4(5dn1db:d ez a4tkc, yotes with a frequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 Hz.v4 (4b.e daictcyk + 1d:f okn,s5dz3d What is the value of m?    kg

  A 0.60-kg mass at the end of a sp4/ep96dnoq-bs p :zxk ring vibrates 3.0 times per second with an amplitude of 0.13bp eqkx9s4ozp-6: d/n m. Determine
(a) the velocity when it passes the equilibrium point,$\approx$    m/s(round to one decimal place)
(b) the velocity when it is 0.10 m from equilibrium, $\approx$ ±    m/s(round to one decimal place)
(c) the total energy of the system,$\approx$    J(round to one decimal place)
(d) the equation describing the motion of the mass, assuming that x was a maximum at x = (0.13π)cos(  πt)

  At what displacement from equilibrium is the speed of a SHO half c4c-gktv ;e1h;l4vu ithe maximum value?;k; c4h c4-gut el1viv$\approx$    A

A mass attached to the end of a spring is stret 8v9(dxh en1klched 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 spring is stretchem 8tk +2cq6hye ,z zhh*4s7hlad an additional 0.130 m and released, how long does it take to reach the (new) equilibrium po4h+*l tca7sh 6mq y82eh,zzhksition again?    s

  An object with mass 3.0 kg is attached towfx 6-j ,4vbdwd: tn.k a spring with spring stiffness constant k = 280 N/m an6x kvd.jnd :wt,4wb-f d is executing 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)w 2foxkja(5x d; m3um m to “load” ad o w2x umm3(5akf;xj) 0.180-kg ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is at.e1nftifr0 2muiq u74tached 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 qrf 7ut4ii 0.2e 1mfnum. 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 according to the equation x = 0.,+iqq l5t+le;uc52 kevb io1 d45cos6.4t where x is in meters and t is in seconds. Deter bqek2; eic1,l5+5tudl+qovimine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equilibrium is the energy of apc-vgs 0o.*r ypvk-/c:5o nzk SHO half KE and half PE? ± cps k orovv0*ny.z/kc--g5 :p   A

  If one vibration has 7.0 times the energy of -rpt 7rdkq 5dy p*xv*d2i+w ,ra second, but their frequencies and masses are the same, what is the ratio of their amplitudqd+5tk2xdp 7r rd*, p-w*v yires?   

  A 2.00-kg pumpkin oscillates from a vertically hanging lx7id0hz4 pc l1ight spring once every 040dc7 pi1hx lz.65 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 supportu9sc86s6f1nn8j b9cyl qcfe 4 ed by two identical parallel vertical springs, each with spring stiffness constant k (Fig. b ff6n9 1uqy498cnls j scc6e811–49). What will be the frequency of vibration?

  A 300-g mass vibrates ajwz0c;l 2ywu*ccording to the equation x = 0.38sin6.5t where x is in metl0;c2jyuw zw*ers 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 examples of SHM, labelh)6 ;lfhfhq0i+ r/93zj rupo(/b 0yj-r mxugged 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 hwu)w ,1sn/c lhsnau xr2 )4t:iorizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.96m/s De,s1nu):s clx 2w uhrwn a/4it)termine
(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 spv6q.u2qvsm 2s ring stiffness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0)s smqvv26.u2 q 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, wite8ut;m c7sl+b h 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 attached to a fixed horiz au*h;znq)vscd)b0 x2ontal spring whose spring s hq);a*usd0czn2 b)v xtiffness constant is $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with mass 65.0 kg jumps from a high bridge. Afigosxl a2u jz 36)0ax:ter reaching his lowest point, he oscillates up and down, hitting a low a6jxu: o li0gsax2)z3 point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrations in exactly.h u9 tz9fcd;g. x;fwn 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendu j8;my p.b9rljlum be if it is to make exactly one swing per second? (That is, one complete vibration takes exactly 2.0 s.)j by;ml9rj. 8p    m

  A pendulum has a period of 0.80 s on Earth. Whatu-v).bwn5d:m2 whvsx2 ainua w7d 8l3 is its period on Mars, where the acceleration of gravity is about 0.37 that on E:n7 lv8da 2wi av2- dww.suxnu35mhb) arth?    s

  What is the period ol5n uayxppl)ke /8 e ;u1h..rcf a simple 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 pech9)7z :neop5v :nggrndulum bob has a mass of 365 grams, and it is release9p ocgneh5g7zn :vr ):d 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 cloc kq(2+x nece*tk loses half a minute per day, how should you adjustcxt(n2eqk*e + the length of the pendulum? shortened by    mm.

Derive a formula for the maximum spe gihc/p3w*7a ded $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at a frequency of 2.5 Hz. At ie0h r8ex 0/22l7m cbdhmtd*zg t is released from rexez2l2r/t 0 7ec mg m*h0bh8ddst starting at an angle of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests pass t8jbl du v. 5gdnz5/2njhe bow of his anchored boat every 3.0 s. He measures the distance between two crests to be 6.5 m. Hojb2 zl5./5dnugnvj 8dw fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 26 s/5;: mi xp saw3k eyc5rf y/kid8xffcpn35982 Hz and travels with a speed of 343 m/s How far apart ai pp:n w3y9rc c5a/5fsexik3k; 8fyms/8 x 5dfre the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (kilohert8 /6l)hunyfhsz7x/qv )j wvx6z) and travel with x/6un8)qysvvxflj76 /hzw) h 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 551dpz 9bh jdwlongitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic )ou;4x,mnbw je:o d/ rmodulus, but one is twice as dense as the other. In which rod will the rnuxdojm o:)e/4wb;, speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched betwee )d 3xk mhdh)5)z(s9 zr(vfp6of0 kpjrn two supports 28 m apart. If the tension in the cord is 150 N, how long will it take a pulse to travel from one support t0dvor f 3 zjshz6d9kpk) x(rm)fp() 5ho the other?    s

  A ski gondola is connec dc edr+8kedffy69+x,ted to the top of a hill by a steel cable of length 620 m and diameter 1.5 cm.r+,f+y6eded8 fdck9x 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 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 jusndguyg wq,/c5vyb/5;pj*t x5t below the surface of the sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is tg/cv xpw5t*nybu5;, jqy/5dg he ocean at this point?    m

  P and S waves from an earthquake tra d4qe**vy* czhvel at different speeds, and this difference helps in locating the earthquakevc d*z*y*h 4qe “epicenter” (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 sinusppo4jgz0 u; g5oidal 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: Set the acceleration j4g;guop0 z5pa>g]    m

  What is the ratio of (a) the intensities, andhwj4i, ms/yxjw)* b3c2n r-yx (b) the amplitudes, of an earthquake P wave passing through the Earth and detey-2rjj *w,b4hx xwy n3ci)/mscted 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 todwn(9al.ogkz:91 yf( q + t44tujcy md be wu9k.myg dty9+ o41zdfj4:na q((l tc $ 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 58zsf.hrgkrp7hkm;am 84, lwtravel through the same portion of the Earth, but one imwz8kh7 falr;s,4 5m . gpr8hks carrying twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string70(uszec1 ynb have the same frequency, but one transports three times the power of the other. What7u(ze 1ncby0 s is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move up and dow y,a/clbn4/2sns/vsy n a total vertical distance of 6.0 cm, from the lowest to the ysn2ba/4lvny s,s/ c/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) Sketch t yhing3g (4 -wsay8d+vhe 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 has happened to the e-4vwh+ag i( ysng3y d8nergy at this moment?

  If a violin string vibrates at 440 Hz as its fundamental frequency, what ytbc 6 m 2z3 1pch6xeha)r7-blare the frequencies ocm73 l2h6)tazb-hp xcy1e b6rf the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibratesx+ lt knb7f.c6;f+dpn8kik 6m at 294 Hz when unfingered. At what frequency 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 standingk7x bf;ldnpkki.f+8m c +66t n wave.)    Hz

