Give some examples of everyday vibrating ob2a) nv bygf+*v3 iku+ )b*ecqijects. Which exhibit SHM, at least appn)e buv f+bq 2v* )iikg+cay*3roximately?

Is the acceleration of a simple harmonican97qap;rea gsa(99nc.; +bv-zr djp oscillator ever zero? If so, where?

Explain why the motion of a piston in an automobile engine isjpi* 2r 3nx-u3;wl srr approximately simple harmo w33-jrlpni*x;r2 r usnic.

Real springs have mass. r iv bb*.ed:n5,g ju;hWill the true period and frequency be larger or smaller than given by the equations v .h;:*bd grib nu5,jefor a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximpu(g+0b krx)j8(urlbum speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scale, and thd vs/khsb( )syftthc5n 8,wv* +agk)4 en is released. D),t/vfc +dnhs)4ws*k(tgb5h8ky a s vescribe the scale reading as a function of time.

If a pendulum clock is accura ozqaiw2x3y ,ug )*w2ote at sea level, will it gain or lose time when taken to high altw ouiywog, 23*) zx2aqitude? Why?

A tire swing hanging from a branch reache7 ww (xr+/oules nearly to the ground (Fig. 11–48). How could you estimate the height of the branchu +(ewlx 7owr/ using only a stopwatch?

Why can you make water slosh back and forth in a pan only if you sr xyt 409*2, wxylufm2ze 2qyghake the pan at a certain frequency?9t2xyw mqez,0ry2f4y*2gxul

Give several everyday examples of ref07z6d qsh fhyjk*3i+3/ hqqy sonance.

Is a rattle in a car ever a resonance phenomenon? Explainnp/wna7g x9(ezf z;y7)f 4 i6nf wz4kf.

Is the frequency of a simple periodic wave equal to the freqdns 5qc(v6/ i nd)3qequency of its source? Why ord)qs/ine n3 c5vqd(6q why not?

Explain the difference between the speed of a transverse wave tihfk a a+ n5f r-l l78:41lwa3jtm)lraraveling down a cordkh l78 aj35a 4fllrl :1 afwat-+)mnri and the speed of a tiny piece of the cord.

Why do the strings used for the lowest-frequency notes on a piano normally havej;ph;ak:0mr2gbo2n s wire wnm;a:rk o h;p2sj02 bgrapped around them?

What kind of waves do you think will travel down a horizontal metal rod if youyj-glv r40 agjmu(+7 r strike its end (a) verticag-u+y(7 0mvarg4jl j rlly from above and (b) horizontally parallel to its length?

Since the density of air decrea7ocwzwqf;e79 ses with an increase in temperature, but the bulkwwzef797 qc ;o modulus B is nearly independent of temperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular watehl)*y0 4fv3 r kapf)kur waves decrease in amplitude as they travel away f))0vkuf* h3ka 4plry from the source.

Two linear waves have suflz,-;pcm3 the same amplitude and speed, and otherwise are identical, except one has half the wavelength of the othe-us,cp3f ;zml r. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two s h 73mj-guu1 -w)gftslections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocity d7gmw-1 hs-u3g)juflt o change). Explain why.

If a string is vibrating in three segments, are there ane o6ii)e 0clu-y places you could touch it with a knife blade without disturbing the lc0i6uoee -i)motion?

When a standing wave exists on a string, q qe ahw21ua09the vibrations of incident and reflected waves 90haqa2u 1qwecancel at the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one place tod+ p+vq,j:d ky another, how might we qpdk:v+ yj+d,determine whether the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is ph h(qqo60x0k the total distance it0k6hh q 0q(xop travels in one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from iwgqk 8)a+)pm: 5wji -fz5qic;tjl l-yt but is 85 cm long when wpij5k):lw5z ca; -g-yq8+ itmf)lqj 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-kg car compress 5.0 mm when hl4xhpotdi5;x-k e6; its 68-kg driver gets into the driver’s seat. If the car goes over a bump, what h54tpkdxh6xe;-o ;il will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs from it. (a) Wh.ka5+ mhfa(ihat is the spring stiffness constaki+hmfa a .h(5nt $\approx$    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 frequebdt/-l gw10(loel z l2ncy of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency if only 0.38 kg ha l0-(tleolg1 2lb/dwz ngs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. 11–2 at times t xmwnw v tbpy 2.i6ln,hqmr o 90l/279e= mq .bl20v9nly,7 mxtw oiw/26hp e9rn0,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 spider’s web. The web vibrates / ldi1 gzll)0qpredominately with a frequency of 4/ id0zql lg1)l.0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a spring vibrates with a frequency of 0.88 Hz yl7chz)6ub+ h2e aaykixo27* . When an additional 680-g mass is added i72aae yhu7 *2bk zh 6y)coxl+to m, the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of azr h)pb-nc3m/ spring vibrates 3.0 times per second with an amplitude of mrc)b3n z -hp/0.13 m. Determine
(a) the velocity when it passes the equilibrium point,$\approx$    m/s(round to one decimal place)
(b) the velocity when it is 0.10 m from equilibrium, $\approx$ ±    m/s(round to one decimal place)
(c) the total energy of the system,$\approx$    J(round to one decimal place)
(d) the equation describing the motion of the mass, assuming that x was a maximum at x = (0.13π)cos(  πt)

  At what displacement from equilibriu(n: :qa3nps b)hw1i+ egf)nhmm is the speed of a SHO half the maximum valuq e)+w:hnbip na:3n ( )hfmsg1e?$\approx$    A

A mass attached to the end of a spring is stretchec q hvm7e.jll):d)o htlfv) ;1d 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 0.3p5(+od2i+mjr wkkt) r15 m. If the spring is stretched an additional 0.130 m and releaj5r +kr(2mdt )wp ki+osed, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a sprin sm0cp;x )k1mjg with spring stiffness constant k = 280 N/m and is execut)sx1pj0 k mc;ming 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 comprec b349gadsyg:ss the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will the ball leave thegc dy:4g9 3bsa gun?    m/s

  A mass sitting on a horizontal, frictio0d f:oa0o4fa tnless 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 compressed, the mass eof0:a afo4t d0xperiences 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 = 0.45co 673m;n+whrh is u7lcts6.4t where x is in meters and t is rm iw 7hnl3h;c7us6+tin 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 energy *,a0eykulbr53lk y4qgw 9 h9wof a SHO half KE and half PE? kqr9349e k,y lu0*ww hlg ya5b±    A

  If one vibration has 7.0 times the energy of a second, but their frequencih0)z ew+ja 8185,a5zpye pts6j nd viies and masses are the same, what is the rat5h s ji5pyz1,aa8dp 8+)6e ze wnjitv0io of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanginub6rz s 84d,gk7vq dh3g light spring once every 0.65v 48s drz q,db3kg6hu7 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 two 6 zgb:cg ,)zuzp2(u*.vx bimy/beam 6dvjb++ identical parallel vertical springs, each with spring stiffness cong):mbj6b2uceg+v(azubxz .zb,*ym / dip6 +vstant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t where )jv0xynzwlj.o/9emwj;ur2o / x cq9m;e7x, q x is in meters and t07j)q9,9;lumqz//v ew.e yorxx2xj ;j c onwm 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, labeled A and B. For each, what i,n6gdj cm(sy9s
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on the end of a horizontal spring (k = ( t5ptvm6nldn143* kxabm3bt124 N/m) is struck by a hammer, which gives the mt6 mtk nmdl*vx3bt 3n p(4a51bass 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 vtm9i)relo dg7 n-10 doibrates with an amplitude o)9m10od degt rlo7 ni-f 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) with positive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected t)(- w;yo(),usyyrbn tsgd9pn5hkxv8 o two springs, with 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 attacheol 2ww( o4py:l (8nbre )jfsw6d to a fixed horizontal spring whose sp:l64w)f( wy(rl owp 2n8bjesoring stiffness constant is $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with nn/5/+age swk5p;hz n mass 65.0 kg jumps from 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 briw/nn ;p/ z +hsgak55endge. 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 exactlyy5 t))i6j rg4lkxfz(3kyvnd 1 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if i: poytrl)acw, z(* x u7kbzd(9t is to make exactly one swing per second? (That is, one complete vibration taalor9y: wu( k7tb)*cx(zp d,z kes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period3e2 fyp w+t.zpc6u l5w on Mars, where the acceleration of gravity +pu .52ytw fzcp36le wis about 0.37 that on Earth?    s

  What is the period of a simple pendulum 80 cm lo3craqiwqm */(pxu n* 1ng
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 m (ibru(v8 b8 k3v2nkpt, the pendulum bob has a mass of 365 grams, anki(38bptvrn bku 8v2(d it is released 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 loses jaz7y6yq.) t thalf a minute per day, how should you adjust the length of the pendulum? shorteaz6y) 7tyt jq.ned by    mm.

Derive a formula for the maximum n*v)pz a p;(a9pz: px tzo:dm,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 a frequency of 2.5 r40j mu hu 9rq-ia:q*96dethgHz. At it is released from rest starting at au0r9j h 4q96-emdr *giu:tqhan 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 cre:qm8el e wfs87 y:,autsts pass the bow of his anchored boat every 3.0 s. He measures the distance between two crests to be 6.5 m. How fast are the wla,mu t8q:e w7:ys 8feaves traveling?    m/s

  A sound wave in air has a frequencyy3,o-raic cv9 of 262 Hz and travels with a speed of 343 m/s How far apart are the wave crests (compressio ra9i-y ,3ccvons)?    m

  (a) AM radio signals have freque6 m 7c juiia-nkum;n5rvwtn34h4m *b)ncies between 550 kHz and 1600 kHz (kilohertz) and travel n5w3km4-a6irjn 7m4iuvb h c)tun ;* mwith 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 waves in xbbi. i(t8q( z
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, butl-k z0f8knqd +gwxq+ +, e:ybq one is twice as dense as the other. In which rod will the speed of longitudinal waves be greater, and by what factor?0qy n +wfd,lqg kbxz8 keq-++:   

  A cord of mass 0.65 kg is stretched betw+* vfp(eo *0 ihq3xkaween two supports 28 m apart. If the tension iwfp a* o03he+(kvq*ixn the cord is 150 N, how long will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to the top of a hill by a steel cable otor.,xmn:w y; f 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 tyt n.rwm:ox ;,ook 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 be c3ozauq:0f 7 5;juyfxlow the surface of the sea. He hears the echo of x5yau fz;c: 0f7jq3ou the wave reflected from the ocean floor directly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at different speeds, and this din-ooeipc3k 0+ fference helps iie3o nko-0pc +n locating the earthquake “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 sinusoidaji h ,rm3o6n,rl transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include ,jmh or,r3 in6a mixture 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 (acrb q7;e :4ed6 vsu5ns) the intensities, and (b) the amplitudes, of an earthquake P wave passing through the Earth and detected at two points 10 km and;s6v4u5qe7: sndrc be 20 km from the source?(a)    (b)   

  The intensity of an earthquake wv6e)l b3qo2 . 1jghrtmave passing through the Earth is measured to be oj2te)v bhq6m.r 1g l3$ 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 j9 h vtc21jleo .ihliem-5osma9z,.) the same frequency travel through the same portion of the Earth, but one is carrying twii1sit 2 ,hhl 9jeajvm.le5-o .mc)zo 9ce the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same fregi3+r;3l d 3zj):i/zn ayew)6r zviroquency, but one transports three times the power of the other. What is the ratio of the amplitudes of;yor zgrvi)aen/ 3r3ildz :j+wz)i3 6 the two waves?   

  A bug on the surface of rx2y;k 3 c elfevy)8p4a pond is observed to move up and down a total vertical distance op3xe)r; ke42c lfyy 8vf 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving t, bwjg(2mar alvl71bl 166 hqroward 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. (c) In Fig. 11–36a, at the momen1mw7,2 g6lrha q (val1rbj b6lt the pulses pass each other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundamental frequency, what areecqw fpvcp)i54 **:tey8f 8jb the frequencies of the first four harmon*:b twpj ec e)f8yp4vfi*85qc ics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingeb kbvc 1yf5 p6b0fs43kred. At what frequency will it vibr13bk bckffbypv5s460 ate 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.)    Hz

  A particular string resonates in four loop9k. pb:awe/5kctj8 fns at a frequency of 280 Hz. Name at least three othef pkajk/n :.wet bc859r frequencies 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 stan-,afgjp2yd jm2j v p.5b yi(0mding waves is 475 Hz, how far jp-0 pm jb.vj(dm2 2yf5 ay,giapart are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 z/flm1)v *yi xHz and 350 Hz, what is the frequency of tx*v/ 1mfizy )lhe fundamental?    Hz

  A guitar string is 90 cm long and has a mass ou+u,ghks w-c9 f 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 overt kgh,9-+u cswuones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, but it is measu. fx ):cmrdh+b;(4.dpdvy2ls nk iws9red to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?So the three frequencie m2ypn4:l.wr divcx;dk+d 9). shbs (fs are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is suppose)x 7hcr(a6*eu7qumig d to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to cor*egr7u7(uq )c i6xahmrect the frequency? decreased by    %

  One end of a horizontal string is attached to a s.e3k , gpc.eo(ky r;o4e7 atksmall-amplitude mechanical 60-Hz vibrator. The string’s mass per un.tyep3k.4r ak7 ose , (cgkoe;it 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 mam2l5xz 9s7x573wr/zr aytu(tf u.w poving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying af z23pxazx5y twr7t7u/ s9urw( lm5 .L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at just the rips(g 6tyz+* xkght 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 of the wptzy( *x+k g6sater wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundary within the Earth b9isx0 m *r+g5jdk)kjl2)p sqgetween two kinds of material. If it approaches the boundary at an incg)p j+2g0lmk )jqskds *x9i5rident 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 2.8 0 jcst1n;6cq mm/s to 2.1 m/s If the incidenq06mnc1 j; tcst 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 o f :a; wdcz+ 03zh0t9zvbzu6mcf cold, dense air. If the sound wave hit d3z+zt zubcv mf0zh ;:609awcs the cold air interface at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave strikes a boundary between two types of ruan38 )yjt 4c-1nzr +emh/jhmock at a 3 mzmh )a/j ncrej+h4 n-31ytu88 $^{\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 manuan o+ j*ixta68zl, the dish has to be pointed in the directa+xtoj6i*zn8 ion 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 wavelengt wv1 bs3i0xn0th 250 km and velocity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning st0w3x0vn 1ib, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing z4hu+h z3 dav2car bumper has a spring stiffness constant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of ene4a 3+vdhhz2uz rgy.]    m

  A 65-kg person jumps from ap37 imx*ooiy/ window to a fire net 18 m below, which stretches the net 1.1 m. Assume that the net behaves like a simple spriimo3*ix7/p oyng, 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 pb yh/ v.s6q r5m)gwbep*:nj/dlaced on the end of a freely hanging spring. The mass then falls 33 cm before it stops and begins to rise. What is the freque.rgbj *6)n q//dyms5vp :whbency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a cehj3yj/bws5mtb9 (jco v) 4-;xysi2speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the sprijj(2x9-mjy5 /3cc ehbb 4s vitw; sy)ong 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 ca0ytkhxozvbb*5 )s )nocz/5 ;offee (diameter 8 cm) at just the right pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spilo boz*k0stcvya/ ) ) b55;hnxzl over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a cert*i oar:6p -riuain groove 10.8 cm from the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequ:u-arp*6 io riency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t wy 6z/d9huf-*1qmo dw+oeeq4 i here x is in meters and t in seconmeo 1o6qd*di/qwh4z yu +9f e-ds. 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 3 glyq ows.( 5/at-brka)sv2 )hav4alits frequency if it accelerates at 0.50g (a) upward,5 l go.rhwv3ya 2/bs s)a)a (a4-ltvqk    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on the raftn tugd6v0+ :he egp*sil;m/ o,, it sinks 4.0 cm deeper into the water. When he steps off, the raft vibrates for a while. oegpe 0vs/ml6;h,*:t ig dun +
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a musical instrument are tuned to play at 392 Hz (pj/jntz8yyb6g3b 5eoou35q (G) and 440 Hz (b5(uqj63oy/ bpn8o 35zegytj A).
(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-paxf7wnh5q4ef(v d byzu05x +,ort 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 ratioo 47y0w,nzfq5b5xh fu( vdxe + 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 frequencyluxz p3r5 xqu0;tojwd 3 a/)1f of 264 Hz, and the tip of each prong moves 1.8 mm tzjuluw/1 ); ftr350o qpdxa 3xo either side 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 hauh-fv-g83 1wz gg d)xprmonic motion of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board cax udp)83wvgfh--g z 1gn 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 i0a -waui06u ozz0g*u “free” end if that end is attached to a ring that can slide without friction on a vertical pole (Fig. 11–wuu *oazi-z 6ig 000au57). Determine the wavelengths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum)9t 92d4;n (oar xebh,xtcqpz has a period of exactly 2.000 s — each one-way swing takes 1.000 s.c,e(qtz p9 bx; a2n4dht 9r)ox
(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 vqtm1/*y o5hwm ertical direction or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontal swinwq*/h 1t 5myomgs, 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 stretch7 . k 7zcm+wgfvl(uw wh p8ujy.6payx(z 497xhed under a tension of 255 N. A pulse isul97zx4y .h(pmjwfz xkg+ucwa 8y7 h67.pvw( generated at one end, and 20.0 ms 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 b ;xb6io+w ( 4dubl-rsxm ,,ffey a spring with spring stiffness constant k. A penny of; f-+s m i,xxwdb,(fel6rb u4o mass m is placed on top of the block. What is the maximum amplitude of oscillations that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the rp:dwwd1 )7ma+ z mj7qjunkyard. 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 cablad7zqm)+17 pwd j: wmre. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate a+5/b*6l cti sj nf.cpms shown in Fig. 11–58 (which also gives the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this vibration, given m+ i*csp .b 6ct/nf5jlthat the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz