Give some examples of everyday vibrating objects. Which exhibit Sec5qdxysn g a +u,g bqv4.5gy3e4k63i HM, at least approximate+g3usy vg4i5y,e aq g k.c3xbndq6e 45ly?

Is the acceleration of a simple harmonic oscillator ever z7xxmji8i 7k 1i wdwq.gvad 5/r83uma.ero? If so, where?

Explain why the motion of a(g9vg b1qeok3hph p av uojv5-j94(i; piston in an automobile engine is approximately simple har9vb3-og;h v9jh pe51 (kgo(u 4q ajipvmonic.

Real springs have mass. Will the true period and frequency be large ev/c6aidl4z m8y8yvwr cw/irf370 m )r or smaller than given by the equations for a mass oscillating on the end of w83av)fwv7li/ yid6c8m /0crz4e m r yan idealized massless spring? Explain.

How could you double the max)qf./g j ear3lni(d(qimum speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scale, and theli(b z 5ml(.sdn is released. Describe the scale reading as a functionl.5l(imzsb d( of time.

If a pendulum clock is accurate at sd5t: )eam5uuchl u9m9ea level, will it gain or lose time when taken to hig 5)du uemuhc9 9tl5am:h altitude? Why?

A tire swing hanging from a branch reachv,1mw io1w1 rves nearly to the ground (Fig. 11–48). How r1o1 wvmv,w1i could you estimate the height of the branch using only a stopwatch?

Why can you make water slosh back and forth in a pan only if you shak p0pmk1 i76hxqe the pan atkixp7m160h pq a certain frequency?

Give several everydaya g nhi )zncr74k ,k-uer/h,v/ examples of resonance.

Is a rattle in a car ever a resonance phpee gsnj24ikp x *4s*4:bx;zhenomenon? Explain.

Is the frequency of a simple periodic wav6hfnk y)p9)vve equal to the frequency of its source? Why hvp9ykv)6 )nfor why not?

Explain the difference between the speed of a transverse wave t 2km5ra,8jtshrp mit/)lb e,d2z: .pxraveling down a cord and the speed of a tiny piece of the cordmr e:x)t,rhplk5.bs8 ma /2dtzj p i2,.

Why do the strings used for the lowest-frequ6ggpz ug4 ln7dg* 7i)qency notes on a piano normally have w)6ig u pg4g*n7qz 7gldire wrapped around them?

What kind of waves do you think will travel down a horizn1kc +h kr;uz.ontal metal rod if you strike its end (a) vertically from above and (b) horizr ;.uknh 1z+ckontally parallel to its length?

Since the density of air decve5djv :c /qtsq(-94s erade0 reases 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 vata jv5q9v-e0/ :deq rds(e4csry with temperature?

Give two reasons why circular water waves decreabq2ajz2z wpupgf;: x;s2z l.s3 v2x. rse in amplitude as they travel away from tzwxl2jpg.q;22;ubx pssa.zv2f r3: z he source.

Two linear waves have the same amplitude anyuz2a 2c*bplt7/j*lqd speed, and otherwise are identical, except one has half the wavelength of the other. W22 *t aq7p/j l*yzucblhich transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two s3rh ,gi 8xuf dw5c9(bjections of cord as in Fig. 11–33, the frequency does not change9ghj , 5cfrwi(b8uxd3 (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, abt;cq*o 8 s0vji +x bvoxqu3;,re there any places you could touch it with a knife blade without v0qi x3 +stv boxj*cub8;,q;odisturbing the motion?

When a standing wave exists on a string, the vibrations of incidj9m,8g gzpw5pent and reflected pgwg9z8 5p mj,waves cancel at the nodes. Does this mean that energy was destroyed? Explain.

If we knew that ener6 a 7zuxa8-x. vx1ombxgy was being transmitted from one place to another, how might we determine whether the energy was being carried by pax u.max1ba 6-8zvoxx7rticles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the total di* /7)ostukvai (ya3ld stance it travels*yak/ti7)3al vs u(d o in one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it but is 8, kp2 )jgi9wvu5 cm long wheip)j,9k v2 guwn a weight of 180 N hangs from it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg driver getsk 5ow7 mv6jwzr m6,hs/r0y qs( into the driver’s seat. If the car goes over ,rvs qm7s6/jyz( 0w5hwor6mk 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 flbso hr;dc c ah+ 1l+x4w 7;/fh0scw2orom it. (a) What is the spring stiffness coxsw ;swc;2l 4ob cloh0a h +1/rd7ch+fnstant $\approx$    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 m /2 g0dz ouv+xqeee:+xass of 0.60 kg is hung from it. What is its frequency if only 0.ue +qx0: o2gezd/+ exv38 kg hangs from it?    Hz

Construct a Table indiiq-dtb df3 .()7 zpghg4mjn eq (2:jaqcating the position x of the mass in Fig. 11–2 at times t =3f4-m2g :jd nd ()etq.hq za bqpj(ig7 0,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.aywtvdul( ok z6lt14w) s- )g(25 g is caught in a spider’s web. The web vibrates predominately with a frequency ogvw6 ol a()s1t- ut 4(kzl)dywf 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 sp29klxmswx8 8nring vibrates with a frequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 Hz. What is kn28s 8xwx9lm the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per second*ukm cm m f/n* rk+dr2k,m 1 bm7xhy7e4ny9)eg with an amplitude om2m yfr9 1 *emkdm 7+7h/kgb)c*yn, xuem4n rkf 0.13 m. Determine
(a) the velocity when it passes the equilibrium point,$\approx$    m/s(round to one decimal place)
(b) the velocity when it is 0.10 m from equilibrium, $\approx$ ±    m/s(round to one decimal place)
(c) the total energy of the system,$\approx$    J(round to one decimal place)
(d) the equation describing the motion of the mass, assuming that x was a maximum at x = (0.13π)cos(  πt)

  At what displacement from equilibrium is the speed of a SHO half k hzxf.u i:5ssg09wddn6b4va 9lm4 0rthe maximum valvsb. n9 4ikr090wmdadsh4u:zl6fg x5 ue?$\approx$    A

A mass attached to the :b;cww 5 sc,vr z;us+oend 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 spring is strxgf74- k4,*woduj sfo5 .bfw9amox9petche-ows57uf.x9,agomkw f 4fd j*x94bpod 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 attached to a spring with spring stiffnh+bpjs xcvt- 7xec l)w 4016ogess constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is moving with a sp)x0-vs w b4 +cc1j7oe 6pthlgxeed 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 popgu plisu- .34g(nk(cz6lpiuvt 3 n 0.200 m to “load” a 0.180-kg ball. With what speed will l3cz i-s. p3( 6pkintugu4vl( the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to one ujyz 0/o2rpz1 end of a spring; the other end is 2uorzy1/ z0pjfixed 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 thu0 s/xe7 4j0u.n bsjtjf v;rl5e equation x = 0.45cos6.4t where x is in meters and t is in seconds. Determinsrx unbl;jj0 s5/e0fv tju .74e
(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 equiliasw9q5;z3e se;akci xa,* n2u3if gd48k-obtbrium is the energy of a SHO half KE and half PE? ± 9s;3 dqeanx f ;kgaso3a8wz45cu2t-e*bi,ki   A

  If one vibration has 7.0 times the energy of a second, but their frequ3(,n)afb oup qencies and masses are),b p (q3nouaf the same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically 8c0hj v k; /jg+cey6bthanging light spring once every 0.6860c;ky e/+ gbtjvjch5 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 verticwgjo .oey.) av: p*y6aal springs, each with spring stiffness constant k (Figp*.jyyaow v:oag .e )6. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6nr n;i;/ i7umy.5t where x is in meten;u ; ny/rmi7irs 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. nk:id f(ie +;vFor each, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on the end of a horizontal spring (k = 124 N/m) is r--(fv 3o r)vs lgzdg1struck by a hammer, which giv1)vsgzor- v fr( ld3g-es 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 witw km2ed 8g(x j psa2wpx* ,2k(z33sexxh spring stiffness constant 305 N/m vibrates with an amplitude of e323(p 8mz22,x xkex (ds w wsx*japgk28.0 cm when 0.260 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 spr0 3y0rkt3u ryrings, 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 attache55d ljin( /yphd to a fixed horizontal spring whose sprin ynh5(pj5i/ld g 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 65.7v;pxi-n oqwm3c;jd5qg 6a0a 0 kg 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 level of tqvxm oa 3pigc;-jdq 65na7;0whe 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 exactlyy ajm);-kez, r 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if ittk)f-gjx8y/ (p6gh qr is to make exactly one swing per second? (That is, one complete vibration takes exactly 2.0 s6yg(gqp/k hjrf- 8xt ).)    m

  A pendulum has a period of 0.80 s on Earth. What is its p 6gk4qk j6pfrn. d7*iueriod on Mars, where the acceleration of gravity is about 0.37 thk7 qpfidu kn. r6*46jgat on Earth?    s

  What is the period of a simple pendu**m) c8-schjjheq4ye lum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendk7 (3cip7sz pjptso72 ulum is 0.760 m, the pendulum bob has a mass of 365 grams, and it is released at a3(27s ocz7 kjsti7pppn 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 pendul78uuzt: 7u f0d /hzoaxum has a length of 0.9930 m. If the clock loses half a minute per day, how should you adjust the length of the pendulum? shorteox7 fu/z u0zu dth:78aned by    mm.

Derive a formula for the oed( o * n emulprn9c66qq-a24maximum 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 frequene/uvydxx q3m j5)+ddy: v ps.ha1zi:4cy of 2.5 Hz. At it is released from rest starting at an angle of m zy d): v3y4.+ :hsej1/5xdpdavqiux15 $^{\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 b32tr v1obj- qi 83nicbow of his anchored boat every 3.0 s. He measures the distance between two inb -v1o tc2qbr3i8j 3crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz a(i / - m((e;gvke c fwpo)g9dn+sjwd5knd travels with a speed of 343 m/s How far apart are the wave crests (compr +dwgk;wfo(9ise-/ec (5gj(nvkm )p dessions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz bpbcc9( o.w-j+-qr n. qrac:v(kilohertz) and travel with a c c+ j(ow-r. cb.rb9apqn: -vqspeed of $ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

  Calculate the speed of longitudinal waves in vkn-jc7t*td fho737e
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elanyct walmysjz;(k- vw..m/0 ;stic modulus, but one is twice as dense as the other. In which rod will the speed of longitudinal waves be greater, and by what factorljs /w0z ky .w ;.c;vtm-yn(ma?   

  A cord of mass 0.65 kg is stretched between two supports ;n+b x;mj8z9:aqkgv4,cyixd .q3 m l i28 m apart. If the tension in the cord is 150 N, how long will it take a pulse to travel from one support to the other?vq8,9g3m+x c: md4;nia.lzjkix ; q yb    s

  A ski gondola is connecte:)mj7.6qau za9pfaxu 9t1 n/ 7tgym xrd to the 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 the terminal and sends a wave pulse along the cable. It is obse7 9mm6 qz7)1rutyaxpgax/ 9a:nu t.fjrved 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 ox4kmrt:0 dql /f his ship just below the surface of the sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is the ocean at this pointt/m4lqd:x 0kr?    m

  P and S waves from an earthquake travel a1h4hoqiqjb6 ; t different speeds, and this difference helps in locating the earthquake “eoj hqi hb;q164picenter” (where the disturbance took place).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced surface wave can be approximated by a sinusoidal trans/d 0jpzv11.-6nyg,qu m+ lbv1lzfpd jverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), 6dvz+pz g1p1.1d/nvj0ulmq b fj,l- ywhat 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 a:l )7bi 2fs8x5th-rpcvqd,va l j 4v-hmplitudes, of an earthquake P wave passing through the Earth and detected at two points 10 km and 20 km fro-4h jcsvi2brt7haf 5d )l:vp-xl ,8qv m the source?(a)    (b)   

  The intensity of an earthquake wave5j jjqhh1 9084.l t u:anjalys passing through the Earth is measured to be 0j haj5nals81 q 9tjhy4 :u.jl$ 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 travel tkj* tk g /j;yh.zuw++dhrough the same portion of the Earth, but one is carrying twice the energyy;* w jhkjzg.+k t/+du. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have 3*u 0jnrl7azc(: cigcthe same frequency, but one transports three times the power of the other. Whatzcc0urc7 n3 gl:i( j*a 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 total verticalp(rz9l2n0l 8oqdue/ 7vlh e )u 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 bug’s maximum (rl)9/l2z 7lud8oevqnu 0ehp KE change?   

The two pulses shown 1km9hp y70p pcin Fig. 11–52 are moving toward each other. (a) Sketch the shape of the string at the moment they directly c9ym 1p07phk poverlap. (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 at 440 Hz as its fundamn rp*1mlk.nw3qwp txq:-f)t fl.qt:7ental frequency, what are the frequefq1qm ltr )x3t*:wfnn:l-kw.qp tp7.ncies 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 unfingerev 1o58gfqqs z9d. At what frequency will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of the stvqq of 1s95zg8ring vibrates as a standing wave.)    Hz

  A particular string resonates in four loops b -v+og1 js9eb e;)ndxat a frequency of 280 Hz. Name at least three other frequencies sg b-jo;nve 9)1+ dexbat which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string iihvq 0isp44 bb 9de2h3s 92m/s If the frequency of standing waves is 475 Hz,b34 qisehhd v20bi9 p4 how far apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz anl4nxa60i.s 1f/ lyqb s)qfp ln(0n4u ed 350 Hz, what is the frequenc/ n.sxu) pe41nllq( f0y4s l6fb0qn iay of the fundamental?    Hz

  A guitar string is 90 cm long and has a mas, msudnyo9 27x1mb y.ps of 3.6 g. The distance from the bridge to the support post is L = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundamental and first two overmy sy.m un72pb1x,9dotones?    Hz

  A particular guitar string is supposed6.1gj dq.qfn7oc2ki qas8( phxo) *pa to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string b(*ignood).ph. x p1qk6f2jq 7cq8as ae 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 20v.-la cli (gr00 Hz, but it is measured to vibrate at 205 Hz. By vgila .(-l0rcwhat percent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string d twbcoq(687v is attached to a small-amplitude mechanical 60-Hz vibrator. The stringqd 8v7tcwbo 6(’s mass per unit length is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of the string may be adjusted by movin d0u7i )kh0nulg the pulley. If the hanging mass m is fixed at 0.080 kg, how many difdi lu)07h un0kferent standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back 7alx) yp+y fdojd4g:3vf -t2x 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 f xx7dd+2p o-lty43:ajf) vgy 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 kmj*dst+rbohu++: 0 f ki/s strikes a boundary within the Earth between two kinds of matedr+s+b+ io t:j k0u*hfrial. If it approaches the boundary at an incident angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “shelf” where the a. euv:w-*xvbvy , f /8ixgif3velocity changes from 2.8 m/s to 2.1 m/s If thi ba -g,xi8*wvy./vxf:f3ue ve incident wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air when it hits a layer of cold : )a,d9pznrikgurge-8l(0b uy /mz+c, dense air. If the sound wave hits the cold a0ni/r )lgkcru 8bzdp-:zgmu9 a y+( ,eir 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 wave strikes a boundary between two 4lx+ b;ej5wmu8uj:8fy gh2 o ltypes of rock at afjby2x84h l lum;ueg+w j8:5o 38 $^{\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. Accordht +ae2fg3df*71i gtding to the user’s manual, the dish has to be pointed in the direction of the 7tdh +af*f2ggd t31eisatellite, 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/hks54ka- dye; w6seez0 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 ;d-k0 ze ys5 eeaw46sksafety? (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 car5 giwn vto)t68/gr5i c bumper has a spring stiffness constant of 550 kN/m Find the maximum compressg5tw)6iivnot rc85/ g ion of the bumper if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a windgn/7;hes3lo axv+v9og6 mf 4l8mew,fow to a fire net 18 m below, which stretches the net 1.1 m. Assume that the net behaves leegwv8a,mnm; s3 lh6l/+o g 7f4o vx9fike a simple spring, and
(a) calculate how much it would stretch if the same person were lying in it.    m
(b) How much would it stretch if the person jumped from 35 m?    m

  A mass m is gently placed on the end of a freely hanging spring cdjd/gw,cs5abi91um -p +1j a. The mass then falls 33 cm before it stops and begins to rise. Wajs ,w1capb-/cdg1 d u+i5mj 9hat is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of rz4tqdf:,mfd6x f dejg0 kj qe 7jc4 .3m5ow2*22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stk: jj5ef* mmzqg6 4 c4d0 qor wd.7j,f32efdtxiffness 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 o krgq,0dnik +yl,r g(7/wj q+tf coffee (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 sqy/rn0d igkrg7wt,+lj+(q ,k peed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the cen ka0 g5:yvb3smter of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequency of the sound emitbyk5: 0samvg 3ted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t zhcwj;(6 i5p/ csk8w swhere x is in meters/8p wjik6shz( cs ;5wc 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 frequ8*;qtj*s 3 h8k4 wgruei+zk jdency f. What is its frequency if it accelerates at 0.50g (a) upw;84 ks gjidw3 + *rek8zuthqj*ard,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on the raft8a8fhc 6cjix8, it sinks 4.0 cm deeper into the water. When xi8hf8 ac jc86he 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 ()i-il xbt5 kk13z u9wnG) and 440 Hz (A).-9xz1itil3w kk5 ) nbu
(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 twed7s vq*s 8my*o-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 frequency is the same in both sections. q7dsvs*ey*m 8 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, aw- 8)g l0o 1n0o rswut9d2wqbjnd the tip of each prong moves 1.8 mm to eith jwr81s 2l twubow9 0g-)qod0ner side of center. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simple harmonic motion of frequency 1.30sd/5cl mgq498we; uo be wq2:dacto dtt1+v5 cycles per second. What is the maximum amplitude withwtt40uct:d/ 1w 3e8bqe q +95d;mv gdo aol2cs 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 4f wwbhax wi tan-32(apv7bzh v6;4gr98gye 9attached 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 xr vzp-9; w4(9b3 fgey7hwa2b w8 4vniag aht6with one end fixed and the other free.

  A “seconds” pendulum has a period of ex1 h86zo 4ln h:4wxtfhuactly 2.000 s — each one-way swing takes 1.000 s. nfou 1xhh84w zth4:6l
(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 directiu0ugko4) k7 hagooue26b/gl;m +l0h i on or can swing as a pendulum of small amplitude, b gao6uh/2l h)ou 4b ;lugmoik+0keg07ut not both at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontal swings, and by what amount? [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 255 N. A mi(kr524t br+snqjl fyh1 dt;9*1kntpulse is generated at one end, and 20.0 ms later a second pulj*4tdkl5 yqk1 rinhmr(s ;9+1 2f tbtnse 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 j pd,j)do)j w;a spring with spring stiffness constant k. A penny of mass m is placed on top )j,jd) jo;dp wof the block. What is the maximum amplitude of oscillations that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel cranedgs 3 )lcq,vr. 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 Tabl. vq)sgl d3,cre 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (we v,qrku9pn,-::wan ubpft-;hich also gives the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this vibrationn9- -uepa:knu;,bp : vfq,trw, given that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz