Give some examples of everyday vibrating objects. Which exhibit SHM, a ) vpgdldf+gok0x60 r:t least approximatg)r l gk0pdf6+vx0o d:ely?

Is the acceleration of a sim6 v/+qp zvedfto0*sv 66zk3hjple harmonic oscillator ever zero? If so, where?

Explain why the motion of a piston in an automobile enginel: 5 m0.umyag* w-)caq igl*h7 eepdo+ is approximately simple harmonige*5gcl p -i aom:0wqam+hu7*y)ld .ec.

Real springs have mass. Will the truhwolrq3 9t)8 he g8g8we period and frequency be larger or smaller than given by the equations for a mass oscillating on the end of an idealized mathogg9 3rh8l)ew8w q8 ssless spring? Explain.

How could you double the maximum speed of a simple harmonic osciwe4c 8b4 kvc lpy46vg5llator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring s*torry z4*r*da 1y9cqa29o ficale, and then is released. Describe the scale reading as a function of ti42ar arqy 91*ytf*9i*z roodcme.

If a pendulum clock is accurate at sea level, will it gain or lose time when trh84n qaya40 did;o p7aken to high ypno8 h40idd qa ;7ar4altitude? Why?

A tire swing hanging froj:k9qwq( -uz lm a branch reaches nearly to the ground (Fig. 11–48). How could you estimate the height of the branch lqjw k9-zq u:(using only a stopwatch?

Why can you make water slosh back and forth in a pan only if you shake thi:n0vfhq d w52o3 odh7e pan at a certain frequency?od2vh3w7 f5hiq:don0

Give several everyday examples of reson6sbct00ua 3 psvlg (,mance.

Is a rattle in a car ever a resonancltjlq 3 ewd+vzp884l5 /rv6dge phenomenon? Explain.

Is the frequency of a simple pera4u2ne:l9 yb g32zvfliodic wave equal to the frequency of its source? Why 42bfyl2zu:evn9la3 gor why not?

Explain the difference between the speed of a transverse wavvh0buss+ w5. m qzx0c ;((dfdqe traveling down a cord and t5(0d+f.dm;q 0s xubzvs(cwhq he speed of a tiny piece of the cord.

Why do the strings used for th8i9 v t81hdiwck ul2,ze lowest-frequency notes on a piano normally have wire wrappedi81uvlhi tz29 w8,dck around them?

What kind of waves do you think will travel down a horizontal metal rod if yn;1wybjsn b97 ou strike its end (a) vertwsbj7bn ;n 9y1ically from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase in temperature, but the buldp/8oz5:xenqwu. 3by )4a9gmohyx .f k modulus B is nearly independent of temperature, how would you expect the speed of sound waves in air to vary ww hz yg n8:q3oe u /xa5fyo4xpd)b..9mith temperature?

Give two reasons why cirqu2b;ci xu3r 69yf4 lycular water waves decrease in amplitude as they travel away from the souruiqyx4f9 2 c ;lyb3ru6ce.

Two linear waves have the same amplitude ( t7:xl*)tjkkjri 4b 7c;ibzb and speed, and otherwise are identical, except one has half the wavelength of the other. Which transmits more energy? By what factor4c;j) ii:7x7j btkzr l(b tbk*?

When a sinusoidal wave crosses the boundary between two ib,lwan cu8 aj*:.v p(sections of cord as in Fig. 11–33, the frequency does not change (although the wavela*na.pvci,b:u (8 w jlength and velocity do change). Explain why.

If a string is vibrating in three segments, are there any pl.dbx9bfbax09 ap0e0qad/z 3 j 1(d mhlaces you could touch im./ eapx0hq01(b bad 3adxfjzdb 90l9t with a knife blade without disturbing the motion?

When a standing wave exists on a string, the vibrations of incident and7cf6tf lruc;oo d9m+) reflected waves cancel at the nodes. Does this mean that energy was destroylfu7rc9 +);6cof om tded? Explain.

If we knew that energy was being transmitted from one place t cpfh(z4 jz7v.sgf i e2jb,/x-o another, how might we determine whether the energy was being cav bp/x7zhf e s(i-42j.zc gjf,rried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is p-m)/ hgbz4wn the total distance it trm 4pw nh)-gb/zavels in one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it but is 85 c*qsy n/b 2rr.cm long when a weight of 180 cs/ * nb2ryr.qN 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 its 68-kg driver ge2 u+x x.b*qis2svv7g tts into the driver’s seat. If the car goes over a bump, what will be the frequency .x7bv2u tgvs2q*x s i+of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7663dvgjo:p gv -kg fish hangs from it. (a) What pd6vj g: go36vis the spring stiffness constant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a frequency of 3.0 Hz when a ma whufs l660xw6ss of 0.60 kg is hung from it. What is its frequency if only 0.38 kg hangs frwu60f6hl ws6 xom it?    Hz

Construct a Table indicating the position x of the mass in Fig. 11–2 at sd ys5v*-om d0times t = 0 dmds 5vys*-0o,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 spid1 ;2zs qjvso/ner’s web. The web vibrates predominately with a frequency of 4.0s 1vs2;zo/njq 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 sp9 4: dfb+gbi:+hjsbgoring vibrates with a frequency of 0.88 Hz. When an additional j +ob: hfbsbdgi+94g:680-g mass is added to m, the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times/h z caiuq7f5; per second with an amplit7u;q/5fhi zca ude of 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 equilibrium is the speed of a SHO half wb .b 8;3o wnoyy.o3iwthe maximum valu.ooibwy3n yo; 3w.8bwe?$\approx$    A

A mass attached to the end of a spring is stretched dt,/cxitki mt) ec s9s yp1kd+*96ap8 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 verti8v1ao do/k. ezcal spring 0.315 m. If the spring is stretched an additional ova/zko e8.1 d0.130 m and released, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with spring stiffm,:-jo p*uwe0u0)mp v(qgmfnness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is movo 0en gf,*um-mpv0)m qpj:wu (ing with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compress the spring of a toy popgun 0.200 m to tpbo741a5ih f“load” a 0.180-kg ball. With what speed will t7o4hbtf51pa ihe ball leave the gun?    m/s

  A mass sitting on a horizontal, friz,tsdo6je5 3i.yhkj3 ) ;knhu ctionless 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 experien3jh5ke3j.ok); zh un6stdiy , ces 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*r(oc5 oes2ut/eav +l.45cos6.4t where x is in meters and t is in seconds. Determitcas lere/v ou(2+o*5ne
(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 y6(yy p . ;win02ibflia SHO half KE and half PE? ±i2yy;ny wipb(. l f0i6    A

  If one vibration has 7.0 times the energy of a second, but their freq+ *mm9hmfg/pqhvf5b. 0 xf. uauencies and masses are5mvb. xf/ghpf+*fuq am m90h . the same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light spring once even s wq0+wzxl9 15dmsh(ry 0.5+dx(l w1nws z09 qhsm65 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 identical parallel vertic zh 8 qww3aag/8a(,kbt 7yhp7dal springs, each with spring stiffness constant k (Fig. 11–49). What will be the frequency of vibr8aa7wz( hq /bkayw37,hp 8dgtation?

  A 300-g mass vibrates according to the equa m .8kg/gua3antion x = 0.38sin6.5t where x is in meters and t is in seconds. Determia g3k./8mgua nne
(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, g: qurp)jt-r t70(7ov6hjydxcs 8vt / labeled A and B. For each, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest oqbglh*e8m x s nxryl/+;s mc, t)x,39xn the end of a horizontal spring (k = 124 N/m) is struck by a hammer, whichgh3;yl+8r s9m) enbqs tx, m ,xxclx*/ 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 constan9le+i2 s l)nou0; fqrhj8jrjk.+,zfasj7s +st 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium poinso . j,e)l+ slj k+ 0rn89s;+z aqfsr7ji2jfuht (x=0) with positive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two springs, ws 0onw97y hid)b1u8pfith 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 horizontal spring w/e6uuh2-p z rdhose spring stiffness coe /-2up6hdruz nstant 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 e-v uxfm4-g*9 m0zlk) d0smf va high bridge. After reaching his lowest point, he oscillates up and downdg4)msk-z * 0vm 0 9umfexvlf-, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 viz- woc 3bn,tv-f;jcy;-9y-m au n i6jwbrations 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 sigzsx 844/i+yuytk, o wing per second? (That is, one complete vibration takes exactl o/ysx4g+iy8zk i 4t,uy 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on jn*/w1n2xbi bMars, where th1*nx b /b2iwnje acceleration of gravity is about 0.37 that on Earth?    s

  What is the period of a2x/zba 5q,o ,r+vz8 gca4ogkj 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 pendulum bob has a mass of 361usi8i)ru1tc 5 grams, and it is released at 1)rt 8sui1ciuan 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 hqkqt3j,n;g2,mp :i a hi0ho8m/1 rssjqp12ri0 ;asmo: nis th,mqg8,k j3jh/alf a minute per day, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the max r 2tmw9m*mzo(:k 82ifyhi* piimum 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 Hz. At it is rzkz 69 xtfpy(; e2pkuys+h7z. eleased from rest starting at an angle of 15pe pk.y+;2z(us k67y9 t hzxfz $^{\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 crestt626v cr/i5djzwh ct 5s pass the bow of his anchored boat every 3.0 s. He measures the distance between two ritv 6c6w5cjdh/z2t5 crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with a sp fyko213wehi6otju7nkm +z5q -w x( e:eed of 343 m/s How far apart are the wave crests (comp5ok uwwj2qme17hz-6+ fne xy(i ot 3:kressions)?    m

  (a) AM radio signals have frequencies between 550 9 n3dto1d7cyb al-,p ukHz and 1600 kHz (kilohertz) and travel with a speed o1d3-nalpc y btud79, 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 longid-3y4mcb f +fbav+0( baj wn7itudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one is twice as dense as the yhkuevwislq 1 +x:2o t;;b9p -other. I9elt:pwbh; s2 vyuio1+ -;qkxn which rod will the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two svab 7 qci xzph-;u16*gupports 28 m apart. If the tensii pzu1cbgva -qx7h*6;on in 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 connee f; eepoaq .6re6;hn)cted to the top of a hill by a steel cable of length 620 m and diameter 1.5 cm. e6f 6a.q;ee h npr)oe;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 just below the surface of thd27waco3; sz ge sea. He hears the echo of the wave reflected from the ocean floor directly below 3. aoz 3gd2sw7c;0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at different speeds, a/a1e0 chrtuhqc9c:f )nd this difference helps in locating the earthquakecftecc) ha9/uq: 1 0rh “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 au qbym01vg 7(tzp)qv: sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture(bt0qg) vm 1qzyuv7p : of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensitig3*mkusn)45y.nom u.f81 xv 8rpt cvwes, and (b) the amplitudes, of an earthquake P wave passing through the Earth and detect wm* s8m).8 u 54g3fpk v1tnvxon.urcyed at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an eart:,q z eguxhl+ g989(;zd nahmh/1mip ahquake wave passing through the Earth is measured to be (8:dh1n9x9; , / aheigagh+ zmqzmlup$ 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 travel through the same . xf+s9tlh9lbportion of the Earth, but one is carrying twicet+hxs9 f. 9llb the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched strin3n ba7+xb8( j* jq4suxpm5xnzg have the same frequency, but one transports three times the power of the othnbus(bmx*n jz843ax p57j q+xer. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move up * :3 is*wwwkpe:dsen 6and down a total vertical distance of 6.0 cm6nesdw kpwsw*e*: :i3, 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.t:3 o4.df3jy0rkvfxk 11–52 are moving toward each other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a,4r0t3f:y3k k xf.vd oj 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 at 440 Hz as its fundamental frequency, wh 8yaotgrw, 6ae(k g2+tat are the frequencies of the first four harmonicsgoa 2te ,+ky(wr ta8g6?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered.g0+mgz )x4.y:w(do 7ri xt bgg At what frequency will it vibrate if it is fingemg: r g zyo7(bt+ .4xgigwx)0dred 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 loops at a frequenc(; ;xydy3 6nz3wsk aeay of 280 Hz. Name at least three other frequencies at which it will resonaz6; ;n3dey(sw a3aykxte. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on e2wcc).l gwhq-u)0 mqa string is 92m/s If the frequency of standing waves is 475 Hz, how far apart are two adjacent nod .-wc g02)l hmucq)weqes?   m

  If two successive overtong3e 8g:rtbdvy*9 uslk /w; w+ces of a vibrating string are 280 Hz and 350 Hz, what is the frequency of the fundam*8wt r+dy swvu;cel /b g93kg:ental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distance from6g 1swpx*jv1 wn q56sc the bridge 6pcw1sws 1*xq65n vjgto 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?    Hz

  A particular guitar string is supposed to vibtmv+rpwu1,d( l8gh - mi9e :dcrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequptigd , lvdrhc(u:e-8 +mwm9 1ency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200d+ )rxx zm4 aq-xpo3q9 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct tq9rqa ox-d) 4m3x+zpx he frequency? decreased by    %

  One end of a horizontal string is attached to a small-amplitude mechani0 . u6728a2cdaitdtgzq uopp) cal 60-Hz vd aa8z)t u6 tpo7i2cg.d p20quibrator. The string’s mass per unit length is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of the string may be adjusted by mdi 7cedk-*utt7u*4btoving the pulley. If the hanging mass m is fixed at 0.080 kg, k-u *iuet7d*tc47t b dhow many different 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 justkxu5n*la +n.:dx t.;z dh. itw the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Supdx:.dit ktlzx.+nn .u h;w*a5pose the frequency to produce 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 s6;q ivtdd+ 3.htr1n i1u x.pygtrikes a boundary within the Earth between two kinds of material. If it approactr..diq; du6y3ti1vnp1+hxg hes 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”/6q :c c*v2.ct poneeq where the velocity changes from 2.8 m/s to 2.1 /e6p*qq :c. 2eccnotvm/s If the incident wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air when it hits a laye/r sgxrn m,z 4i1/maa9r of cold, dense air. If the s/s xz/grm9,ri m na4a1ound 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 strikes a bocs95j3 oz.k smr /wqz8undary between two types of rock at a rw qzss58/k.3czjo9 m38 $^{\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’xs)tlrl d7o;7k* cl,hbs w8w2 s manual, the dish has to b o c*wrlh )77sdkswl;lxtb,28e 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 ) :jr: vn*cckjvelocity 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, people have died during tsunamis, some of them attracted to the shore to see stranded fishes a nc:)jjk c*:rvnd boats.)    min

  An energy-absorbing car bumper has a spring stiffness conmqf 6qvm/rxt)( fe5hoq:7 9xpstant 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 energy.]mt7q( q/ xvoh9 6e r5)ffqp:mx    m

  A 65-kg person jumps from a window to a fire neto md z/85xlubd-ryc0bb n27k) 18 m below, which stretches the net 1.1 m. Assume that the net behaves like a/bkcl7om unbr x ) -5y80db2zd 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 plp35y1 m/xjylkaced on the end of a freely hanging spring. The mass then falls 33 cm before it stops and begins to rise. What is the frequency of the os xlyyp15/m jk3cillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 11–54), l :-qf q k:,k,uu2wfspcompressing the spring 5.0 m. (a) What is the spring stiffness constlup:qsq ,-fu2 w, fk:kant 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 c1 p9wb5ah;tp toffee (diameter 8 cm) at just the right pace of about 1 step ab9wh1 tt;5ppper 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 coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the center of a 3p ,f b5nycf74s3-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequency y45s ,pbc7 fnfof the sound emitted?    Hz

  A 2.00-kg mass vibrates qq de4:)jsji (according to the equation x=0.650cos7.40t where x is in meters andsq 4e)djq j(:i t in seconds. Determine
(a) the amplitude,    m
(b) the frequency,(round to two decimal place)$\approx$    Hz
(c) the total energy,(round to one decimal place)$\approx$    J
(d) the kinetic energy and potential energy when x=0.260 m.(round to one decimal place) PE$\approx$    J KE =    J

  A simple pendulum oscillates with/ecj 6xto3mh* frequency f. What is its frequency if it accelerates at 0.50g (a) *6mexoc /j3ht upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands ei)n 4-j 9hbi)3hvydel5ozq+ on the raft, it sinks 4.0 cm deev)) 4ie-ij+d eo93lhhn5bqzyper into the water. When he steps off, the raft vibrates for a while.
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a musical instrument are tuned to play at 392 Hz (G) and 440 Hz (*s7hcy6 yolv)l z 6+ydu eo64lyyso66 7 l+cydz4luvhl*o)e6A).
(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 travelin9xxs 0e5spr//e 06 h7mua4a vn*; r 3auqnpgrqg down the stretched two-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections.sqe5raepg3/n qn um/*ha 6upra4x 9 07v x;s0r Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, anlxq(a-il n w(,d the tip of each prong moves 1.8 mm nl(,qiw-lax( to 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 oscillatess/oh pf m9- wwcx*20weckmx97i*o1 fv with simple harmonic motion of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the boam 9 mw ko1*-xew 2p9v7wfchfo c0s/i*xrd during the oscillation?

A string can have a “free”g 4us 0vjui+cu7zz j-q642fzj end if that end is attached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with one end fixed anu-qz724u fgs4 vuzjjz0ic 6+jd the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each one-way swing takb4ys;-vwaa .9/v ypuo2 6zhtp es 1.0zp9va;yu/6vhpow4 a2.t b-s y 00 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 ipkx (fe6*rd69+ hml+o axj8dvn the vertical direction or can swing as a pendulum of small amplitude, a+*x 6 rf(8lxjpdkdvoh +9m6ebut not both at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontal swings, and by 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 ofc(4t3enm( b5(hpv sc j 255 N. A pulse is generated at one end, and 20.0 ms later a sep(csv te(n 3h mb54(cjcond pulse is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is:jm6 wi* ixp1k suspended from a ceiling by a spring with spring stiffness constant k. A penny of mass m is placed on top of the blowkp*mx ij:6 i1ck. What is the maximum amplitude of oscillations that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel crane cable i kjms7k/)a pl;s 22 m long and h k)s 7jal/pm;kas a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (w s64u9.-sitw kk hgi)ahich 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 k ut9sg) i6a.kiws-h4vibration, given that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz