Give some examples of everyday vibrating objects. Which exhibit SHM, at e)wws)(zz e5a9u8)7uerwbdn least app d9)uze8 ruws 5ee)a(b7ww)z nroximately?

Is the acceleration of a simple h4ff7zldo(u, z l4 cet9armonic oscillator ever zero? If so, where?

Explain why the motion of a pi ff/jann m1a6)nx t4pl)6x4fvston in an automobile engine is approximately simpl nf64 ax)1pltvnf xjn)4 a/f6me harmonic.

Real springs have mass. Will otk,wl2: b.u aq g+m baph,bg-5rh ;)xthe true period and frequency be larger or smaller thana. ktb :apg+gbbwl2m, q- x5hoh,u r;) given by the equations for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum sper: ;oxoho8- ttr c5t.aed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scale, and then isxrb3kv) mv y/i8rsk92 relea mxv)kb3/vi syk298r rsed. Describe the scale reading as a function of time.

If a pendulum clock is accurate at sea level, will it gaa1cklo2 6uk5kd0 ez t9in or lose time when take2o0kd5k t 9zauel 61kcn to high altitude? Why?

A tire swing hanging from a bran.jqd8, (hfz qdnob f)cg h2l:2ch reaches nearly to the ground (Fig. 11–48). How could you estimate the height of the(2 b.gqcd8f2z) , hq:fjlhno d branch using only a stopwatch?

Why can you make water slosh back and forth in a pan only if you shq cp.,n ib0m6hake the pan at a ce6qnp,mc0i hb.rtain frequency?

Give several everyday exam)dr)v conmxlte.r 1-/ples of resonance.

Is a rattle in a car ever a resonance gxac- s :*;lywphenomenon? Explain.

Is the frequency of a simple periodic wave equap) ppsoe, :*-hii9q gcl to the frequency of its source?ce oppp 9*h i)gqi-,s: Why or why not?

Explain the difference b)f(g l22sod-u ,cmxtietween the speed of a transverse wave traveling down a cord and thoxm (d2ics-lt2 gfu,)e speed of a tiny piece of the cord.

Why do the strings used for the lowest-frequency notes onu 55n3(mvcs jn a piano normally have wire wrapped around them5vnj 35u nscm(?

What kind of waves do you think will travel down a horizontal metal rod if yeihx,*:wnz2z0hh 5po ou strike ,:hzihe*h2on zpx0w5its end (a) vertically from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase in temperature, but thecy1p2 .nflu1j bulk modulus B is nearly independent o1u jly2n1fp. cf temperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in amplitud )ovv 2-rqj7swe as they travel away from -7)j 2rvvqswo the source.

Two linear waves have the same amplitude and speed, and otherwise are identi77f7agbe fp s9cal, 9 7beg77s fpafexcept one has half the wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sectiogy jwt03. irilhqz(1a62g: nxns of cord as in Fig. 11–33, the frequency does not change (al :t( in w.rz0jh1ygq32ag6li xthough the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are ti4(eon5iej 9zvz k ;.fhere any places you could touch it with a knife blade withouez; 4. znej(vif59ik ot disturbing the motion?

When a standing wave exispf 1be5l 7*/:k entdbfr 5sl/0jb5c vzts on a string, the vibrations of incident and reflected waves cancel at thj7 nt5 cfd lpb5/b zlksr1 bef:e*5v0/e nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one place to another, how mjie7m1n,y a v)aopcy :15iz9 yight we determine whether the energy was y:p 1iz,7 v n9cyjaya)om1 e5ibeing carried by particles (material bodies) or by waves?

  If a particle undergoes SHM wit3y *mb59zp toxh amplitude 0.18 m, what is the total distance it travels ibp5*z x yotm39n one period?    m

  An elastic cord is 65 cm lo 98e;bvdt5e agv;: sy paiy+;ing when a weight of 75 N hangs from it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” constanpge y;avs 9;ety:ia+d; 58bivt k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg driver gets inw/q:91wg)yjxciodbh 80 s *xuto the driver’s seat. If the car goes over a qs1bu o* d chj:0xx9yw)gw/ 8ibump, what 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) Whae :h98f/dlf pst is thed:l9/ 8hfef ps 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 with1d8u olgvoi:50+ hir s a frequency of 3.0 Hz when a mass of 0.60 kg is hung fro liro0u85d1os+h ivg :m it. What is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. 11–2 at times t 5pvz; ip .+uma= 0,t umaz5 v i;+pp.= $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 w.g9r hhe48vkw eb vibrates predominate.4rh89 gkvwh ely with a frequency of 4.0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a spring vibrates with a frequencyne7hez/m /o.h 28ov sx of 0.88 Hz. When an additional 680-g mass is added to m, the frequ .7mhe8xz/ vheo2 /onsency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the edq:g3p2.9t z6f ahop5. lhh cqnd of a spring vibrates 3.0 times per second with an amplitude of 0.13 m .zh po q9l6h ct2p:dh.g35qfa. 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 to-y 7395 osaurjxqr. equilibrium is the speed of a SHO half the maximum valuot9o57-. x u r3jaqrsye?$\approx$    A

A mass attached to the end of a spring i55 gcn: 5 zdj7b6c6boqthn4gt 6q)w+rd eiuu0s stretched a distance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stre:df7nhoew -:dtches a vertical spring 0.315 m. If the spring is stretched an additional 0.130 m and released, how long does it take to reach the (new) equilibrwno7 :d-:fdeh ium position again?    s

  An object with mass 3.0 kg is attached to a spring with spring stiffness conqtaxlv-7v9* pn y*0znstant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its n7nx9*lz0*qt vpy- vaequilibrium 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 m to kllep) 0bht (+“load” a 0.180-kg ball. With what speed will the ball l0lhk tb e)p+l(eave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to oa3zyt0+ y8z fl90kxbw78 eaahne 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 experiences a maximum +ef73zaka wzt y089lbh x8ay0 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 eq+.x*7mtfw wcwuation x = 0.45cos6.4t where x is in meters and t is in seconds. De.fw cm7wxw+* ttermine
(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 a i8/nv d6*dzpv SHO half KE and half PE? dvv8z/p6d n i*±    A

  If one vibration has 7.0 times the energy of a second, but their frequencieho h)zv5+fn j7s and masses are the same, what is the ratio of their amplituzvnj)h 75o+hfdes?   

  A 2.00-kg pumpkin oscillates from a verticall bf6c hwo35-o- axxjb/y hanging light spring once every 0.65 s.5xfb3c6-h bo/j wxoa -
(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 par+ (h.3i:jqnk jd pcs:w-w2c7d/qxk jmallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What will be the frequency of vibratq: j x+/ci(7wj3ndsjm-.dhk :qp cw k2ion?

  A 300-g mass vibrates according to the eq 53kel/crm*wnuation x = 0.38sin6.5t where x is in meters and t is in seconds c/ml*nr53 wek. 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 2.hn nqbt9m ;ais
(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 8fhlejvos hd+u4qa*p-;a5e; on the end of a horizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an inip j+ a8oas;edv* e lf;uh-h54qtial 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 tp3spn*, 7 -wpgwsre7305 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) with positive velocity at st7r p37wse-pgn* wp ,
(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 connecte l36qa.a(letzd to 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 block6mb::*fz es pa attached to a fixed horizontal spring whs:am:*zepf b 6ose spring 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 mass 65.0 kg jumps froqeu*;-ianorme : l 9j+3c7vtum a high bridge. After reaching his lowamut;q ul+e9ir oc- n*3:v je7est point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and 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 vibra, gk x7id63 gi:lda,ryb4aay9tions in exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it igi94kiav;9 hs x+kxo8s to make exactly one swing per second? (That is, one complete vibra4axk9i8okxgh i9 v ;+stion takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its peri+e z+gbx6r khpg4hg) ,od on Mars, where the accelerg p hrg) 4+6+ebzhgx,kation of gravity is about 0.37 that on Earth?    s

  What is the period of a+d0jgv1/.xs cmp w2u,4 z 6qnb fom,em 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 odr3w( jmu1v g-f 365 grjgv rdm13w- (uams, and 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 0zwdbyykv * qxq5;+:5 y.9930 m. If the clock loses half a minute per day, how should you adjust +vqky w 5y5:z;* bqxdythe length of the pendulum? shortened by    mm.

Derive a formula for;7d,exc4t) +g yp u nayf)3utq the maximum 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 released frn5s 5 r:vbwq0+.1zy6hxryd jwom rest starting athd:0 .xy +s5rb wrqnjwy61vz5 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 cq, r: n *,fn jxqs:bpr3x2r4sjrests pass the bow of his anchored boat every 3.0 s. He measures the distance between two crests to be 6.5 m. 2b:x:sqn4q,, rxr fs 3*r pjnjHow fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and traveg 0af zf-ie2k8ls with a speed of 343 m/s How far apart aa2 fi8e k0g-zfre the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 5 (rviefmc;tfl0e: r* e5 3 z)xc: rdi)h:3gelo50 kHz and 1600 kHz (kilohertz) and traver ff:li5e0*e: xth(3ceoze) )3; ricdvl:gmrl with a speed of $ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

  Calculate the speed of longitudinal waves in*d3r-gjzv +gj co1.yv- x:hul
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic s zv 2uty +vg9-qhqp0(modulus, but one is twice as dense as the other. In which rod will the speed o0tshgy +q-q9 p2uvv(z f longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two sup.d9 ax,aev)t-+lfk xwports 28 m apart. If the tension in the cord is 150 N, how long will it take a pulse to travel fwf)d x+a xtlva -.,ek9rom one support to the other?    s

  A ski gondola is conne8;a9yz b.j j(x, 8ebrwkoh0frcted to the top of a hill by a steel cable of length 620 m and diameter 1.5 cmh0 w .j8rb y(ob;8,aerk f9zjx. 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 belvb f/mdfzbl2tu4(go t70o5.aow the surface of the sea. He hears the echo of the wav 0. d/fbao7t fzmvg(bl4ou25 te 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 differegyo p tc9ww(l(og8 u6z5yn48jnce helps in loc 5gzow(nou8py 8l (cyj 496tgwating 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 sinusoida- z6th vl e o108 84cct3rry9-f ragh:youldi;l 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: S ry3h:if0lo8rd crgt u e6--htaly1o9 ;c8z4vet the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (uv 8*tb +bo:v.b plrq55.zefdb) the amplitudes, of an earthquake P wave passing through the Earth and d.eoz. bru b8f :bvlq5pv5*t+detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave pasd78eyy)f vzk* sing through the Earth is measured to be y8)yfvzk7 e*d$ 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 tx f:8q domzl5sr684 gfhe same frequency travel through the same portion of the Earth, but one is carrying twice the energy. What is the ratio of the ampl46frlxoqm5 z8s:dg8 fitudes of the two waves?   

  Two waves traveling along a stretched string have the; x/9d spl k 3cn:g3g/irplcz+ same frequency, but one transports three times the power of the other. What is the ratio of the amplitudes +c9gc; kllix :s/p pdznr3g/3of the two waves?   

  A bug on the surface of a pond is observed to move up and down a total verticajn *hsy9 l 3.zld7s1xgl distance of 6.0 cm, from the lowest to the highest point, jdxsl93sl 1*yghz 7.nas 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 movin h -acyzg*bs 9y:3jvn+g 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, at the moment the pulses pass each other, the string is straight. What has happened to thy+ns *- bay g39cj:hzve energy at this moment?

  If a violin string vibratee tu 4u9:d eyeh77 6n4 9.sq2btdc krhlrm9*zus at 440 Hz as its fundamental frequency, what are the q. u7rm2 :nhudrk4469 dezeh tlt9s9ebcu7y*frequencies of the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingergo p0n*3v6zds1l qg7 z+vl8hned. At what frequency will it vibrate if it is fingered one-third of the way down from the end? lvp17sg*g z68hn z+q0lnd3v o(That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequency of 280 Hz. Name aw7k* dq(. gum4cm4qujt least three other frequenciesku 4mq ug.wd*4jq7( mc 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 standing wavei xrd(j6edewc)n2sn9 ( lo)n -s is 475 Hz, how far apart are j9 (rndx-cse2nw(nol6 ) )die two adjacent nodes?   m

  If two successive overtonenl spy(77;1u;vyufe m wep3o6 s of a vibrating string are 280 Hz and 350 Hz, what is the frequenc l1m7ys 3y(p;p6w ; nuvoefe7uy of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g.t;n ; yk/jn0pb8cx .39uakrbw The distance from the bridge to the support post is L = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundamental and first two overtones? k 9/k8b .;bcpnwrtxujn;y a03   Hz

  A particular guitar string is supposed to vibrate at 200 Hz, but it is measuredl q5xptn3 ;pjf:mh 78a to vibrate at 205 Hz. By what percent should the tension in the st8: ;5pl j axtn3p7mhfqring be changed to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hz, but it i)irya1yje r :knb; 7:qs measured to vibrate at 205 Hz. By what peirq1aj)bk7yny:r e:;rcent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontale 9kn6b1j)n zfi 5kfb i/:b3mg string is attached to a small-amplitude mechanical 60-Hz vibrator. Tg:mk/3 b9ne 51 n6f)ibibfzkjhe 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 theovx u1g d .g*sk1ng21l string may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying L beu2dx1k glos 1.gg*vn1 tween 10 cm and 1.5 m?   

  When you slosh the water back and forth inm:q( i)hwcd fxk,bo/xk;1 wk0 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 produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. What x :khx)k ki fd10w(/qmwo;b,cis the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundawr/whji5nz8+ ry within the Earth between t5 r8hj zw+wni/wo kinds of material. If it approaches the boundary at an incident angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “shelf” where the velocity cha;u 1n,hn w f71b6ow li:vwovp8nges from 2.8 m/s to wbh ;w8,ionunp1f 6: 7v1owlv2.1 m/s If the incident wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air when it hits a layer of collso v uwy45m f-pe+u,nz:ul aj8*xj7 +d, dense air. If the sound wave hits the cold air interface at an angle ofz 4y7nj-sfalju +e ,58p *ux vm:w+luo 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 ofgrx2 re4m7m;mcph cee3o7(i 2 rock at a 4r gp2h 773;x2(re cemmc ieom38 $^{\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 diametk15*n rrn 3,gxh0 ,kdwpdqz7der. According to the user’s manual, the dish has to be pointed in thed*q,xznd3kh0g rp r n,d57wk1 direction of the satellite, but an error of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 250 km and velocity 750 km/h travels across the Pcs 9otw fu ojn*m8-f56acific 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 abs*mfojtsc85 -uwon 6f9ence 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 carh40frb .qad. 1oaa jfsq20 z3g bumper has a spring stiffness constant of 550 kN/m Find tqzag3do a0 fb. s24.rq10ahj fhe 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.]    m

  A 65-kg person jumps from a window to a fire n,0 z o5txopgw*et 18 m below, which stretches the net 1.1 m. A0p*xz,g tw5o ossume that the net behaves like a simple spring, and
(a) calculate how much it would stretch if the same person were lying in it.    m
(b) How much would it stretch if the person jumped from 35 m?    m

  A mass m is gently placed on e ow ei538-)q zkurxt1n82rjd the end of a freely hanging spring. The mass then falls 33 r8oz rwqiux )5k2 -n1tje ed83cm 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 (Fig. 11–54ax5j:mu5 shss)8- /ipyoh)qe ), compressing the spring 5.0 m. (a) What is the spring st j -:)/mu)xh apsose5q5i8sy hiffness constant of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of coffee (dilkelyf 0v 31gmdj5a16ameter 8 cm) at just the right pace of about 1 step per second, the coffee sloshes1mfyj350v 16lkdaelg 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 33-rpm phonldh8/:*i b.xbj qa 3wlograph record have a wavelength of 1.70 mm. What will be the fre l3h 8*bd. :ai/lxbjwqquency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7c2a8k xzdf72r1dymv 3.40t where x is in meters a2zkf87 mc3rx1v2dyd and t in seconds. Determine
(a) the amplitude,    m
(b) the frequency,(round to two decimal place)$\approx$    Hz
(c) the total energy,(round to one decimal place)$\approx$    J
(d) the kinetic energy and potential energy when x=0.260 m.(round to one decimal place) PE$\approx$    J KE =    J

  A simple pendulum oscillates withnrf w*mx8-zpn4 .g nv6 frequency f. What is its frequency if it accelerar g4pz x.8v w6mf*nnn-tes at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake.leyf: q(v3,i 7k(cml d When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the raft vibrates for av d3(i(k: eq 7mfcll,y 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 musicat xyo4 .yaf)g*cle 5g.9afl*dl instrument are tuned to play at 392 Hz (G) and 440 Hz (A). 5t. f*ll c)gx9ag.yyd e 4o*fa
(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 st/6hrgp*ad;z ap g7 dv8retched 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. (T *6dgvpadah;z7p8r g/he 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 frequency of 264 Hz, a ;qo6h b2+q+hkynr e9lnd the tip of each prong moves 1.8 mm to either side oo6rly+qhh+; 9bkqe2n f 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 ha5g*k4rm ux /p-c2 :ygmh 2p5rlp7 0mbj2wuytormonic 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 plbut4u:2g7mg*rm 25-pr x w pko/ y20mj5lcyh paced there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that end is attached to a ring that can sli+l s2fykxc1 .*du3 oimde without friction id fm.xsy *+1ol cku32on 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 ik73eiquy-c)h j .+ xsexactly 2.000 s — each one-way swing takes 1j-.hii+y 3 qe)7c skxu.000 s.
(a) What is the length of a seconds pendulum in Austin, Texas, where $g=9.793\mathrm{m/s}^{2}$    m
(b) If the pendulum is moved to Paris, where $g=9.809\mathrm{m/s}^{2}$ by how many millimeters must we lengthen the pendulum?    mm
(c) What would be the length of a seconds pendulum on the Moon, where $g=1.62\mathrm{m/s}^{2}$    m

A mass hanging from a spring can oscillate in the vertical direction or can swil j q 25kr46ini;1*1vgxagtgrng 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 swings, and by what amount? [Hg jt rkgn1*6v;1qixi 4 a2rg5lint: 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 underl)hk tx2kns+-q7rs9 v a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at the opposite end. Where will the two pulses first29+snk- 7 kvxtlsrqh) meet?    m

A block of mass M is suspended from a ceiling by a spring withp *qh8.i4dyj.fvjhh;ob 14q r spring stiffness constant k.d h*fh ;ovqb1 hpq484i .jy.jr A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillations that will allow the penny to just 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 is +j-*zup041 s tf tjmea22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. What is the period of ttu10 jetjp m4-as*fz+ he bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (which also gives i* ecq19ge7 ydyf59 kythe 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 that the shear modulus (Sectkd c y59gfe7y qi9*e1yion 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz