Give some examples of everyday vibrating objects. Which exhibit SHM, at *nmgq)g 4*lj gleast apprnl g* m4*gjg)qoximately?

Is the acceleration of a simple harmonic oscillr4j8,i + tsv3ldskz,czb n vo*.4-jbvator ever zero? If so, where?

Explain why the motion of a piston in an automobile engine is a zk-wirrm,o6, :ebmd 1pproximately simple harmon6 -,i: dr1rekbwmmo ,zic.

Real springs have mass. Will the true period and frequenc/*ky 44)fgjlsbmy-vky be larger or smaller than given by the equations for a mass yb4g*4-slm jfykk v/) oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple harmonic oscillatox,n ,9y; ljg42 fst qyeqn7.jcr (SHO)?

A 5.0-kg trout is attachedr9(j uz 9af2lv1b, khb to the hook of a vertical spring scale, and then is released. Describe the scale reading as a fzj, bh1vk9l(r9f 2a ubunction of time.

If a pendulum clock is accurate at sea /d(fe ) scmfq-y*xnrfy7z ccbjp2 l9:)q6yo 6level, will it gain or lose time when taken toq2domcbp:s/fn l6( 9z6y eyq f)c*frxj )- 7yc high altitude? Why?

A tire swing hanging from a bl/ m;5fn-kzu8vut*9 w xo 0qoeranch reaches nearly to the ground (Fig. 11–48). How could you estimate the height of the branch using only a st5 wnx l/q*0kf- 9t8 muzeo;vouopwatch?

Why can you make water slosh back a 4ei3 fd4u3yrdnd forth in a pan only if you shake the pan at a certain fr3 d3y feu4idr4equency?

Give several everyday exea3;8 tr+g85paf qke zamples of resonance.

Is a rattle in a car ever a resonance phenomenonwi o2mg1u4gu mdd4u1 -? Explain.

Is the frequency of a simple pg2 2/1ggrh-hol;qek deriodic wave equal to the frequency of its source?geh hog/k 2dl-2gq1;r Why or why not?

Explain the difference9qp2v b8;ekn2yk9x vg between the speed of a transverse wave traveling down a cord and the speed of a tiny p9bxypvngv9q2 kk; 82eiece of the cord.

Why do the strings used for the lowest-freat+5 +txql,yz04ksm zquency notes on a piano normally have axt t,yq4+ +50 zmkzlswire wrapped around them?

What kind of waves do you think will travel down a horizox fet( yw-jj32ntal metal rod if you strike its end (a) verticaly-t jxw(2ejf 3ly from above and (b) horizontally parallel to its length?

Since the density of air decreases with an iiae0obi ./d feeq 385vncrease in temperature, but the bulk modulus B 3iaf 5 v0/e.eeqdbo8i is nearly independent of temperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in amplitude a6 g0aam8(4tvxu 2majy s they travel aaxa2t vmj6g8 u0 (ya4mway from the source.

Two linear waves have the same amplitude and speed, hzkf;)( 2oxis:rw d/jidf14loqw/ ) yand otherwise are identical, except one has half the wavelength of the other. Which transmits more energl) is)1ijd fd;f4zqh(k/2 :w/xyo r woy? By what factor?

When a sinusoidal wave crosses the boundary between t 0r vhns8;4mtcag*/t;)dttmy wo sections of cord as in Fig. 1;tt/8)amn4t s mrhvd cgy*0t;1–33, the frequency does not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there any places you could toucseg h0o;l+ bw7h it with a knife blade without disturbing t b 0gl7e;hows+he motion?

When a standing wave exists on a string, the vibrations of incident and s,ym5vf1ngj )reflected waves cancejy5g1nmv,f) sl at the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from l3oqejkq fqxs,m,tk+*3s -;upmc 1 8ione place to another, how might we deteum -+ko;f8 i,pc,q 3sqqm 3 e1skjl*txrmine whether the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, wh2gu 9s8elp-jtat is the total distance it t8 ls2tjgup9 -eravels in one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs frow)2pf wnt8 -ufm1.wa njo t1h4m it but is 85 cm long when a weight of 180 N hangs from it. What is the “springtn8h1)wm- w n21jafpu4.w fto” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg driver gek:.f ye (0f llsf 18wuw,tcqly /)r5vmts into the driver’s seat. If the car goes over ay/wu m 0kflqftclvs:r)5 l,wy1(e f .8 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 i4s+6n ckv8g0k t osz0tt. (a) What is the spring stiffneszok nv ts08k4gs0+6 cts 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 3.0c wq50eks5z-of2m ywt+yv;u 0 Hz when a mass of 0.60 kg is hung from it. What is its frequency if only 0.38 kg hangs fromz5yw2q+ ;5 futoy0sw 0 evmck- it?    Hz

Construct a Table indicating the position x of the1vrxe*.crucr-n.;fxb/ o hw 0 mass in Fig. 11–2 at times t = 0,t xx0 . -*1frnrchcb.v o/r;ewu = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 0.2f- sw3-z cdsxl/5o,hwz)ps5r 5 g is caught in a spider’s web. The web vibrates predominately with a frequency of 4.0 Hz. 5zssw/ ), cw--5h3 dspolrfz x
(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 frequencnf09nb;h: - xo*xic ecy of 0.88 Hz. When an addithno;f - xx0be9cc*in:ional 680-g mass is added to m, the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per seco/ l90niuy;ox6yt qilonlcdr u8p41-8nd with an amplitude of 0.13 m. Determine n ii xtulo/qp; 4y809ycl6u-1dn lr8o
(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 the maximum 23vlylsl.;ea value?valys;l e3 l2.$\approx$    A

A mass attached to the end of a spring is stretc4nuw g f18-pqohed 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 stretunc p2 6yhnj12ched an additional 0.130 m and released, how long does it take nhn2cp16u2 jyto reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with spring stiffness co ccqcni8.2 - s:/ndz.o -esjrdnstant k = 280 N/m and is executing simple harmonic nc .onss8e-qr:d c2. jdcz/i- motion. When the object is 0.020 m from its equilibrium position, it is moving with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compress they1:j,cl+vzz. j)abrj spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speej+ ,ya:z1v cljz)bj.rd will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached t*.u- ( blkjfhfnw)uf 5o one end of a spring; the otheun*f kub )wf-(j 5.hflr 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 6 ;hkby3kee1+tfppde (aokr3k,t 4 d7equation x = 0.45cos6.4t where x is in meters anp t e;kao3+ p7fdh dbk3(, t4e1rey6kkd 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 energy of a SHO half KE and hawt 7jwe8/w.tqlf PE? t /qjtwwew.78 ±    A

  If one vibration has 7.0 times the energy of a second, e0)l7 u9xyaoq but their frequencies and masses are the same, what is the ratio o0)q o7ux9 yaelf their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertice kur h;,o*wo6np27ieally hanging light spring once every 06 k2i;ohno7rewu*,e p .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 yk:.88 yvt/xo: tnfdqtwo identical parallel vertical springs, each with spring stiffness cons/t kx:yd8q:v tyn. f8otant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates an,4yi 12 tdknrccording to the equation x = 0.38sin6.5t where x is in meters and t is in seconyi4 trn1d2k, nds. 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, what is kw9f;twe k/9+pw- pw t
(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 Nbhwph8 9qq: vpi9,rd;k0xv0v /m) is struck by a hammer, which gives the ma9 qi;vdk8 h0v pxr9:bvp0w,qhss an initial speed of 2.96m/s Determine
(a) the period and frequency of the motion,    s    Hz
(b) the amplitude,    m
(c) the maximum acceleration,    $m/s^2$
(d) the position as a function of time, x = (    m)sin(4.08$\pi$t)
(e) the total energy.    J

A vertical spring with spring stiffness e.xo3wc/4yic ni8xy 0 constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs fr0ic/ wy x83nice y.ox4om 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 springs, with spring stiffnf;k 1f(-lmznlqt w-a) ess 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 sd2yv7j x9s,ja ba,7y kpring whose spring ,j2dyavsyak79bj7x , 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 65.0 kg jumps from a high bridgvu,56 pzczzz3; nndqg c 1fq-,e. 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 the bridge. Calculate the spring stiffness constant and the unstretched length,6uc5zv- g1qqpf,dzznncz; 3 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 s.v,4bh+ :wl6c) xrj4ngo2.q uxppp xz2 What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum bewm) +lq84hir ,gjdm ee,n6io-..,izi+ ckdux if it is to make exactly one swing per second? (-x,im8iik4 i+ d gdl).e,n.+hj e,wz6mrocquThat is, one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its l e1yvsndkxugvyijfogu o(u +79-41.7- glx. period on Mars, where the acceleration of gravit+lyu g4..xx(d7vkujg oen1fl--97o svuyi g1y is about 0.37 that on Earth?    s

  What is the period of a simple puynfzdeq8fd: b8 o +77endulum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 m, the pendulum bob has a mass of kebw ,x4vd7i .365 grams, .vexd4,i bwk7and it is released at 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 length of 0.9930 m. If the clock loses(-6ttito9 vvl half a minute per lt-(tov6v t i9day, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the mpmhu9v0;0j o 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 ivks,jz8 1gk e2t is released from rest starting at k2,sz1 jv8 kgean angle of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests pass the bow of his anchored boat e+ sww2lj ho1,wvery 3.0 s. He measures the distance between two crw jo w+,1hw2slests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and eb8qv4jk i6 bs8fj cuf32e8w7 travels with a speed of 343 m/s How far apart are the wave crests jebwbq2i3 8k8 f f7js8ec4uv6 (compressions)?    m

  (a) AM radio signals have frequencies bepz 0zf ulp(-3*vcrue9i 1q6i+: vpqqp tween 550 kHz and 1600 kHz (kilohertz) and travel with a sz6up:9pq3-rv+cvzup if01 *le( ipq qpeed 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 a 8cw,huqn s07
(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 de(s *gb9us3dz ynse as the other. In which rod will the speed of longitudinal waves be greater, and zgb*(su39d ys by what factor?   

  A cord of mass 0.65 kg ,k/srjjq k-2 wis stretched between two supports 28 m apart. If the tension in the co jrwj- s2/kqk,rd is 150 N, how long will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected -u 20 rn8di py6sfv)dqcvw+i /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 alongipnv+2 dqvuiwfcrd) / 06s-8y the cable. It is observed that it took 16 s for the pulse to return.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

  A sailor strikes the side of his ship just below the suryk)u0d6u3ubvw l0p z, face of the sea. He hears the echo of th lu 6uw3 )vkzb0ud0,ype 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 t-3x;wmw)vhr 2ij7o1efw)ri t his difference helps in locati 7xjwroe)mh -if;r2) v t31wwing 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 cap(ig :ye 2b4-isvo9cu40nl n dn be approximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (tc4io n-p(9b di40s:n2evyu lgypical 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 inf 74 xtteefh1*tensities, and (b) the amplitudes, of an earthquake P wave passing through the Earth and detected at two points 10 kh*fett1 7xe4f m and 20 km from the source?(a)    (b)   

  The intensity of an earthquad)6; y jfge33g/vrqbh 6dlf12:io oleke wave passing through the Earth is measured to be i 6gdv1qdgr:/ ooehf)23ll; j f3be 6y$ 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 fre9*u 9l,deq lfspz,+ bbquency travel through the same portion of the Earth, but one is carrying twice the energpbd zulsf, 9,*l+9beq y. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched st),wd ,zm4 cs9): y2zbgtexo hfring have the same frequency, but one transports three times the power of the other. What is the ratio of the o2)sf49mxzw ), yezhg :bt,cdamplitudes of the two waves?   

  A bug on the surface of a pond is observed to move up a q0 )v2cp*xnqynd down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the qnx yc2)*pq0vripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig.*nw3 iud :+ 4ij,t+meiusrjx: 11–52 are moving toward each other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the i, :4ni3wjermxtjd+i+us:u* 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, whv yk/ ed20efpn+o )1ubat are the frequencies of the first fournfeye+k p2 0vb1)odu/ harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294p 2s60;9ekeri+t,vqz* (;jc vd f/vb pfnts /e Hz when unfingered. At what frequency will it vibrate if it is fingered o2 rs*9st,kb v f0j6dneep + /zf(pci vq/vt;e;ne-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 o(.us qxb o00eresonates in four loops at a frequency of 280 Hz. Name at least three other frequencies at which it will res .oo(ub0e0 xqsonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the frequency of stani wc 025k1uiiz su;,zwding waves is 475 Hz, how far apart ar wzw20ii15iszu cku ,;e two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz aq 4ye: wmr ja2a;2:/s-3;2ljei rsdr*dnrs pgnd 350 Hz, what is the 2:m;:/is r2glarqrd2d saey*ej3 ;nrp 4s -w jfrequency of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass 6rd(i+jm+y fmj w:+ rgof 3.6 g. The distance from the bridge to the support post is L = 62cm and thj6m+m(++dj yiwrr:fge string is under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, but it ih z6y m7mmlcte ;a 5mcx1 s(inl-))5mss measured to vibrate at 205 Hz. (mcls my;tl5 16in)sa7m-)e 5mmxchzBy what percent should the tension in the string be changed to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hz, but it is measured 85z 0dr x.bwqx6 k1y xyp47by7c oyax6to vibrate at 205 Hz. By what percent should6xx6x47y5 pb7r cd8yqky0o 1zay b. xw the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal strcx k0b5es6s agu b5l0.ing is attached to a small-amplitude mechanical 60-Hz vibrator. The str. bsb c50ux 0k56gleasing’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 moving the pulley. I1k :+r k3uqyx)97gb )dwdgbj lf the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying gk1rdj9+u3 b7 w)qx dlg:y)bkL between 10 cm and 1.5 m?   

  When you slosh the water back andewdt 1(r-tpk- 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 such a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the speed of th(p--t kt1 erdwe water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundary within r4kqkq4*m k 78h1ae j*awvz5zthe Earth between two kinds of material. If it approaches the boundaryv4*ea5hkmkjk 1a* q78q rzw4z 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 dq /7qw h6*ia/v2 g5mnehj3kg“shelf” where the velocity changes from 2.8 m/s to 2.1 m/s If the incident wave hqdm5gg/2wk 6i7vhq/n e3aj* crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm q;wiq 37v3 oab dvl.l7;wklmzn7.du)air when it hits a layer of cold, dense air. If th7.mlo;b3qdzlv a;nqwluk. i )7d wv37e sound 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 wave strikes a boundary /ks d u )6aqds6gs2(u3cib l)8hsuab 1between two types of rock at a 38 2cs/)6usab ka61 gshsd)3bqul(d8 iu $^{\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 user’s mangd 4y +o wpjp96hm;y(zual, the dish has to be pointed in the direction of the satellite, (myw;+ yo4z9d gj6p hpbut 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 veloc 9srz*adh2z3h ity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusuals d 3*ahz2h9zr 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 xr:tp9l0 2d j72.+freped tkrhas a spring stiffness constant 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 enldrx2erfd. 9pr 0kj ett+p2:7ergy.]    m

  A 65-kg person jumps fro2sq*qfxgle4s2;s 9f jm a window to a fire net 18 m below, which stretches the net 1.1 m. Assume that the net behaves like a simp l9sfqsqg 4s;e2* x2fjle 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 placeb: z*m0skrby0d on the end of a freely hanging spring. The mass then falls 33 cm before it stops 0 : bb0*ymrskzand begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a hugq-2 9bo uxkdwlm q,l-2e spring at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffness constant of the springlqo w2k9lq m,2bu-x-d ?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of coffee (diameter 8 cm) at jus lv*dv7a9q/d st the right pace of about 1 step per second, the coffee sloshes more and more until eved7lvv9*/q d asntually it starts to spill over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the center of a 33-rpm phonograph rn;g 9dvxh+;khecord have a wavelength of 1.70 mm. What will be the frequency of then9 ;;hhkv dgx+ sound emitted?    Hz

  A 2.00-kg mass vibrates according to th4da fmp4.b kz7e equation x=0.650cos7.40t where x is in meter .db mpa44kf7zs 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 frequency if it x 9y0q0avk9tl accele9k9qyv00l t axrates 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 the raft, ityy-576fu(ft i ,bf ujm sinks 4.0 cm deeper into the watbfj5fyyu tf 6m, (u-7ier. 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 55 9ftu 3e itqn5xlzire*(/jg392 Hz (G) and 440 Hz (A). /gu*l eq5itt x9 5nf5j3rzie(
(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 co3 i0 o-ij,.( tqdx*bxt beqop5rd 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 tho q(p 5*e jqt- dixb.bxto3,i0e 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 the tip of eac/ jpuied1d3sz)4 ukz1h prong moves 1.8 mm to e4 z)1ei kpuujzd/3 sd1ither 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 nkk8xu2:f0fu w6ndk e5gs5d1frequency 1.5 cycles per second. What is the maximum amplitude with w86 :5nu0ek1xn 2gddufs5 fkk 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 attached toht717ok3 m*kn. tj.t 7ourzq m 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 with one end fixed and the otherhmjurokq7.1m t*to kt7nz. 7 3 free.

  A “seconds” pendulum has a period of exactly 2.000 s — each one-wz6sudh 035yj .k- ujwvay swing takes 1.0 zk0swj vhuu.5yd 63j-00 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 oscillawco,mr/r;evc d:+a7 yfpz,z. te in the vertical direction or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontal swings, and by what amount? [Hint: Lryf wa zo/pz,,cr+7;de. mc:vet $l_0$ 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 pub 73r 3ecvk1ywlse is generated at one end, and 20.0 ms latervryw e1 3cbk37 a second pulse 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 a spring with sprin1u:- s att6j -o-espilg stiffness constant k. A penny of j-s-oieal sput 1t:6 -mass m is placed on top of 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 cranef7t/yk/) nc .q dc 5c:ze3hlrx 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. W/tq5dccn3k/)zl h . ec7 f:rxyhat 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 (whip)(6fv c, hejaq6q zorpt4) f:jclk/*ch 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. Inplq k/frc6jc : ,zofv )p)e(tqh4a*j6 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