  A particular string resonates in four loops at a frequency ofly ,bsod kx3g p,0l0:q 280 Hz. Name at least three other frequbl0 y03kx, q:spdl, goencies 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 of41yyrizaof*3 standing waves is 475 3 y1o4*ariyfzHz, how far apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 350 H56lh-ug im4v fz, what is the frequency of the fun5lughvf-4 6m idamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. Thf)k2 kpzq36 ,fs v7ggbe distance from the bridge to the supp zf3g6vf7p 2)b,qsgkk ort post is L = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is sfp3i7-vij qc9h)- xo fupposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the svfi-oc fh79 )i3xq jp-tring 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 crnuc9x m012p at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tensionnpm9r c21 x0uc in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-amplitude mechanical bkk7t1j 0 *p;/vj. t0acyqryb60-Hz vibrator. The string’s mass per unit le/y0yp 7jaj.rvk; b1t *kc qt0bngth 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 leng gyhf; fj0:b2ogp3 h)xth of the string may be adjusted by moving the pulley. If the hanging mass m is fixed a3fhho:f2) gy;bg0 x jpt 0.080 kg, how many different standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water bacs4/h(tc z/tl uk7:pqok and forth in a tub at just the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to pro(sqh/:pzkttuo 4 lc7/ duce such a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundary h-*k5 x7*9lskevzky :d b3uehh *m/kbwithin the Earth between two kinds of material. If it approacmdby:h s ekbkz9-3k*hx*l7/kv5* huehes 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 “shi4dw k6 (/n9o7w6n8liggfmf 9y,lcz relf” where the velocity changes from 2.8 m/s to 2.1 m/s If the incident wave cre/wcf yii6 o7m nnw 8gz 69l4,grf9(kldsts 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 c6ar j5kbr8: ac+ bdtn,old, dense air. If theb:j,bar6+ n r8atdck5 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 strikes5mcyw,-y5il ler*fu c/ p3i, h6kz.nr3y *vc q a boundary between two types of rock at a 38 rqh nci5u yml*w3 6v*c, -/y elfrz icyk53.p,$^{\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 0.58;i 1xa brw2jsbs:of+ m in diameter. According to the user’s manual, the dish has toa:ifb 8bwj r ;os2xs1+ 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 a:*oi 8ksruqvn5s:. xwcross the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how rn:kosi5:xsqwv 8*.u 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 constakafz50mh3pze 08q /mdnt of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, 8 m5h zz 3km0/0fdpaqecollides with a 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, which stretches oz2tws2 zkx z.i4,ww7 the net 1.1 m. Assume that the oszxwz 2,.wwz47 i2 ktnet behaves like a simple spring, and
(a) calculate how much it would stretch if the same person were lying in it.    m
(b) How much would it stretch if the person jumped from 35 m?    m

  A mass m is gently placed on the end of a freely hanging sp0x *8g+ +lados y*dnkdring. The mass then fasd on0++ k*lydax8*dg lls 33 cm before it stops and begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (4 ,iocnv+) r 53ezyh vdj.gxp(Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffness consta +cxv) or3n,4zgj5i e(dypv. hnt 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 (dia 9mh5hfr984tg2wn h nfmeter 8 cm) at just the right 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 coffeent hn2r4hm8995hwgff.    cm/s

  The ripples in a certain groove 10.8 cm from the center of.vkxavxe+ff05.9x 3o ditlo ; a 33-rpm phonograph recorl.. f x o0vx5do;tefa+vxi 9k3d have 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=0.65c; ytrlpwt8;50cos7.40t where x is in meters and t in seconds. Deterplrctt;5y ; 8wmine
(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. hok , e;675fq:zo wpwjWhat is its frequency if it accelerates at 0.50g (a) upwak :w,5w;7jpe zfh6qo ord,    f
(b) downward?    f

  A 220-kg wooden raft floatd1nh rq8- p 0dn7l0ti4ajx0 bbs on a lake. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When hr j8a- 0h0p t7xnd4iqb n1lbd0e 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 i8e)hxtk 0ccov( y)2a xnstrument are tuned to play at 392 Hz (G) and 440 Hz (0 2cceyxo8 k(taxh) )vA).
(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 z ,thpwoossw53- /.usthe stretched two-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of 3ot, 5- zhs.wswousp/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 section of cord or the lighter?

  A tuning fork vibrates at a fredxbyg +f60eq/: v e)gpquency of 264 Hz, and the tip of each prong moves 1.8 mm to either side of center. Calculate )gv q:pye+ bd 6/gxe0f
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscilla6u0jt+.o9vei+ lv qr5 q4fmrktes 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 (qi+merv5.6kf 9r 0uotj 4+qvlFig. 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 caxx uukf5 1 d2t;w42ncbn slide without tf uxck4n ;du512w2 bxfriction 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 exactlet7xeda sf8/jm7t8ayl9 9.q. e pqf7 yy 2.000 s — each one-way swing takes 1sdfme. qeat8py 9j7etl7x9f7a8/. yq .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 a e pd* 9x*2oaj1bwp:ha14cc sor can swing as a pendulum of small amplitude, but not both at the same time. Which one:pw9 d a s1a*j1bhx2cc oa*4ep is longer, the period of the vertical oscillations or the period of the horizontal swings, and by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

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

  A 10.0-m-long wire of mass 123 g is stretched under a tension of 255 N. A, :sg ct(mryg08m*po f pulse is generated at one end, and 20.0 ms later a second pulse is generated at the opposi: gmr8m,0fty(p c*gsote end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spring with spring stiffnebe0+ zaff22 sl( c8;jn 9bbnkzss 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 j2nz2b;(9cb8bf0 en+a flzk jsust stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel crane cabr52j2 ki (sveb /eqjiglr/7 .jfm)3jqle is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at th32 v (jj .m)b g5ij iq7s//rreqeklf2je end of the cable. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (which also givyr7zvxk :1.; y izr*jwes the dimensions of the block). You 1* k7z;vw: ry.jrxyzi push it sideways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the 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