Give some examples of everyday vibs,m8 wz*im:ds bw5x f)kfc67mrating objects. Which exhibit SHM, at least approxi 8 xbwmm :mw7sd)6fzk c5s,f*imately?

Is the acceleration 4r au-vi6u+cg: lf3f kof a simple harmonic oscillator ever zero? If so, where?

Explain why the motion of a piston in an automobile engine is approxij+ rimby 5kh0ym1y(jg0jsdkjyv,.+ 2cl1; rimately simple hark m ydv k.y;ir 0b1jcjh2rysl1+,gj5y+0( m jimonic.

Real springs have mass. Will the true period and frequency be larger or smbd n-o/41fnf faller than given by the equations for a mass oscillating on the end of an idealized massless spring? Expln/bf- ffon1 d4ain.

How could you double the maximum speedr+.vr te sp*9r of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vert7ll0r;s9 u k3 6jlwqdgical spring scale, and then is releasel rlq d7w3sgk 09ujl6;d. Describe the scale reading as a function of time.

If a pendulum clock is accurate at sea level, wjs3 0c4w2 ddajill it gain or lose time when taken to high j4dcsj 32wa0daltitude? Why?

A tire swing hanging from a branch reaches nearly to the ground (Fig.j,+epbvbpb( z:vfyl 6( 3ik0 t 11–48). How could you estimate the height of the bilb:3v(0p6et(p+b,byz vjf k ranch using only a stopwatch?

Why can you make water slosh backos ,/etfyx3w,gh 0/il and forth in a pan only if you shake the pan at a certain freqtsxof /0 /e,ygi3h,wluency?

Give several everydamen7 g.h 5zad g5,sg-fy examples of resonance.

Is a rattle in a car ever a resamc ekp w kav)n9) 7)ul2xaf/5onance phenomenon? Explain.

Is the frequency of a simple periodic wave equal to the frequency of its s6ny- n/c 2 hayfeai+f4ource? Why or why nn 46-yafea y/ncf+i 2hot?

Explain the difference between the speed of a transverse wave trave0j ero 7fa6mtn (fw+5rling down a cord and the w6jrte+(nor 57ffam0 speed of a tiny piece of the cord.

Why do the strings used for the; 2ld4b 8yaxhbqmmay( t((e:s lowest-frequency notes on a piano normally have wire wrapped eaadmbmlq42x;y h8 b y((s(:taround them?

What kind of waves do you think will trave(5,l cpf7trxy l down a horizontal metal rod if you strike its end (a) vertically from above and (b) horizontally parallel to its length?y rxft 7(pc5l,

Since the density of air decreases with an increase in ten* gy0oaz6h,ng2f/w t mperature, but the bulk modulus B is nearly independent of tempng/z2gy th6n*0,a f owerature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circularmdv52n fwq (57ds9hylz r)si h89jb,r water waves decrease in amplitude as they travel away from the sourc 9 ms d9nr8(bhdh,wir)qsvz 552 fl7yje.

Two linear waves have the same amplitude and speezunt* l04ns f*r*n: wyd, and otherwise are identical, except one has half the wavelength of thr*:* 0fsl n4utw*nnyz e other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sections of cord 0i6h lpt/ t,zhsd98oo as in Fig. 11–33, the frequency does not change (although tlh d09z/6 ptt,oo8shi he wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are thw ftq9 ,/9kj:l wvwlo8ere any places you could touch it with a knife f/kw j:8wo 9twvqll,9 blade without disturbing the motion?

When a standing wave exists on a strins za.r3 n(cyi -;bky;ng, the vibrations of incident and reflected waves cancel at the nodes. Does this mea-(;zc rsy3nik.; anybn that energy was destroyed? Explain.

If we knew that energy was being transmits j*om ,8crq p;yx.,slted from one place to another, how might we determine whether the energy was being car*.cxmsqosplj,,8 yr; ried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.1 n( 7 k u2h3s:jt0gaxakt;9qnq8 m, what is the total distance it trhnq:;(tu j03a qt k xn7aks2g9avels in one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it 5isywa(, 6 mrbugtg: 0but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” constant k of this elas0btsm:u6 ga i (g,5rwytic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg driver gets into tw/*-j - il-4hknkhyhc he driver’s seat-ny* l4/c k-hiwh -khj. If the car goes over a 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) m 4u-f: 9: 3 ln,t.uhadoovuwuWhat is the spring stiffnd luonto w3,a9u -f.:uvm4: huess constant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a frequency of 3.0 Hz when a mass of 0.4 / pqi, igmzz6ncc;m;60 kg is hung from it. What is its frequency if only 0.38 kg hai m6 mz4;pq/,cc i;gznngs from it?    Hz

Construct a Table indicating theq l0 gxt)ly)wpw-5 +ndfy9f9n position x of the mass in Fig. 11–2 at times t = 0,t = 9 nndy0+)f y w)5pllx- 9fgtqw$\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 vizcn)f4mv 5vx;xtha1g*9 2iae brates predominately a9ci*hx emxnzat 45 2gv;1vf) 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 r,: wrodv54tq spring vibrates with a frequency of 0.88 Hz. When an additional 680-g mass is ad: vqrd,wt5o4 rded 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 secon(ab-w:hhks ;j9pbig- d with an amplitude of 0.13 m. Determiwab:;ip-9-( b kgjshhne
(a) the velocity when it passes the equilibrium point,$\approx$    m/s(round to one decimal place)
(b) the velocity when it is 0.10 m from equilibrium, $\approx$ ±    m/s(round to one decimal place)
(c) the total energy of the system,$\approx$    J(round to one decimal place)
(d) the equation describing the motion of the mass, assuming that x was a maximum at x = (0.13π)cos(  πt)

  At what displacement from equilibrium is the speed of a SHw4-2 2zz*5chm thc-qray *qkyO half the maximum valuq2h* a5y2 -ckczw4* zhytmqr-e?$\approx$    A

A mass attached to the end of a springrzf32,v81 qup k mx)8omjoyj * 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 thh8dtf mn/tfag 4b7*e :e spring is stretched an additional 0.130 m and released, how long does it take to reach the (new) equilibrium position again f/:d4 ftb7mg hta8e*n?    s

  An object with mass 3.0 kg is attached to a n)gdb lrz6ne-6 ,1shkspring with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 mh, 6nn61)ksgd- rez lb 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 popgie jq ohjy;82 8qlgk:qer036aun 0.200 m to “load” a 0.180-kg ball. With oleaj:e 86iq32r;j0 kygqq 8h what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless y/xw wnk -.f duu1-esc67c5yesurface 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 y-1u exke-5sn7c6fw c/w dyu .spring by 0.12 m. If the mass is released 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 = 0.45qdi;;;) m9 0wxoenqn 1m5yktj cos6.4t where x is in meters j ek9ny t0w d5m;1)mqo;qn;xiand t is 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 ene3i 3sa:/f 7kb(eyeaggrgy of a SHO half KE and half PE?gaebe gs/ fka(y3 i7:3 ±    A

  If one vibration has 7.0 times the eu0ls)lu8 rnrn (rp9cq(l1 q0nnergy of a second, but their frequencies and masses are the same, what is the ratio of their amplitudes? c800uun1 )qs(ln q l9(r lnprr  

  A 2.00-kg pumpkin oscillates from a vertically hanging light sprin.8i,phwade: lg once every 0.6 w:8,liehpd .a5 s.
(a) Write down the equation giving the pumpkin’s position y (+ upward) as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. y = (   m)cos($\frac{2\pi t}{0.65s}$)
(b) How long will it take to get to the equilibrium position for the first time?    s
(c) What will be the pumpkin’s maximum speed?    m/s
(d) What will be its maximum acceleration, and where will that first be attained?   $m/s^2 $

A block of mass m is supported by two identical parallel verticyu92 ivij aenl/s -9a0al springs, each with spring stiffness constant k (Fig. 11–49). What will be the frequencyinj 99vs/ -e20la iuya of vibration?

  A 300-g mass vibrates according to ticp z 6)9a w5p1.rorpthe equation x = 0.38sin6.5t where x is in meters and t is in seconds. ci)ptp9 .p6 z1woar5rDetermine
(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 c3hz1u(n ty/ jSHM, labeled A and B. For each, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest /i(bdxq mep7q ipmq i4s,f11dd*a,f9on the end of a horizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an iq(s daq/9 1fdp pim4,*imbe, 71qd fxinitial 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 vibrates with an amb;4s1jr 2w o+cmne*p5m f()l we:dspbplitude of 28.0 cm when s*)lfwpmdjs+ewm52orn b(4c b; pe :10.260 kg hangs from it. The mass passes through the equilibrium point (x=0) with positive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two nm6qusdcwq/ 1 cg 093at:dej)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 0.60(oke*.mh3;eg g.u vwu0-kg block attached to a fixed horizontal spring whose spring stiffness coem.e3. oggvkhu;w u*( nstant is $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with mass 65.0 kg jumps from a high bridge. After reaching 9-w0 pqg0xj i3s /jfhihis lowest point, he oscillates up and down, hitting a lo jijpf0 3/sghw0-x9iqw 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 vibrations in exactly 60 s4p+**qj as wxmxj(8ow . What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple 2 s/emc ikqs8ge sve 2ja-, l0fi::k7opendulum be if it is to make exactly one swing per second? (That is, one complete -qgejss2 mok /i l 2avc,0sk: 87eef:ivibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on Mars,ha3,/b7tgxd azfrc0 ) where the acceleration ofdt0, c/73x fraaz)bgh gravity is about 0.37 that on Earth?    s

  What is the period of a simple pendulum 8x5kvyk3 o-atl,p,jttea7 8 1x o4x5y f0 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, ttjso:ah9-- d)gh /ed ohe pendulum bob has a mass of 365 grams, and it is released at an anga sh:/d9oe-jo hd- )tgle of 12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’s pendulum has a length of 0.9930r69 a+ .cwbkx78hnr cr m. If the clock loses half a minute per day, how should you adjust the length of the pendulum?68k w.abr9r7nhr +cx c shortened by    mm.

Derive a formula for the maximum speh,d)vut;a3a )aazvg7 qrt5ll t, v zo5-p5od2ed $v_{max}$ 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 ifhk:j)zz-w l3s released from rest starting at an angle 3z lzf )wj-:hkof 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 pass the 3uzq67 p./)dm7fa hezbkpmru g c).0bbow of his anchored boat every 3.0 s. He measures th0 b m37)gud z76p.fbk/zpahqme.)r cue distance between two crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262;qpospl*.6 bxb 9zlv ,*zdc2 h Hz and travels with a speed of 343 m/s How farz6;l9h.,* bpv scd bl *xo2zqp apart are the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (ki(ew6kp yeeug1nq5//r lohertz) ande6ew1nk 5e/qg p /yu(r travel 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 inl7vm*y 3gh i1d,v 8iod
(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 den-tg 6ugd4xes qxj9r,(se as the other. In which rod will the speed of longitudinal waves be greater, and by what fa9xtj6dgu s4(g xr, qe-ctor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apah4xk, v5yap5nrt. If the tensxnp4 5ka5hyv ,ion in the cord is 150 N, how long will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to the to wljbz.a19szhb: .:edgnx,i f80v4 vcp of a hill by a steel cable of length 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and sends a wave pulse along the c84bxn 1 .0s,dbz jze9.:wl gich :vfavable. It is observed that it took 16 s for the pulse to return.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

  A sailor strikes the side of his ship just below the surface of the sea2lzn r9 /i6vpzjecf.). He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is the ocerj f/2zel9c6zin.) pv an at this point?    m

  P and S waves from an earthquake travel at different g ;e7g:br0fynspeeds, and this difference helps in locating the earthquake “epicenter” (where:e y;ggr07fbn 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-produceml1o+ -r1(rvfx w i8 lyqkqm7ef 5,m 4b4zhqb:d surface wave can be approximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typicalf+844bmm1-(15v :qyqfzq,wk ble ixl7 mhrr o of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplitudes, of an earthm bxnm.u;. u7hy4m hmshd5y dl4g q o0)yd);+pquake P wave passing through the Earth and detected at two points 10 km and lp7m0g.5y +sodh)4;n yh;bym)q ddm mhu. ux420 km from the source?(a)    (b)   

  The intensity of an earal u;bzhyp; 5: t.9 qdsj1s.wtthquake wave passing through the Earth is measured to be l.qsuwast1jt:5. ;bdp;hz y 9$ 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-b)i(9x xmk lg of the same frequency travel through the same portion of the Earth, but one is carrying twice the energy. What is the ratio of the amx k-l)(b g9imxplitudes of the two waves?   

  Two waves traveling aloncl /dlzauw8e-u9dx*, 4 si ie+g a stretched string have the same frequency, but one transpws/ i,lz uu9deie+*x48d- a clorts three 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 move up and down a t9xs7;vnnqya2 ( t.f aaotal vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease toan92st .q(fyvx;7ana 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11 (jk exophjb(shdw6//k2i- . q–52 are moving toward each other. (a) Sketch the shape of the string at the moment they directly ov jpx s /e(bdoh-q2/hijk(w6. kerlap. (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 the energy at this moment?

  If a violin string vibrates ata fb:kx3(0( *xknfecg 440 Hz as its fundamental frequency, what are the frequk(xc0bgfe3xak f:n * (encies 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 unfingeredl/ :gso6i29nj ce;cfl lc6j4,d-y bxs. At what frequency will it vibrate if it is fingered one-third of the way down from -l4o,ncg:9 2j6dsxfi l/6be cyslc;j 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 28dw- 3o4s; sq(j7 ;a h2ektcgdl0 Hz. Name at least three other frequencies at which; h-k3swcd7o(st4d2 ql a;gej 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 fw/ i m,wyf:tad9ukv4 5requency of standing waves is 475 Hz, how far apart are two atu9wfvyi m: w/5,ak4ddjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 350 Hz, what isz c5.oy ois-3k the frequency of the fozos. c-i5k3y undamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The dis 5(;bycnfy)uotance from the bridge to the support post is L = 62cm and the string is under a tension ofnb fycuo5)y (; 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed tocx7b,1a.l2urgy ) ihb vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?So the three frequencies arecg21i)yrubabx h ,7.l,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar strin2ggs 5,y ff rta/5jf*zg is supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tensir sga2zy/fjff* 5 5tg,on in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string isuz z y,jnc5w0 56nrf t2pyz*w8 attached to a small-amplitude mechanical 60-Hz vibrator. The string’s mass per uwt552y0j8nzwfy 6 z,rzup*ncnit 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 hcya2zu-1lfqk2+a/h string may be adjusted by moving the pulley. If thh2kuzafhqlcy +1/a- 2e hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at just the right frequencysjjnco4 1 vx(-, the water alternately rises and falls at each end, ren4jv(sjo -1cx maining 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 boundary within the Eap (cxk. f0 ccauom:d p46n5u:lrth between two kinds of material. If it approaches the blxn (mc5fuu6:oc .pakd4 0pc :oundary 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 changes from 2as-6ko8q phur 5f;6sa .8 m/s to 2.1 m/s If the incident wave crests s;6uof8a 6h qk5apr-smake 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 a uu)wf/;eaid d76rk/gir. If the e7igdu6r)fauw ;k //dsound wave hits the cold air interface at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake lmhb )gce )+;m w7ew/jc yck.zfut1/+wave strikes a boundary between two types of rock at a 38 humc+ ce17) g;wt/kcyz e/)fbw m.+lj $^{\circ} $ angle. As the wave crosses the boundary, the specific gravity of the rock changes from 3.6 to 2.8. Assuming that the elastic modulus is the same for both types of rock, determine the angle of refraction.    $^{\circ} $

  A satellite dish is about 0.5 m in diameter. According to the us2dkkhc rbopmh8 + e04)er’s manual, the dish has td 2eho4 )+ hkcpkrm0b8o 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 km2kc,-h gn:yscyp-1vki 9i ny1 and velocity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamiskpn2i-s:,ciy9y1 k-yh 1n gvc , some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness 6luv/84 q4ch(jli m4 .ent-ihpsn do7constant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.] v m6j h/iq8hp. sn444un7l(il-ce td o    m

  A 65-kg person jumps from a h;zt68yh dix2window to a fire net 18 m below, which stretches the net 1.1 m. Assume that the net behaves like a simple spri2x8hdi6 z;yh tng, 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 m xg5g0a q3)qhstt,jl46 q5*btbs ek* a freely hanging spring. The mass then falls 33 cm before it stops and begins to rise. What is the frequency * ms6h0qtkqt 5jbgslbe ,*t x g)34q5aof the oscillation?    Hz

  A 950-kg car strikes a huge spring a a 9qb uq+9)gf*x 2jnu)ziduav(;,uiet a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) Wh*vnz)qe) a;iu+au( f2ib,9jx qu gu9dat 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 coffee (diameter ox-30xf;* w8 n,4uzt pvtbn pc8 cm) at just the right pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the vw pf-o*xp;u nct03,xn t4bz8top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certai jipc4,7 9-g( hjjc6 rr,qtwmqrg+0ocn groove 10.8 cm from the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequency of thjc(ggjmwrr, qcthpqi - r,j7+ c4o 690e sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t whercaqjva0)c+t*/iok0t e x is in meters/0q v+aca0kjo)t*ic t 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 with frequency f. What is its fr gbga0ugl :qs6d na:3+ mx pq-ai*c)o-equency if it accelerg)c:ba*a q 3x:60qdpi +mos- glugn- aates at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on n. fozz+o9u p/*cxct; the raft, it sinks.octnxzoz+* ;fcu/ 9p 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 tuned to play at 392 Hz (G) and 4r .cb6u+pxo1wneyv)8h fu o96 40 Hz (A). ocfnh u6y o+epx91w.8bv ) r6u
(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 Fi ox 6e2 hp-ii(uiw75bzdkoes9.a/l9z g. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter sec s29ah.7 ikxpu zee- /ozi95lb6odwi(tion, 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 of 264 Hz, and tda74kh ezhmb s0h)8 p0he tip of each prong moves 1.8 mm to either side of center. Calculathmz)b0ke0hd ps7h4a 8e
(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 frequ iiqq9/p dtxl50lvu/)8bmv*a ency 1.5 cycles per second. What is the maximum amplitude 8m )i/qplqaxtlb9v*d0i5 /uvwith 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 “free” end if that end is atta-z 2in)kpy1b+/t ncp6l f tfv6ched to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string wzf/nfvyk6 tc li+tnp2b- 16p) ith one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — 84b k le(ga3ireach one-way swing takes 1.000b 4lre8ag(k 3i 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 f g md30zpandfidnn;p1)y5. dk ,z,- nor can swing as a pendulum of small amplitude, but not b,d zdp ndpa3 nf,i0.-f z15k mygn;)ndoth at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontal swings, and by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

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

  A 10.0-m-long wire of mass 123 +wr 4 a76egnzsg is stretched under 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 t67 ger4szwn+awo pulses first meet?    m

A block of mass M is suspended from a ceiling by a2 z 6 p/m59kgon*rons04byxyz spring with spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillations thatnngz6zo byo42yr50s9x*m p k/ 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.b)hnao z-tsc.y3ldw e)x62q9 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 the period of the bouncing? [Hint: Refer to Tatohlxcby n6.wa) q2 des3)z-9 ble 9–1.]    s

  A block of jello rests on a plate g5 ph.s, vvmpds* w.(3gwpadt2tun2 *1bi7voas 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 toi* hb.d 1*w(p 7w2tv saundp.tvmvg,gp s5 32o 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