Give some examples of everyday vibrating obtp(z3jh/r.u t jects. Which exhibit SHM, at least approt 3/rhjz(.ut pximately?

Is the acceleration of a simple harmonic oi (2jsynr+23a+ jk0iuv 5dc 36sds dp-dz bqz5scillator ever zero? If so, where?

Explain why the motion of a piston in an automobile engine is approx/m (wjwg+f 36- uudirgimately simple harm iug/3r( 6w-j fgmuwd+onic.

Real springs have mass. Will the true period and frequency be larger or so:. obxzus,r 6q;h;si q92n(z7 sa hpomaller than given by the equations for a mass oscillating on ,h(q.bs;x 7qho96iz2 apuso;onr:sz the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple harmonic oscileddnnh y;: me q8;/zt*lator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring9w4v(p zcr)p g scale, and then is released. Describe the scale reading as a fur(pwvp4 )g9 zcnction of time.

If a pendulum clock is accurate at sea level, will it gain or lose time when tak( rxn;c-hfa sbs6ao 5,enn;hf5 ocsa(x bs a-,r6 to high altitude? Why?

A tire swing hanging from a branch reaches nearc 4wq1vrav:v r57n+fs)dsm v *(ca4ygly to the ground (Fig. 11–48). How could you estimate the height of the brn4g +y4rs)5 :*fr1ws cvvvavq7da mc (anch using only a stopwatch?

Why can you make water slosh back and forth in a pan only if you shake the )jj*ln8kk+ v. mnto)epan at a certain frequee) nmlvk8+ot k)n*jj .ncy?

Give several everyday examples of resonanz0uc9x p0l 78ja cv,goce.

Is a rattle in a car ever a resonance phenomenon? Explnu tl*1/vs:; w3ff :br/gd nxbain.

Is the frequency of a simple periodic wave equal to the frm/dx2zlwmp/ f0hh /k0equency of its source? Whdw//x hfp/ zk00m lh2my or why not?

Explain the difference between the speed of a tran 40mmjsa(; umlkbaz2(qze y)6 d25gd ksverse wave traveling down a cord and the speem q m s5)gkj m;zuz(d(0 yakl2b64ed2ad of a tiny piece of the cord.

Why do the strings used for the lowest-guwu9hyx q z4o6 4l+.xfrequency notes on a piano normally have wire wrapped around 44+9 uylgqoxuhx 6wz.them?

What kind of waves do you think will travel down a horizontal metal rod 2a)nyc7 psf )s3xnt(dif you strike its encn(s)xad3yf)pt2 sn7d (a) vertically from above and (b) horizontally parallel to its length?

Since the density of k jynk4lkl1g71 x75 m5c xztx6air decreases 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 air to vary with temperglc5klk xzjm7yk 54n7 t16x1 xature?

Give two reasons why circular water waves decre)t59f)u (q;t f86mdtunh jhuuase in amplitude as they travel aw fhnt(muf56u) t9;tud h8uq) jay from the source.

Two linear waves have the sa 6yvl0e8 l, v7gw/v qagazh3f)me amplitude and speed, and otherwise are identical, except one has half the waveleng)vz8lf a/ g3,vge6haywl07 v qth of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the qhdk1d5fit 5q kyk1 42boundary between two sections of cord as in Fig. 11–33, the frequency does not change (although th2 5qd5h1i kk 14tfykdqe wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there ajd-ljc,1w c+ v2atph,ye6w 2 bny places you could touch it with a knifyh,2l2,c6wb 1vtewj c+dj- pae blade without disturbing the motion?

When a standing wave d mp uyyfww 2ik64.k6+exists on a string, the vibrations of incident and reflected waves cancel at the nodes. Does this mean that energy was destroyed? f mk 24 6wypyk.u+6iwdExplain.

If we knew that energy k*t l: oirq*hmd3 mamd.cw-* pb53:l cwas being transmitted from one place to another, how might we determine whether the energy was being carried by*c **. :dp adkm:mwlq33rml -o5hitc b particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what ifr/ eogull)o q n. 873z-2nwggs the total distance it travels in one8nog/wq.o gflu27 e-)ng l rz3 period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs 20pga :3d15 llyqyfsgfrom it but is 85 cm long when a weight of 180 N g1daq0 fsll:p 3gy52y 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 dbqnp, ui )6qw5e4fvm8 river gets into the driver’s seat. If the car goes over a bump, what will be thwip u)v,fq n 586q4bmee frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm wh3sqso grq**f* ugvd 83en a 2.7-kg fish hangs from it. (a) What is the spring stiffness co *d8foq*sv33ggqur s*nstant $\approx$    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 frequenxq,ssnxx+0 ic/jd6n )ctgaa- :cl :b8cy of 3.0 Hz when a mass of 0.60 kg is hung from it.:c qxbal :sst0g+ax-d/n6xni c cj ),8 What is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the pos(+c-84q s4dnu.tv extoh 3 xvxition x of the mass in Fig. 11–2 at times t = 0 ov4ncs.( -x+ xhq4dtv3 euxt8,t = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

  A small fly of mass 0.*ipw 9ny +ry:h25 g is caught in a spider’s web. The web vibrates predominately with a frequency of 4.0 H:9 rwynhp*yi+ z.
(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 fkcm+anl7ahe+;zb -y4 t:4 zehrequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 Hz. a :4ee4my ;7-b + kcnhzhl+aztWhat is the value of m?    kg

  A 0.60-kg mass at the end on( k(9 upu fj-it82plof a spring vibrates 3.0 times per second with an amplitude of 0.13 m. Determine (li 9p8kp(u - uotfnj2
(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 speedpovy/2 ns + vh*j*1tbp of a SHO half the maximum valujv sp*1y hv/+ *onbp2te?$\approx$    A

A mass attached to the end of a spring is stretched n enae6 8:-wzom31k rka 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 sta.: bbgcyq*v3c60u qxretches a vertical spring 0.315 m. If the spring is stretchedba v:qcb.u0c* qgy x36 an additional 0.130 m and released, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attuchwd4s9 +r )( xsb56ep jdrmil6 q7c:ached to a spring with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. Whej7+5wb:l6cie d rm( sx6s)dqu9p4hcrn 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 tcnc n cz0oij)r)56:z vhe spring of a toy popgun 0.200 m to “load” a 0.18)ncv )cn c rzz:o5j60i0-kg ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, fbre mtz-xb,f6 s.l(0prictionless surface is attached to one end of a spring; ,b zs0rfbpm(t x-le6 .the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, the mass experiences a maximum 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 equatioxtg:x zrehf*d k)3:p2vf*n /vn x = 0.45cos6.4t where x is in meters and t is in seconds. Dete*p:fgxrke vf23 *xh nz/vt d:)rmine
(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 equilipkougvg;1wev27 84nk+:tcu8hb b *dubrium is the energy of a SHO half KE and half PE? ± pgkw +b g27hdu184:;vo8*btnkuuc ve   A

  If one vibration has 7.0z;e:0h )gz b+urofvi 5 times the energy of a second, but their frequencies andfiz;:5e 0u) bzvor +hg masses are the same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a q;/m,u9g,azeqssxagl s s 6fayl10+ 9 vertically hanging light spring once every 01ay, lsss;/muf l0saaxq6egz, q9 +9g.65 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 paralltq1 smz2bt+l7el vertical springs, each with spring stiffness constant k (Fig. 11–49). What will be the frequencylt 1q +7tms2zb of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t h,a awduwa5(7 where x is in metad5hww u (aa7,ers and t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows two examples of SHM, labeled A and B. For each, whadhrm23oz648si t)wt rt 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 th ah2vd(tpfe4, e end of a horizontal spring (k = 124 N/m) is struck by a hammer, which givfh 4a2,(pvdtees 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 gw1rpa8alfw ms-o:jkk6(3 5e stiffness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibriu 85-a oa3:6egm fkljwk(p1rwsm 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 spri2 (xkfu)roqu*m j*b6dz3l u, nngs, with spring stiffness constants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes a 0.600-kg block attached to a fixed horizontal spring ql+w7:6/k zy d3m a oqqd*gc7qwhose spricwymqq ka7z +d36 qgo/d: ql7*ng stiffness constant is $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with mass 65.lgp. 8r-v)9qujkrq v:0 kg jumps from a high bridge. After reaching his lowest point, q.kvg 9 rq:p-j8lrvu)he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrn pgph+t6v7p a av3h4:ations in exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly onnmjx bd ,y6tt u1+m8r-e swing per second? (That is, one complete vibration takyrmtx b-m+ 8jtd6nu,1 es exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. Whab-r xugl erw(-8v 1w2wt is its period on Mars, where the acceleration of gravity is about 0.37w -rwvr12lx8b(e ug- w that on Earth?    s

  What is the period ohas1jemohr )n(;5 uv ,f a simple pendulum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum igvo4 ilg7/c o0s 0.760 m, the pendulum bob has a mass of 365 grams, and it is released av/goig o407 lct an angle of 12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’s pendulum has a l2(nrj) .sgwo rength of 0.9930 m. If the clock loses half a minute per day, how should you adjust the length of the pendulum? shor(r2.ws rgj)o ntened by    mm.

Derive a formula for thf(8zg qsd+37c j) gwjwe maximum speed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at a frequency of 2.5 Hz. At it is relef2 sq + qtw+,orf)nx2mased from rest starting at an angl2,fst++n wqqfmo2 )x re 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 pass the bow of his anchorplf.f +s ife13ed boat every 3.0 s. He measures the distance 1e. f i+flfsp3between 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 H/)y/x uf68x)(vzl;-ucz rxi-6; o brpvutdqu z and travels with a speed of 343 m/s How far apart are the wave cre--l)id uc q/f8/; )r6r o6 up;xv(zbvuxz tuxysts (compressions)?    m

  (a) AM radio signals has4-a:(*lzk/x m7i m o4 7ilphwnqxr,xve frequencies between 550 kHz and 1600 kHz (kilohertz) and travel with amap/ n4mwxixrsiq7z*-h k 4ol, l:x7( 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 .3cyub )qaklgzr(x2xr4. s3v longitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one is twice as dense ca.fg5t ovbxj5s3. 1nas the other. Infn.jaso . 3t5xb51v gc which rod will the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apaqamq7a4l 3zfc,z 0m0krt. If the tension in 37mqakqc flz ,0mz04a 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 tho ltng0he ,w+pnybzh.l;)5 -ee top 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 z;.o)5l0+ enyhng-welbtp,hthe 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 th tk6z ods+6k)ie surface of the sea. He hears the echo)+ dsoki 6kz6t of the wave reflected from the ocean floor directly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at different speeds, and tq)6p tv gty(yxhfthlyu7vw 78q *: r45his difference v r(yuty4hl75gtxypf wq8)v7* 6 ht:qhelps in locating the earthquake “epicenter” (where the disturbance took place).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced surface wave can be approximated by/szf 7bsy8y1yh7bd2 m a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplituyb7hs dy1fb2 s/yz87 mde 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)hwx e2a a7,bl2 the intensities, and (b) the amplitudes, of an earthquake P wave passing through the Earth and detected at two points 10 km and 20 km from the sourcebelwh22a ax 7,?(a)    (b)   

  The intensity of an earthquhrb) (2 wsytm6ake wave passing through the Earth is measured to be sr m26yb(h w)t$ 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 frupbat 5i5/*ns2*r 8yk-scwuiequency travel through the same portion of the Earti*2-knb 85w 5u/i*ypc usra tsh, but one is carrying twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have thh aqvp t77swvv l2-km +7qx3q;e same frequency, but one transports three times the power of the other. What is the ratio of the amplitudtaw7 mqp q+hk3xsvl;q7v7 -2ves of the two waves?   

  A bug on the surface of a pond is observed to move up and down a total vegt jdb(nvjub*0-t 9; dsoyu*2 (ox5se :, lorrrtical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm, by what factor does the bu- us o5 ;d*ry(rog2ts n j(vdl* 9:uob,x0jebtg’s maximum KE change?   

The two pulses shown co0.8kfj/tf: ye (:tc stk x.xin Fig. 11–52 are moving toward each other. (a) Sketch the shape of the string at the moment they directly overlap. (b) S :texjxk.t0fs:kt c/yo 8.(fcketch 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 at 440 Hz as its fundamental frequency, wh*8 xn q3sm6wx9r o(vueo h08zo6bv qa4at are the frequevnuo6svxm4ow 9o qxa6(8 q e38hz0 r*bncies 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 unfingered. At what freq40by e -nfp m6e5z6ajvuency will it vimaj 6v-y np0zb45e fe6brate if it is fingered one-third of the way down from the end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops aostci(1j81 q1ygy b5k ht 7v/ft a frequency of 280 Hz. Name at least three other frequetho1iybs /vk t f 5c(jy1g7q18ncies at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the frequen(j .kstird/xj+g2 w -qcy of standing waves is 47/ x2+ikwqdsj(r-.gtj 5 Hz, how far apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280v0i0)zb j+vh i Hz and 350 Hz, what is the frequency of the zvijb0i0 v+)h fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distance from; 7lzz-td9f9 dq saba, the bridge to the support post is L = 62cm and the string is under ltzf aqz9bd7,s a -9;da tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar strj :gw3 pz+ ;)ktcmgov+ing is supposed to vibrate at 200 Hz, but it is measured to vibratmt:;p3v+wjg+ oc gz )ke at 205 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, g vp o6glc6p72but it is measured to vibrate at 205 Hz. By what percent should the tension in the strinp67 gop gv26lcg be changed to correct the frequency? decreased by    %

  One end of a horizontal stringj+0h,d hj- auaw d.pt5 is attached to a small-amplitude mechanical 60-Hz vibrator. The string’s ma d j.p +-utah5ahwj0d,ss per unit length is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of the string tiv+bq2vth)9v 92on ur6qv.jmay be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by va iuv6tn9t+vo 2v j.) 2rbqhq9vrying L between 10 cm and 1.5 m?   

  When you slosh the water back and fort6g7xn g w7bm+be-fkw/ h in a tub at just the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. gb x+f b-enmw677kw/g 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 Emx;o ,jo;w+ lparth between two kinds of material. If it approaches the boundarywpxj ;;oolm,+ 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 underwaw 8/(0zuyyafktuco/b (*(wyater “shelf” where the velocity changes from 2.8 m/s to 2.1 m/s If the in(uawywa8o0y u/(z*f /by(kctcident 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 layee6mg;i ms(-d4; cp hkpr of cold, dense air. If the sound wave hits the cold air interface at an angle of 25-;dg kp6hp;si( ecmm4 $^{\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) g1y-h,n/;7agg5us4uooj x+y sax ao boundary between two types of rock at a 38 g4j/7;sh-,u )uy aasxoxna+ o5y1g og$^{\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 abouu) e88; vtaqsdt 0.5 m in diameter. According to the user’s manual, the dish has to be pointed in the direction q8;ue )v8sdatof the satellite, but an error of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 250 km and velocity 750 km/h travels ac.3 d nkk)xyxw(p7j;miross the Pacific Ocean. As it approaches Hawaii, people obserk7mpd( n.)xi3jw;kyx ve 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 has a spring stiffness constuz guy. (6v7ltant 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.7uz(6 yvtug l 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 be7z- bem* hv(plshvg( 9low, which stretches the net 1.1 m. Assume that the net behaves likem-p*l zb(gshe v (h79v 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 vg *all8df3qdz6/k3x end of a freely hanging spring. The mass then falls 33 cm before it lzqd/a* d8glxfkv633 stops and begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed(xpxw++.vzgu of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffness constant of the springxwzx+ v+ .g(pu?    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 9z9ccn- jk) bw(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 spill over the top (Fig. 11–55). Estimate the speed of wavesjz9 - ckn9cwb) in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the cexj (sc.vr2g oman;8 lqz(ntb q+iq-ch04(7ugnter of a 33-rpm phonograph record have a wavelength of 1.70 mmxcs; ( 2a0q7curq +4vbzjggn oh (.n(l8-qtim. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t wher0h0gebc(5e exe x is in meters and t 5 gbee0(x hce0in 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. Wsmea 9mp w.s)7/m fnm(hat is its frequency if it accelerates at 0.50gae.w(mm)m f9 snsp /7m (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on the raft, iiihraes0+tiz:6ai6 - t sinks 4.0 cm deeper into ths-i+ziiah0i6 a: 6tere 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 4ueah3quz )h. -ec6m(rzkj2 ec6.pa9 2ykfw. w40 Hz (A). ewrcqhk -) .zumjca9z2 k.2 wfy3.(euha6 6pe
(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 theg/mthb+. /:cok*,/ qur ivcbpzfy;9 d stretched two-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds cq:ir /zo.b/v h;9pbu+c*d, ktm yg/fof the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 H pikuei,yul* b3fhq bb(gx1 9,,)a w.tz, and the tip of each prong moves 1.8 mm to ebp1 w 3*(huey,ug9x aik)t if,l.b,bqither 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 w4 eezs4 feei pf1v8-v)ith simple harmonic motion of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the bo)e eze4fi14vs fe8pv -ard during the oscillation?

A string can have a “free” end if that endgfqy*h de:)ugf le v5y9p:3x* is attached to a ring that can slide without friction on a 5f yy eqx e**:ldgv ):uf3h9pgvertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a pe 5nr4tp.up,zo riod of exactly 2.000 s — each one-way swing takes 1.000 opnt4zp,ru5. 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 th.nwlw- .av1mahw1 ny8 e vertical direction or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, th av1wnn-hym. w 1aw.8le 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 gxsg5 7v p:q/id is stretched under a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a second pu:7/xig dvs5p qlse is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by 3yi(gv9enmc;r;. .fas dcse1 a 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 that will allow th3;eev fd;(i.s 1a ycrnsgcm.9e penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The 8zx5j3haj ix0steel crane cable is 22 m long and has a diamet08 ih 5z3xxjajer of 6.4 mm. A breeze starts the car bouncing at the end of the cable. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (whig/.4s kgsl66d:sz xw hch also gives the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins t:x6s/ 4z6khdws gl.sgo 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