Give some examples of everyday vibrating objects* y2)vlav,jvm ex);d1 ;qgxnf. Which exhibit SHM, at least approximatelynvdf )j2eymv;vx xl g, )q*;a1?

Is the acceleration of a simple harmonic oscillator evj/9x o;5bxsd eer zero? If so, where?

Explain why the motion of a pi;b0+zeno (ni+wqq p anv3w **qston in an automobile engine is approximately simple harmonip30 ob iwnnv+a(nwz **eqq +q;c.

Real springs have mass. Wil+fw : fmy.:a4bgext9il the true period and frequency be larger or smaller than given by the equations for a mass oscillating on the end o xg4:ft: ywbm9af.e+ if an idealized massless spring? Explain.

How could you double the maxi7f 4n :itwevamalgpo+u. q4;2mum speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook zs vu o-)jg,*fof a vertical spring scale, and then is released. Describe the scale reading as,-gszuo*)jf v a function of time.

If a pendulum clock is accurate at sea leveof+ 0a.sk jfvlv 5v8yvv1m k0,l, will it gain or lose time when taken 1 +vmv.vlf50 08vjksakov y f,to high altitude? Why?

A tire swing hanging from a branch reaches nearly to the gro/ jft /1e28qfrf+q.m6e*3sf espvgi bund (Fig. 11–48). How could you estimate the pgq ms+8/3 /2eqjsvb ff. if*e6fr1 teheight of the branch using only a stopwatch?

Why can you make water slh:,j3x i3v;uydzt*qb osh back and forth in a pan only if you shake the pan at a certainu; hdbqz3 :jty3x,vi* frequency?

Give several everyday examples of remfr9mip kvi6(z r0:67wp ad f*sonance.

Is a rattle in a car(m2 g5gsf w5krclg. t/ ever a resonance phenomenon? Explain.

Is the frequency of a simple peri7hm lw6z g*0nfodic wave equal to the frequency of its source? Wh7hz gnml0f6w *y or why not?

Explain the difference between the speed of a transverse wave tw wt/;vyq (2p +v/xtvnraveling down a cord and the speed of nt;/2(tvp q/+wv wxyv a tiny piece of the cord.

Why do the strings used for the lowest-frequency notes on a piano normallym8.s,1 y4 cl nfte zd --e.8swqzhsa4s have wire wrnc szw,m. t8f-z 44sqyeads81lh-se .apped around them?

What kind of waves do you think 52 ;9dck 4auhvjw*joa7d+q ah will travel down a horizontal metal rod if you strike its end (a) vertically from above and (b) horizontally parallel to+ *7caquk 5dh4a;2jv 9ajh dwo its length?

Since the density of air decreases wi0j/a9p elfcun) (w0.u+y3ec jknjx -bth an increase in temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves in p(ej-+a.yb0j)e3fun cuw0 x 9kcjnl /air to vary with temperature?

Give two reasons why circular water waves decrease in amplitude as theyw9ej g196n* iihl8tby travel away fg8 il 6whb9*jiyn9et1rom the source.

Two linear waves have the same amplitf0vkfg1 g)tl6ude and speed, and otherwise are identical, except one hasf vl10gg6f)t k half the wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two6rna91btrespcr oq51x 2 v 6y8 sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and a69c q p r6y1512snrobr8v xetvelocity do change). Explain why.

If a string is vibrating in three swhly)sdw, (t 8egments, are there any places you could touchw d)s(wh ylt8, it with a knife blade without disturbing the motion?

When a standing wave exists on a string, the vibrations of incidrz:8x.: vyjc37fnr n0xu uf2x 2 beoxc0xws,1ent and reflected wavesxcscrx1 x0znufjn0yx: 3x8v b ru7of, 2ew:2. cancel at the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one place to an bporsl lgh*4wg3w ff9k85pex08 5n;wother, how might we determine whether the energy wa 8ks pf38fwn x0;4lw*hg9p g el5bwro5s being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with ampl5jy1yyw ,zpx3 s55gkczmy 8e1 itude 0.18 m, what is the total distance it travele,wyzys8z1k 15gpyxym j55c3s in one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it but is 85pc y -w-nnpec(-*h5g4bgb .q o cm long whc 4 gg ycbe-.n -(nqphw5bp-o*en 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 whc/*71enlh(agcx 0y6rr ax+ uzen its 68-kg driver gets into the driver’s seat. If the car goes over a bump, what wil0l*+ya 61cearn(/g zxcx u hr7l be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish k: az15 xggsjs,wgt-01s8l mehangs from it. (a) What is the spring stiffnes85sjs 1,10 wmggg:kzxeas lt- s 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 okvn f6:a o5ixs7j 5d;ef 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequenx s:afni6o;75je5d kv cy if only 0.38 kg hangs from it?    Hz

Construct a Table indicatihp , 7xuvbt6we d9i1(nng the position x of the mass in Fig. 11–2 at times t = 0,t = v,pi1w6 utb ndh (x97e$\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 i(jx5fq y*kz- ws caught in a spider’s web. The web vibrates predominately with a frey*z (kjf qw5x-quency 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 frequency of 0.88 Hz. Wheo*v 9y6b7f5z/ tvsy cb6n(ea fn an additional 6 c/t5zsffo 6vvb(*7y ye nab6980-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 per 1f ,g -aduqon,l0whlud0v /2 asecond with an amplitude of 0.13 m. 2owfl1vq , -hnagdu0d,0l/ auDetermine
(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 etjm( ) lgl- -gv5;sqt gr5g9nvgo-p -fquilibrium is the speed of a SHO half the maximum valuq5t;pt-r o- lvl ng-gs mjf)9( v5ggg-e?$\approx$    A

A mass attached to the end of a/xn3 xl6qt4 r ew+shh. spring is stretched a distance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretches a vertical spring 0.315 m. If the spring isnw1zo rku )rt va.sx,fde1)iv ,92: ld stretched an additional 0.130 m and released, how long does it take to reacki,1v l1 x:r tv, en)9d wr.odsa2zuf)h the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring wkh89tsre)n q27 8gbix ith spring stiffness constant k = 280 N/m andhnt87xk) 9bes8r gq 2i is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is moving with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compress the spring of a toy popgun 0.200 m v czf y18;uba3to “loc3 8fuz ;va1byad” a 0.180-kg ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is at l7,kt2b+d e:0igp*2sumtslh tached 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 releaseds,g kd 2*ttilpbm2 +70hsul:e from rest with the spring compressed, the mass experiences a maximum acceleration of 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates according to the equation x = 0.45cos6.4t where x is in tudh wqr(687j:m0lz y meters and t is in se:7mjltd8 0(z ur qh6ywconds. 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 enw n9k,4mgem b*,vfv(oergy of a SHO half KE and half PEv*fnmwe 4 ogkvm( b9,,? ±    A

  If one vibration has 7.0 times the energy of a second, but their freq kr)orp0v6:;+f *fft8bbho tpuencies and masses are the same, what is the ratio of their ampli) ;kph 86f 0tobptrf:rv+*bfo tudes?   

  A 2.00-kg pumpkin oscillates from a vertically hangin:8 +na mi2jdgnutal.5.y: pkf g light spring once every 0.65 s. u:5.nnt ak:.lagdymfj +8pi2
(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 v+k ivbm/ -1 kvip;dz:aertical springs, each with spring zm a+/di ;pk:kb-vv 1istiffness constant 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 x is inbvkv3a.t/j 5b) psw2l meters and t is in seconj2vawlk stbvp)5 ./3 bds. 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, lcy8/ q,qot;myzk/u p3abeled A and B. For each, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi }{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on the end of a horizontal spring (k x ye0h.huvpv,nhas-gz-*(9y = 124 N/m) is struck by a hammer, which g,-.pahuv*h y(n xz-ysvhe9g 0ives the mass an initial speed of 2.96m/s Determine
(a) the period and frequency of the motion,    s    Hz
(b) the amplitude,    m
(c) the maximum acceleration,    $m/s^2$
(d) the position as a function of time, x = (    m)sin(4.08$\pi$t)
(e) the total energy.    J

A vertical spring with spring stiffness constant 305 N/m vobsz r0:+ v.x+hi5atd ibrates with an amplitude of 28.0 cm when 0.260 kg hangs fromro t hsabv.+5i:dx+z 0 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 to two springjnt7i1- hab8sl i8l:an8u pe* s, 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 strikestli 5vz m.b:uu;2qyxl(bt- e+ a 0.600-kg block attached to a fixed horizontal spring whose spring stiffness constan +v2(blm 5yb-let:qxtiu .u;zt is $7.7\times {10}^3$ 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 juqbos;9c -i 2e*17e5;zmgodzwxe a5f zmps from a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low poincx; sm ;qo dzwaz -be*7ie55oz2e1 9fgt eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrations in exa 9 shd(o ;6+rv lry-9p gn8txo 18,yekqmhyxc;ctly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum bebrcwz :8 . jkix5cl p074vyc l*:s2)tvlbp:ee if it is to make exactly one swing per second? (That is, one complete vibrj:l i2c: rcc0)bz7v :b58xple ewpv4tyks l* .ation takes exactly 2.0 s.)    m

  A pendulum has a period ofadw(q 2/rwq bpkz,i* 0mx/x y1 0.80 s on Earth. What is its period on Mars, where the acceleratioxwwa y p(dz21im, /k0rqx*/bqn of gravity is about 0.37 that on Earth?    s

  What is the period of a simw1yg *h4*i tij7r e0m ts6yfz/ple 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 mm5jbnuin7) b/ov/uq ;ass of 365 grams, and it is released at an angle of 12.qn/o m7j5uu ) i/n;bvb0 ${}^{\circ }$ 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 ujln76/35s 8gd 3y tpgtlra(qloses half a minute per day, how should you adjtl(uy3 5agr3tj8q/ sdnpl7 6gust the length of the pendulum? shortened by    mm.

Derive a formula for tpl:ms*( dlzu+ he 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 oscillv0ymbie ;*z (yates at a frequency of 2.5 Hz. At it is released from rest startinvb y;y zi0em*(g at an angle of 15 ${}^{\circ }$ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    ${}^{\circ }$
(b) t = 1.60 s ,    ${}^{\circ }$
(c) t = 500 s ?    ${}^{\circ }$
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests pasc o:vmx, vgz5-s 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 waves traveling? v cog,5vx -z:m   m/s

  A sound wave in air has a frequency of 262 Hz o 70 xapqgrf-:and travels with a speed of 343 m/s How far apart are the wave crx-7gp or0:qfaests (compressions)?    m

  (a) AM radio signals ly4mz9flb:hu +fi /,lhave frequencies between 550 kHz and 1600 kHz (kilohertz) and travel with a sp,: b9y +lhzmlffi/u4l eed of $3\times {10}^8$ 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 wav xrhywhmahr- :py53-5lm(s7 a es in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but o pr gx):67wpisne is twice as dense as the other. In which rod will the speed of longitudinal waves be greater, 7 ip)w g:p6srxand by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m a4ec-tu ib/9hht,xi; 6oa 4 jrapart. If the tension in the cord is 150 N, how long will it take a pulse to travelrc-a6e hh9i4jxbiau to ,;t/4 from one support to the other?    s

  A ski gondola is connected to the top of a hill by a steel cable of len y ic ajqs(g0 rd mq6:fev40(qgb1.f*lgth 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps int(01:f lbs qa(qgigme .fq0* 6dycjvr4o 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 beldi ng ca /skbcdd1q:u)3oh715ow the surface of the sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is the c)nd5 bs/oahd q1k731:iducg ocean at this point?    m

  P and S waves from an earthquake travel at dif3vg 81wor-s tv rh4xoud*-gm. ferent speeds, and this difference helps in locating the earthquake “epicenter” (where the disturbance to3r-w.u*vs-hrm4 ox1 g 8dgtovok 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 sinusoct2ei cm+.o0:r hmv6.q wm6z aidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitucchz..m v2 atwe q+06rm6 mo:ide is needed so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplitudes, of an )n:,71txd4j+al vknyo9ob drearthquake P wave passing through the Earth and detected at two poinda 1onb4: x97lr+otv,kydj) nts 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave pass(om 3zkka0zx 6ing through the Earth is measured to be 30zk xmak(zo6$2\times {10}^{6}J/m^2$ 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)$\approx$    $\times {10}^{9}W/m^2$
(b) At what rate did energy pass through an area of $5m^2$ at 1.0 km?    $\times {10}^{10}W$

  Two earthquake waves of the same frequency travel through the same porti:5z h8si euarq;gt 01qgln ux(w;l:8won of the Earth, but one is carrying twice the energy. What is the ratio of the amplitudes of the g;g0e (z5hlqi:8w:aq1nur s; lx8w uttwo waves?   

  Two waves traveling alyl8nre/8 7yw1zw ,tacong a stretched string have the same frequency, but one transports three times twn yz/7lt y8 cw,e8ar1he power of the other. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move up and ditda57 ,h9t lrown a total vertical distance of 6.0 cm, from the lowest t t9tla, 57ridho 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. bn t-b+p;mt zh+ 4 (1j;ro88kyneahtf11–52 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, at the moment the pulses pass each other, the string is straight. Wht8 nn +;e(f pa+4b8yt1k;- rjhozbmh tat has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fum.ti jlz h5zf.8/ nipx5/o)pmndamental frequency, what are the frequencies of the first four h / tio. pj5pz58if). lnhmzm/xarmonics?$f_1$ =    Hz $f_2$=    Hz $f_3$ =    Hz $f_4$=    Hz

  A violin string vibrates at 294 Ht .iie)n( w-pfz when unfingered. At what frequency will it vibrate if it is fingered iet-.n)wf(pi 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 foum q1vd4-uw -ycr loops at a frequency of 280 Hz. Name at least three otu-vmc14 qdyw- her frequencies at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  The velocity of waves on /*,v8s*n iaf ; i:rlujzijyo )a string is 92m/s If the frequency of standing waves is 475 Hz, how far apart are two j,8lio*ra;i n ) yj:fzsuv*i/adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz ane nj(/8)him rv *lhrp3d 350 Hz, what is the frequency of thh/v n)rj8(*mip r3e lhe fundamental?    Hz

  A guitar string is 90 cm long and has a massov:zv.+fr.oxg3 hiw- of 3.6 g. The distance from the bridge ..wixfh-:3 ov g+zvroto 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 vibrate at 200 Hz, butn:vfwvg juk j2i:v+,3rx ve81 it is measured to vibrate at 205i+g fr x8,nvj wuvv:j1:2 3vek Hz. By what percent should the tension in the string 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 n;txm2ukl 0p9it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to9mu;tn0k lp2x correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-amplituc88 )f4qjz0ra7u iby lde mechanical 60-Hz vibrator.8yc u470)fijla8z qb r The string’s mass per unit length is $3.9\times {10}^{-4}$ 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 f,;rjl*: v y i*v6z zyq;ara-yadjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns mai*f*-v al rv:q ;jya6,zy;rzyy be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at just the right 4yzggb),6ch u frequency, the water alternately rises and falg,u 4gybhzc)6ls 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 water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boun or9hoipo.hrl ,tu5 (;dary within the Earth between two kinds of material. If it approaches the boundh5oiu ; tprhro(,. 9olary 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 under oko3uu6amrnco6.417il zpk7/ zi3 lywater “shelf” where the velocity changes from 2.8 m/s to 2.1 m/s If the.ol /6c1ruap3oui4m 3 oz zl iy7k76kn 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 cold, dense h-rcu2 7s c0zu .wnef,air. If the sound wave hits the cold air interfu-wn0h,sf cz.urc2 e7ace 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 strikey7( yd7nqaql0 p;vyv8 s a boundary between two types of rock at a 38 yq77 pyal8;dqy( n0vv${}^{\circ }$ 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 y/6s,4 51w 9q(an t.l4spkevoghw: ge;jz ffvthe user’s manual, the dishg(qfl: esw vy/nkj1,9o z a et64fsv;.pgh5 4w has to be pointed in the direction of the satellite, but an error of about 2 ${}^{\circ }$ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 250 km a/wr5/os7lhv fnd velocity 750 km/h travels across the Pacific Ocean. Asr5sh7/ l wofv/ 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 and boats.)    min

  An energy-absorbing car bumper hurf3c 6d t4 g104xfmulas a spring stiffness constant of 550 kN/m Find the maximum compxf4c u1rg0d tum6l3f4ression 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 net 18 m be2cw pl1z)q5gb low, which stretches the net 1.1 m. Assume that l1 bp)qgc2z w5the net behaves like a simple spring, and
(a) calculate how much it would stretch if the same person were lying in it.    m
(b) How much would it stretch if the person jumped from 35 m?    m

  A mass m is gently placed on the end o2 /o wwrrb(des-ni st;sa7, -yf a freely hanging spring. The mass then falls 33 cm before it stops and begins to rise. What is the frequency of tr,sonr bt;7-(y-w2 waisd / eshe oscillation?    Hz

  A 950-kg car strikes a huge spring at a sp/kyefbct 9*j ,eed of 22 m/s (Fig. 11–54), compressing the sp,tb k*/cjf 9eyring 5.0 m. (a) What is the spring 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 co+bggk,/*cm) g ocsd ieh/;+niffee (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 sgg/ i bemd o +,h;*inc/+g)kscpill 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 3uv8p3x am14hsxb7saw,p c , l03-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequency of the suv x01p 4 7smp8axh3 ,las,cwbound emitted?    Hz

  A 2.00-kg mass vibrabi2 36xm)lhwkzqq 6n-tes according to the equation x=0.650cos7.40t where x is in meters and t in seconds. Dete 2wq)3ilnh 66-zmkxq brmine
(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 fogza, 2m j1gd(requency f. What is its frequency if it accelerates at 0.50g (a) upaog2 g1( dmz,jward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 7li ,9ei7lgpwj4ap 75 7oqg f/j5-kg man stands on the raft, it sinks 4.0 cm deeper into the water. Whe9gwq5ajepl774 j /,p 7oigfli n 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 to0y) lecmnq 59m play at 392 Hz (G) and 440 Hz (A).emn9l)5 0 ycqm
(a) What are the frequencies of the first two overtones for each string? G : $f_2$=    Hz $f_3$=    Hz A : $f_2$=    Hz $f_3$=    Hz
(b) If the two strings have the same length and are under the same tension, what is the ratio of their masses ($m_{\mathrm{G}}/m_{\mathrm{A}}$)   
(c) If the strings instead have the same mass per unit length and are under the same tension, what is the ratio of their lengths($L_{\mathrm{G}}/L_{\mathrm{A}}$)   
(d) If their masses and lengths are the same, what must be the ratio of the tensions in the two strings?   

Consider a sine wave traveling down the stretched two-part cord of Fig. 11–qil hea7u vg0krx26 /*33. Determine a formula (a) for the ratio of the speeds of the l06e/kq2r ahv7*u igxwave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency offzjw ;g:*ce-5xbhb - km2l,mf 264 Hz, and the tip of each prong movesb lm5ge-mc ;:- k2h,fwbfx* zj 1.8 mm 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 oscillates with simple harmonic motion of frequency 1.5 cycl;( uaxjb1t17+ gazs 84vzvb gtes per second. What is the maximum amplitude with which the end of the board canuggtaz4s8;tb7 va1v j x+bz 1( vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if y6n :3w8zwkzithat end is attached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the res6n iz3:wyzw 8konant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each oebtwj*vnwzn50 mr7g 3*p a(b4 ne-way swing takes 1.000 j4wmwvg7p bab(r0 nn3e*5z *ts.
(a) What is the length of a seconds pendulum in Austin, Texas, where $g=9.793{\mathrm{m}/\mathrm{s}}^2$    m
(b) If the pendulum is moved to Paris, where $g=9.809{\mathrm{m}/\mathrm{s}}^2$ by how many millimeters must we lengthen the pendulum?    mm
(c) What would be the length of a seconds pendulum on the Moon, where $g=1.62{\mathrm{m}/\mathrm{s}}^2$    m

A mass hanging from a spring can oscillate in the vertical direction or can s f7f*dcba0./wqs)z w dwing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period of the vertical owf*.q/a b)wscddfz 70scillations 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 $\left(\begin{array}{c}k=130\mathrm{N}/\mathrm{m}\end{array}\right)$ 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 stretchedino ..jx n.e-t under a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generi..to nnj.- exated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a sprin-99dh c3ig)i mrqvv4 wg with spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillations that will allow the penny togcih vi )m-3d9vr94wq just stay on top of the block? (Assume $m\ll M$)

  A crane has hoisted a 1200-ky3(kt7jr ;ah ig car at the junkyard. 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 cable. What is they73r(th ija ;k period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a, jam7d3nbj -u plate as 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 that the shear modulus (Section 9–5) of jello i-n3a7 jmdbuj, s 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz