Give some examples of everyday vibrating objects. Which exhibit SHM, at least apzuapjgy/27* lvs p4 k9+e-ak bproximately4*l+-vpgy/ 2b ksj 9eapz7uak ?

Is the acceleration of a simple harmonic oscillator ever zero? If so, /a r;xev q3dd(where?

Explain why the motion ofpuq0 .mqt *,fg a piston in an automobile engine is approximately simple harmonic0tq .q pm*fg,u.

Real springs have mass.r.z uyxyq4l k24,5fsj0om e)m Will the true period and frequency be larger or smaller than given by the )0 or szqejumxy5,f4ym42k l. equations for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double thew8gchu 6)h.5.sm:ym lg9 bfgx maximum speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scale, andi2c0rs8s lw0j*fyq q0 then is released. Describe the 0sqw8ri0* 2 0jl yscfqscale reading as a function of time.

If a pendulum clock is accurate at sea level, will it gain ob*kg3fvqllm2 *ro2 g2 r lose time when taken to high altitude? Whyf*l2b 223mv ggko l*rq?

A tire swing hanging from a branch reaches nearly to th/,/2vf6 xmvxj tnncs2 e ground (Fig. 11–48). How could you estimate the height of the branch using only a sttxx2jm//6s v fnc2,vnopwatch?

Why can you make water slosht,cok 0q9 t2mx scq7i4 back and forth in a pan only if you shake the pan ao q9 c,kti 7sm2x40tcqt a certain frequency?

Give several everyday exam h02b tq 2mqm4(ncd3pwples of resonance.

Is a rattle in a car ever a resonance p+ynf0jpus:06x9xq j+ ijd-h bhenomenon? Explain.

Is the frequency of a simple periodic wave equal t x)7:rpsoa frg 3 8)k3ffci6scks/di1o the frequency of its source? Why or why no:gpca6 8/s idf kssxr1 f) 3c7k3i)rfot?

Explain the difference between the speed of a trah5a3d2fqe-d57 80nzl zno xyr g52t rqnsverse wave traveling down a corg5lqxy 5qt7d 085don-anr2f 3rz h2ezd and the speed of a tiny piece of the cord.

Why do the strings used for the lowest-frequency notes on dde(iuc5adag k ;om/k ux;040 a piano normally have wire wrapped ax di(kkgadu0e4o d5 ;;a/u 0cmround them?

What kind of waves do you th7j(q/b au. bo*h3hvs qink will travel down a horizontal metal rod if you strike its end (a) vertically from above and (b) horizontally pavq3.oq7b ab(hu h/j*srallel to its length?

Since the density of air dzddlx1m l9kvu1gzs- p9s 5v-/ ecreases with an increase in temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves in lgzzk1ud5 --m xsvpl919/sdv air to vary with temperature?

Give two reasons why circular 1;.s c0 .)xtgvoz/vl0mgwiwf water waves decrease in amplitude as they travel awlt i.00m/zf.cw ggswv)o v1x; ay from the source.

Two linear waves have the same amplitude and speed, and otherwiltu2fgq+*tf*ur +.: g1zor dm se are identical, except one has half the wavelength of the other. Which transmits more energy? By what factorrqtgmgulu *d*2rzfo :.f+ +t 1?

When a sinusoidal wave crosses the boundary bvqf;3 u (zr5ga vc5cw.etween two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocity do change). Explain why. cfgcrv.53a ;5 vuq( zw

If a string is vibrating in three segments, are there any places you could touco0+n 1 swt1oa,w4ou gzh it with a knife blad41tous gaownw 10+ o,ze without disturbing the motion?

When a standing wave exists on a stringvq/ uprgm , -qdxum44*, the vibrations of incident and reflecteud*vg4,uqrm-xq/4 m p d waves cancel at the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one puv3 4 ug+iree)1osjm83 )hkof lace to another, how might we determine whether the energy was being carried by particles (ma48j ke)m )vr+ogu1uihe3f3osterial bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the to(d,m k3ytuowg1.3nfn3x+hx fwb l1 (jtal distance it travels1bu(tx3n+f. x3 ygmo,3 j1wkf ldh( nw in one period?    m

  An elastic cord is 65 cm long when a weight of 75 N b 3z1vk4r9o pgfs75+; rmnscahangs from it but is 85 cm long when a weightbnm4g;s1 rakosr z9 +53pfc 7v of 180 N hangs from it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg drivers670z p5cyoe mf5l6yv gets into the driver’s seat. If the car goes over yv f5m07l5 ezpcos6 6ya bump, 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) Wh r1r x3d/by.nxat is the spring stiffness con/r xynr1x3db .stant $\approx$    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 mass of 0.60 kg icr0b,zf jx2q(2j /ux is hung from it. What is its frequency if only 0.38 kg hangs ib,cj/x2zf (x2j0r uq from it?    Hz

Construct a Table indicating the position x of the mass in Fig. 11–2 akb+ + x2kb.4u/kn2fda4o tg ult times t = 0,t = /koan +2u.x 4t 42kudfl+kbgb$\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

  A small fly of mass 0.25 g is caught in a spider’s web. The web vibrates predrava,s z;g jhv5g2+1hnu6bm3ominately with a frequency 1,;j ns3v2abgzgh6+avhr mu5 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 frequency91o arcbsym )y(2 .os,n mfqd7 of 0.88 Hz. When an additional 680-g mass cm 2s7 o.y)1qoa,rs b(ydn9f mis 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 second wla*kjbz i:j5xag )3 z:ith an amplitude of 0.13 m. Deg*a: jkbza zilxj:)53 termine
(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 ofib)9)iymh9ybx (o9du a SHO half the maximum val ih9bmy) bx) iu(y99doue?$\approx$    A

A mass attached to the e)99lcnr mkf; vnd of a 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 sprin2/:xpl/z-q waeor y*rw.tk-k( ie5kxg is stretched an additional 0.130 m and released, how long does it take to reach the (new) eqz/2.yo r(p:e wx--kq5 xi ekk/l*watruilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring wit engj jqhjg4(su ibh )7:o7sora08;-yh spring stiffness constant k = 280 N/m and is executing y(ji 7s-gerq:go 0jb ahon)us87j 4h;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 sprif 3o9bijgj 6u7(j:qrq ng of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will the ball leave thefj6 (r gi:bo79ujjq q3 gun?    m/s

  A mass sitting on a horizontal, frictiovd7ko zp7b+z,b zl ;*skf -z7vnless 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 compress;s7zof b -kz7b,l z *vz7kdv+ped, 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 = 0.45cos6.4i)i:tb0mu(jsy m60.ea.pxed u k z b67t where x is in meters and t i6m mzayeu(.)6t u0i kb7xsedpjbi0: .s in seconds. Determine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equilibrium is the energy of a SHO half KE and ha4qavm6. o -lralf PE?. mo4qv 6lraa- ±    A

  If one vibration has 7.0 times the energy of a second, but their freque07e 34a;licc;u m -pethu tx/dndaa(h 8fk4(encies and masses are the same, what is the ratio of their ah e3;eci 8a/7d htaulf4 k;a4(ucxemt0 ( n-pdmplitudes?   

  A 2.00-kg pumpkin oscillates from pz)we; eq(o8/;rebbp a vertically hanging light spring once every 0.65 8z )oq(p;eb pwb e;e/rs.
(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 vertical springs, each b23b:gj ie1ig0 wha-i,eg/ vvz uf1i 8with spring stiffness constant k (Fig.i ,gvi1 if:bh/g08 2ze3wb-iegaj1uv 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t where ;xgk aig5;uv5 x is in meters and t is in s;vakuix g;5g5 econds. 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 andyx6zrz /ojafy i i(19; 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 hor tt9o 6vv/ nqd eo*yq2wir676wizontal spring (k = 124 N/m) is str di2 qvwot/v* n qyrew697ot66uck by a hammer, which 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 constant 305 N/m vibrf 1l 4v/lq 6y bu0utbuvmh;n.4ates with an amplitude of 28.0 cm when 0.260 kg hangs from iv /4 fvn60;.yu1 ql4ltbuumbht. 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 springs, with spring stiff9/qzsq-lxg2d0 lya8j d,-o poness 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.t1m:uox uz 3*b9egaa7600-kg block attached to a fixed horizontal spring whose spring stiffness constant i motag1bzuxe 3*u 9:a7s $ 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 q3mhhqg+m4z, jumps from a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the l,4mqmq 3h+ ghzevel 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 i0;cdwm/a-o i+ug0o )6gkvuif n6qyq 6n 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 e /mu,i hve.woumqh71+xactly one swing per second? (That is, one co.1uw ume/i ,7+ hvohqmmplete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period p:a8le,k/xwo on Mars, where the acceleration of gravity is about 0.37 tpa/x,ew8k: ol hat on Earth?    s

  What is the period of a svkybyvt+ / ht, e5.n76a9z iolimple 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 aa ;r 9(lnpoi y)be.hf7pms1 x; mass of 365 grams, and it is released at an sb7 ypa(;lh1;mfren oxi).9p 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 clocf9,repvh n) dzv51sxrs;0a1 dk’s pendulum has a length of 0.9930 m. If the clock loses half a minute per day, how should you adjust the ledvrd91s;sv xpz5),er0 na 1fh ngth of the pendulum? shortened by    mm.

Derive a formula for the maximu7s y3k.-usdu bm 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 io d;ragx; x xgn+.q8 (d:*ejyat a frequency of 2.5 Hz. At it is released from rest start8:y.ax idrne;dgx (qx;*j+og ing 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 pap2vnki*id04wha )x g /v o,e9ass 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 travvv*2nkxa 9 e/ wpho0 4,d)giiaeling?    m/s

  A sound wave in air hpkss 93p:bg vbl :2wg*as a frequency of 262 Hz and travels with a speed of 343 m/s How far apart are the ws g3g92kpbp bw*s::vlave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 18v 1:sa ou0zhcpdt0 0s600 kHz (kilohertz) and travspa0 :01tzuvdcs oh08 el 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 waveo/l uoako7.xw21e4b is 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 jwbqalfq 0v82vc*zat 8o 8uf-t;g0g* dense as the other. In which rod will the speed of longvvufoqc 0w lg*t 02azba88q- fgjt* 8;itudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two suppo9992avpf o/e 3bxq/wl lc1ffn rts 28 m apart. If the tension in the cord is 150 N, e9392nqfvca/b 9 1fl/ polwfxhow long will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to the top of a hill by a steel cable of length d jl;fom*p )5k620 m and diameter 1.5 cm. As the gondola comes to the ed5pl;fkj o* )mnd 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 su )2csc.vs 3vnj +k+cs:uoxpthc 2)x)x rface of the sea. He hears the echo of the wave refc)hcpvouxsxjs+) k22t cnx3 v :)+ sc.lected 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 dgrtx,lwwl/m k 8 0j*(qifferent speeds, and this difference helps in locating the earthquakjrmxkt8 l/*(wl gwq,0e “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-producedms88 n0s;p xj:luvevhc)m 2u6e .ayf( surface wave can be approximated by a sinusoidal 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 begiaesu8 (:6 ulpjys. vxe0m2;8f hn)m vcn to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) theq/ j*ttnft09 q intensities, and (b) the amplitudes, of an earthquake P wave passing through the Earth f j/tn9*qtt0 qand detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquw91/ l,mwa cvd qa7* vonpm,4kake wave passing through the Earth is measured to be am9wq na*1,l47w/,o kd pcvvm$ 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 trw)*jwf- m 7*nsi ryfw /,wqy-wavel through the same portion of the Earth, but one is carrying twice the energy. What is the ratio of the amplitudww*smf -q-/nfyjy)*rw, i w7wes of the two waves?   

  Two waves traveling along a stretched string qinkq.tn*w7wld- m w1 lvvfn/6w98l.have the same frequency, but one transports thrq.w1wi*w-kwn vv6ltn9lq lmn7fd8 ./ee times the 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 n5u.i (hd7app4t0v fumove up and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes.ui0t4phapdn5 fu7. v( If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each other. (a) Skepd.w6ha57 ibz tch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments laterz7b.5i 6phd aw. (c) In Fig. 11–36a, 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 u 3(nfn7l7aq2uet wv.x5prd(as its fundamental frequency, what are the frequencies of the first four harmonq 5t7lx7p3vreua.wf2 ndnu( (ics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingere ju.y* cobx 7vodg)b-(d. At what frequency will it vibrate if it is fingered oney .*o(-dxc 7u ojb)vgb-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 frequency of 280 Hz.y26)exkgjs (n5j;zm x Name at least t2gsk5xj () nzyej;xm6 hree other frequencies at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s u7zk v+twqssixt9,+7 If the frequency of standing waves is 475 Hz, how far apart aret+ ktsvu7wz9,7+qix s two adjacent nodes?   m

  If two successive overtct0zzlh c8f8; ones of a vibrating string are 280 Hz and 350 Hz, what is the frequency ofcc;0lzzt 8 h8f the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6tz6 2u1i1zjkrf we1uz efiu pdac)*trw//09 4 g. The distance from the bridge to the support post is L = 62cm and the string is under a tet/w1iij uutr1 c40fw/a9 zpzde *2ke1fz 6u )rnsion 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, but it is 6sf,q3 ;wwqcs measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the fre,c ;sf6qw3 wsqquency?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 is pa9c0)sr t85ntrdx )f measured to vibrate at 205 Hz. By what f5nt)prca0d)tx8 s9r percent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is att-b,hs2ammwjho nzog .;yp fv;a72u/ ; ached to a small-amplitude mechanical 60-Hz vibrator. The string’s mass per uniam;b7;hypja2f-mw/h ,uosz n; g 2 v.ot 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 moving the pulle o/52ijh7 pzcky. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varyi 5hk2p j/io7zcng L between 10 cm and 1.5 m?   

  When you slosh the water u1r8sgcu8 +me back and forth in a tub at just the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce su sc8u+mrue1 8gch a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundary withb c +jmi;*cox+in the Earth between two kinds of material. If it apbx jocc*i+ ;+mproaches 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 low)) zb:el bcj/d;:oan underwater “shelf” where the velocity changes from 2.8 m/:l o/:)j;bol bedw c)zs to 2.1 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 0* ,ws h5epbbe fnzs,70 yn2s+rjge .scold, dense air. If the sound wave hits the cold air interface at an f, js5 gn+e.2by,b0n0hwps*s7 zse re angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave strikes a boundary /ran4mzm :vf3 between two types of rock at a 38m3:fm4 nvz ra/ $^{\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 thfwh5 *eh(,yg he user’s manual, the dish has to be pointed in the direction of the satellite, but an errh (y,*hfh w5egor 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 e qxw)95amcr 0jvg b;1velocity 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 warnin;r0jqb)ge a wc 91mx5vg, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness constant of 5 agq x, tjx0k itq:wzp8r(lll6(6f s3850 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 con:jfx8s q6r l3 0qt(z8atwkpll, gx6i(servation of energy.]    m

  A 65-kg person jumps from a window to a fire netjv.gszw k/ sk )* xvj *cx/ka..tu5x8g 18 m below, which stretches the net 1.1 m. Assume that the net behaves like a sxw/k8v ksxcsvz**jx t../a 5j gug.)kimple spring, and
(a) calculate how much it would stretch if the same person were lying in it.    m
(b) How much would it stretch if the person jumped from 35 m?    m

  A mass m is gently placed on the end of a freely hanging spring. The mmqaa:5e7 ;sj tass then falls 33 cm before it stops and begins toat 7s5:qema j; rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 7exs ,lmh r2s,uw. c2i22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffness constant of the sprin ,ls.r,7hcm2uexiw2 sg?    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 (diameter 8 cm) at just the right pah-: yccbkx/w :fo0z m7ce of about 1 step per second, the coffee sloshes more and more uykb0fwz:cm :c/ o x7-hntil 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 phonognv9rp ,pmtn2c8oxv /zgpa 2):raph record have a wavelength of 1.70 mm. What will be the frequency of the sound emip/8rzo mxnag)2vcvt2:p9 , n ptted?    Hz

  A 2.00-kg mass vibrates according to the equationrmazk+7+qqbinqz51 0 x=0.650cos7.40t where x is in meters and t in seconds. Determine aiq qz +7r 1bmn+5kq0z
(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 osj 9dy9 /edji*jcillates with frequency f. What is its frequency if it accelerates at 0.ij d*9jj/y ed950g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on rvd / 2t./xqano ap51na lake. When a 75-kg man stands on the raft, it sinksqat 521 panvrx d./no/ 4.0 cm deeper 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 tunedp ppuy 6py5x+ tr3d ,ozlqk+)4 to play at 392 Hz (G) and 440 Hz (A). t4 pp+z )dy,6 +u5xqrypo3klp
(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 j9k0b: w,bfqfi0ei mbse82z7 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 frbqf i:kbs2ie0efz7w j8 mb,09equency 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, and the tip of each pron9s.i8msilnn. g moves 1.8 mm to either side of centes.m98isiln n. r. 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 cz-;jfo3t7j js* i: gnoycles per second. What is the maximugz7n;ts*j o j3iof-j:m 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 board during the oscillation?

A string can have a “freet37-rabnc-/xodtp f6wj+ x6 z” 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 vibr6-3/z67jpax+c wt ntr d-foxbations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactl9o8h)f3*9 hd nw54f lzaiknyty 2.000 s — each one-way swing takes 8wk4fzh)y9 dlt*5 fn39h iaon1.000 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 vertics3, /mhz-ro6u hs ( m8jyd1wv7u7cqy +u zr*pcal direction or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontal swings, and by what amounpzqummu* 3 +1,r v6zyuoc ch-w7 (y7sj/hds8rt? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

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

  A 10.0-m-long wire of mass 123 g is stretched under a tension of 25s:nbw) +ok gccv01k6w 5 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generatn) 0cck1 wvkgobw+: 6sed at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by d4c2q,qlvt ndb i7) .ma spring with spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of bdcq.7t2l n4)q ,midvoscillations 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 dj m;lgv1h 8h g)bbs,+the junkyard. The steel crane cable is 22 m long and has a diameter of 6.4 mm. A, bj;dh8)bmlhs 1g g+v 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 (which also gives the p (8:a :vtnizedimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and be(v: 8tinae zp:gins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this vibration, given that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz