Give some examples of everyday vibrating objects. Which exhdnncj;rvl 26:x nv,79dexbpnu ,c (b)ibit SHM, at least approximately rccjn u b2v edn,v),x;(n nx79l:6bdp?

Is the acceleration of a simple harmonic oscillator ever zero? If i)ze 9smd/y 9/ft wyd-so, where?

Explain why the motion of a piston in an autowh5r/pbbw jxwsdw10dm .+8 j 4mobile engine is approximately simpled.s 1+m0hdp / jw8w4jrwbx bw5 harmonic.

Real springs have mass. Will the true period and frequencyhg) 8brbr*0 lnvlgb x9 *dp;i- be larger or smaller than given by the equatl-bgr);i nrpxv9*b8hb 0 d* lgions for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed ksbet8, )-:rozfyf 4tof a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to t bhejckm-2q27 he hook of a vertical spring scale, and then is released. Describe the scale reading as a function of time-hc b72mqe2 kj.

If a pendulum clock is accurate at sea level, will it gagwx sk(- *5/ d3ljqqrrme*wg /in or lose time when taken to high altitude? Why/w-rjqw(sergglxd*53*qm k / ?

A tire swing hanging from a branch reaches nearly to the gwxh3 l rkucj 31d9u-36x5afh fround (Fig. 11–48). How could you ef3 -wx3cd 1hu9ufk j x65l3rahstimate the height of the branch using only a stopwatch?

Why can you make water slosh back and forth in a pan only if you su13pe p*cefvdqp q*gqehd3b27ah(k n ++-4a whake the pan atbdq-edv7(ha3 1hk * eq *ppu 4n+3waeg2c fq+p a certain frequency?

Give several everyday examplespv:b,nk8 khzjr0h::t of resonance.

Is a rattle in a car ever a resonance k*g;2k5.+8yjo bqsvqpca(dceu c 4. fphenomenon? Explain.

Is the frequency of a simple periodic w4wvp v vi12xgm7gy 8i3 eymcy)l3k. +mave equal to the frequency of its source? Why or why yi3iv8wkm)4 me7y3+.y x mg1lpvcg2v not?

Explain the difference between the speed of a transverse wave traveling down a p2y5+e4ehiiokh g*r1 cord a k1gy*e4peirhoi 5 h+2nd the speed of a tiny piece of the cord.

Why do the strings used for the lowest-frequency no8;ngzxo5xaq +jij2 f8vnm2g :tes on a piano normally have wire wrappedj n jfg;882m:an vigoxz+5qx2 around them?

What kind of waves do you think will trag dfk-0n+ezcv a sz3woq--:a+vel down a horizontal metal rod if you strike its end (a) vertically from above and (b) horizontally parallel to its leng+:-awez saq-cvn0o 3k -fz+dg th?

Since the density of air decreases with an incre zd (xyzef/8f+a0uu t5ase 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 tempera(f5u8d 0 z/eya+zux tfture?

Give two reasons why circular water waves tx qd*lekwwo9tu s09:ir46yrq b ;)c9decrease in amplitude as they travel away from the sobsq*)y erlwx6 w9 9:4curk t; it90oqdurce.

Two linear waves have the (j) i ssxbc,r)9p;tpwsame amplitude and speed, and otherwise are identical, except one has half the wavelesps ;i)xp9 trw,bc)(jngth of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sections of co(bd;9;)byc x3.oc ra)qfmrdm ni4 0kard as in Fig. 11–33, the frequency does not change (although the wavelength ancmdo )q m.3ybnra049a) c;kri;dx b(fd velocity do change). Explain why.

If a string is vibrating in thre8of4de uqv7m :l5*dad zbd1s:fas- (;x5pcl k e segments, are there any places you could touch it with a knife blade without disturbing the motion?a o e5dplumdqfxbs ;*7klfcd48- a zv(: :5sd1

When a standing wave exists on a string, the vibrationsrspl.3c 1qc2 b of incident and reflected waves cancel at the n12 p3bqslcr.c odes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one place to another, how migan 8ewm,+8p bcht we determine whether the energ , w8pbcme8a+ny was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM wi0q7p8kfwj 5s;mj19 kridhx 6 wth amplitude 0.18 m, what is the total distance it trave5xm8i6hwr;w1 fk0q p7s 9jjdkls in one period?    m

  An elastic cord is 65 cm long when a weighnna bh iah-12wt*i 1e5t of 75 N hangs from it but is 85 cm long when a weight at2w5*a -n h1inhibe1of 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 er4c 8 s::52zjo jffo 7x+slfvits 68-kg driver gets into the driver’s seat. If the car goes over a bump, what will be the frequenz+or5sjl7j2 ocv:xf8 :fefs 4cy of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fis)j6lll( 2ir qfh hangs from it. (a) What is the spring stiffness constant2 (lqf rl)6ijl $\approx$    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 of3 ;hc a9o))g)eso dadk 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency if only 0.3a)kso39 ;dco ) daghe)8 kg hangs from it?    Hz

Construct a Table indicating the posit-5c h zl-ek-nsnnva ;)ion x of the mass in Fig. 11–2 at times t a- )sv-n nk5nh- zec;l= 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 0.25 g is caught in a spider’s web. The web vib*9 bsmp8lo)0a; 64(lwjizngdd6zaqirates predominately with a frequency m;jni *sd6 4ap9awb(8li0q g od z6l)zof 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 sprle aikpc: zbq ng f.h(96j4.05s(dyoi ing vibrates with a frequency of 0.88 Hz. When an addi ygj(e0q.p 6i .l hdo5bfak 9sc:z4(nitional 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 pltbrs- :hd xn5 hd35)z)ag ;j: uiy*xmer second with an ampli du) md:x 5)3l:;h*tn-ijzy 5sgbrhaxtude of 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 fr)o w-s8o ou2zx ;b5qsdhr0bl*om equilibrium is the speed of a SHO half the maximum valuw5 o2loz);bq rhdo0x8-us*s be?$\approx$    A

A mass attached to the end of a spring is strr(brrt3)vi9zh:i7 u z2wcn 6 hetched 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 stretch4/mfpi2p;l 3nxx:dyyed an additional 0.130 m and released, how long does it take to reach the (new) equilibrium positip dm pn/3 lxf:2y4xy;ion again?    s

  An object with mass 3.0 kg is attached to a spring with sp724 bvhrp4e cbwuy1 (skh v/q9ring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibriu s29rw q4/p4vv h 7uhceyk(bb1m position, it is moving with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compress the spring of aak9hcl,s v)p+ toy popgun 0.200 m to “load” a 0.180-kg ball. With sk+9,lvh acp) what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictaas4d 6/qbjv7-he ;wsjx(nl c; s6uj0 44ojubionless surface is attached to one end of a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is rele ejdaj b4x a;66j/wjo4vc- 704qhsu;lubss(n ased from rest with the spring compressed, the mass experiences a maximum acceleration of 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates according to the equation x = 0.45cos2inj* i7y n*t idk/8,tztg)yf6.4t where x is in meterszi2/j 8 *tn7 dt)yi*y,nti kgf and 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 ank1cc,.x4gb .* 9yc gza vql8jfd half PE.lqz9aggcc y ,1xf.*8cjkb4 v? ±    A

  If one vibration has 7.0 times the energy of a second, but their frequencil- ob3 v+c/m2l4 vnv6qr0pvb3bnvj, ges and massesvrl/ lgpv0jvvb2,3bc436b- mq on nv+ are the same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertix ahy+ 0o2)+65ab clbywa7ngm cally hanging light spring once every 0.65 s. ag5a+ 6bywcbo2m+7lanxhy)0
(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 vertictbm vd6 v l(pgwtl/1+-al springs, each with spring stiffness c/ dl t 1w+mvvglp-t(6bonstant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates accordjkft)xh,8 7 eu igf05ning to the equation x = 0.38sin6.5t where x is in meters and t is in s78 g0,t5 ikuje)fxf hneconds. 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 ;-6gykvm)j dgm0inonn65 4dkof SHM, labeled A and B. For each, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on the end of a horizontal spring (k =ayh)1ska ps 1y/9e8hm 124 N/m) is struck by a hammss hya 1 )8hkp/m91aeyer, which gives the mass an initial speed of 2.96m/s Determine
(a) the period and frequency of the motion,    s    Hz
(b) the amplitude,    m
(c) the maximum acceleration,    $m/s^2$
(d) the position as a function of time, x = (    m)sin(4.08$\pi$t)
(e) the total energy.    J

A vertical spring with spring stiffn3( 8fd2ki peteri:wps+i8 ,phu 9e;1p1k planess constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) with positive velocit2+psn ek up,we8fap lp8ih3ii9 (1 rpt:dek 1;y 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 stiffne;akgq0+ v22fw08v- dr ljxemhss 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 hor-oov5ayd 4w bej +.+ouizontal spring whose spring stiffness constant ouyad oe - +w54+oj.vbis $ 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 hiocm:-a fn(a;k) cup in;1b2rf gh bridge. After reaching his low:nfc1ubfoc )raai;;( nkp2 m -est 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 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 ex:bs5j vav,3kg actly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if itxz*i-w u i*n;k7w 1wvb is to make exactly one swing per second? (That is, one 7vww-ib1*u*i; zx kwn complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period )t4yqh.asnp* x4 vz*r on Mars, where the acceleration of y.q*tnsxzr av4* )p4hgravity is about 0.37 that on Earth?    s

  What is the period of a simple pendulum 80 cm lo6tkehcj.lr yvi.kmz h+ il8:m:x ;r+am : 26dvng
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 7-q.k) xudrn 9fow y6zm, the pendulum bob has a mass of 365 grams, and dqxwu6. zrnk9f -)o 7yit 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 jnbiy x1*moe7f2 fvg),50 rma0.9930 m. If the clock loses half a minute per day, how should y* njm2m af571 xfyrgbo e,v)i0ou adjust the length of the pendulum? shortened by    mm.

Derive a formula for theros8o b)hwrfn2pj t.0m 78c+j 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. A bh t*9v*w+regt it is released from rest startingt+ *vwrbh e*9g at an angle of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests pass the bow of his anchored boat e gqkd k8t., )e45k ;px;bdazkuvery 3.0 s. H8 5pde.;)xzktukqkk,a ;b4gde measures the distance between two crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels 9p 3lcu.i *,bfw +vkhuwith a speed of 343 m/s Hv,f+b 3 uuk9*hwl.p ciow far apart are the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between wb4uvry;3g)t ei0 e.n550 kHz and 1600 kHz (kilohertz) and travel with a speed ebtuw403; ie ry).nvgof $ 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 tmz+e) z ma6paldl19)
(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 as the o //jvzwodq j n*.a 83e7jsr2ddther. In which rod will the speed of longitudinal waves be greaterz q 3 8vdj.n/se2jaodj7w/ r*d, and by what factor?   

  A cord of mass 0.65 kg is stretched betgorsd/f :9 ,5cet8(t32kijor x y)hkikq4 x 1mween two supports 28 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 otro4(kxqd 5e/2t9c g)km8, hfy i ixrot:s1k3jher?    s

  A ski gondola is conne:rvw( hx8(ko mcted to the top of a hill by a steel cable of length 620 m and diameter 1.(r: (hxv8 kwmo5 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 observed that it took 16 s for the pulse to return.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

  A sailor strikes the side of his ship just below the surface of thee mx,a ptw*kab- mj/:/ sea. He hears the echo of the wave reflected from the ocean floor directlyejm,-k/:ax p mw/b *at below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at different spy5l 8 kd88spp1dktu.i eeds, and this difference helps in locating the eark8tdld.p8yuisk18 5p thquake “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 approximae,htowkiqce oy*26 4 +ted by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what k 4eht2qw+iy6c, ooe *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 ams6b 8 lz8xm;3zgvkxr 6plitudes, of an earthquake P wave passing through the Earth and detected at two points 10 km and 20 km from the source?(ax;6l8s8rg mzxkbvz36 )    (b)   

  The intensity of an earthquake wave passing through the Eagved bqp8f)e 1i*ekq,:(7ish ork ;b 2rth is measured to be ,bke : )dirkeivp1h q2 s(bqfgo87*;e$ 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 through the same portion o(d.3j fer(wb af the Earth, but one is carrying twice the energy. What3jbed. wa(( fr is the ratio of the amplitudes of the two waves?   

  Two waves traveling along*;r2d kca 4ym(f( rtvt a stretched string have the same frequency, but one transports three times the power of thed(* ;(r 2trv caktfym4 other. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is rmqw:bz i1. 3lobserved to move up and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If tmw rq.:l3zib 1he ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig.nis9n0 si4k8s 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 4is0sk nni 8s9the 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 frv 2byex6t*7o aequency, what are the frequencies of the first four hb vx7ey2t6o*a armonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz whejp/64x axxv3:qka)pjl 7vz d/n unfingered. At what frequency will it vibrate if it is fingered 7v):pxd6/a /k4xqa jx p j3vzlone-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 fo1c.*dhz.lgol3 u7 lrfd) .qrvur loops at a frequency of 280 Hz. Name at leasll 7d*lcf.qhv)..ug3roz dr 1t three other frequencies at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the frequency of standing waves xjmie7(zsf 3o0;8 sd sis 475 Hz, how fa87fjs;ime(x 3 zssod 0r apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string arbdeq.n5 / fss590idy 8gam.qv e 280 Hz and 350 Hz, what is the frequency of the fundamental/ia 5s. eyd.98gmsnqb0d5 q fv?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distance25cjb4c pyn k( from the bridge to the support post is L = 62cm and the string is 5bjcpcy 4 2kn(under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string ihyy,gdi5 z5e 63+p:p+ w irljis supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to coi6++ p3 d,i5 ryipljwg5yze:hrrect 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 me tthwhvb,b2( i8/x1e )(vhkk casured to vibrate at 205 Hz. By what percent shoutiv(ek(,b 2wxth h8 b/)ckv1 hld the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontae;eft ,b24 qj7xlbk k)l string is attached to a small-amplitude mechanical 60-Hz vibrator. The string’s mass per unit length i4 xfe kb te27l)qb,;kjs $3.9 \times10^{ -4}$ 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 thg10:v:w,xo:rugoqn dx c0c h2e pulley. If the hanging mass m is fixed at u 0q rh :oxwg1gvc:xodc:n02,0.080 kg, how many different standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at just thy cg.5x yjb );pl2q )3d(gmfqqm4xr/we right frequency, the water alternately rises and falls at each end, remaining relatively calm at thgdyqy/fgqmlj5xx 32)4) . rb;cwp m (qe center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundary withi1 sssdawp en,pwbu;474i :4jtn the Earth between two kinds of material. If i44pus7b ti;, sewpjdwan4s :1 t 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 un, thn+ae;,citderwater “shelf” where the velocity changes from 2.8 m/s to 2.1 m/s If the incidi;atc ne,,t+h ent wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warmf p;cqu8cp:.--)myu5 ucs ej j air when it hits a layer of cold, dense air. If the sound wave h:c u-u5j8cfp p)q;. j ucmy-seits 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 wavog8;v-oce ud 9s fec w/)h+-noku8z,2gnxg2 me strikes a boundary between two types of rock at a 3,-ug nm/-ge c uk892) vwo c;ox gdfson8eh+2z8 $^{\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 apd*wakxmukbvq.04 y9 ) 2+v 1lq)zymz bout 0.5 m in diameter. According to the user’s manual, the dish has to be pointed in the direction of the satellite, but an error of z+lup.4w0*qa by)q 2) y vm1mvdxk9zk 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 across the Pkga6rx0:.ep s4 pn xvrjlc5p997 jo;f acific Ocean. As it approaches Hawaii, pe.:nx5p; rcx0e4j7gosrpfval p9j k69 ople observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper i ho8gaeo oa3 v(,95sr/a3re l.uew,thas a spring stiffness constant of 550 kN/m Find the maximum compression of the bumper if the car, with m o8oe ia(g,te9u3h r,w5 3/al eo.svraass 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 window to a fire net 18 m below, which stretches tw wxbr a3km7 *.)t +zrfbwp;i(he net 1.1 m. Assume that the net behaves li( 7p)i mrx.+awzk w*b3f; rwbtke 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 pgshd .)/2tsr j:(vaxfreely hanging spring. The mass then falls 33 cm before it stops and begins to rise. What is the frequs:(drjh/ .g )sxvtp2 aency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 11–54), cf hs/ ti4 sovo2.:d6tdompressing the spring 5.0 m. (a) What is the spring stiffness cov.sh o 6/ti:2o 4tfdsdnstant of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of coffee (diameter 8 cm) at just the right px3y;tbm1h s9)fh:e4vlw1447bo 4 hfkzn himbace of abou bn4xhivm4f4wh9bmo3k4 ls;17hbfeh zy): t1t 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 waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the center of gu)o;e*6s vry a 33-rpm phonograph record have a wavelenvs*)eyorg; u 6gth of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.404;bnlqw:w r m 3 o; 00kezk,a)4kfjmket where x is in meters ; kj4nkazomr kl 3,0e 4;0 k:fb)mweqwand 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 oscillat xg53m8a cgn )ryval/:es with frequency f. What is its frequency if it accelerates at 0.50g (a) upwarmg/rca:8y5xna) g3 l vd,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on the rat (*c-;jtgs cqft, it sinks 4.0 cm deeper into the water. When he steps off, the raf*jqt c(;g st-ct 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 39 x((86sskkf8gn (piy1 q2lnu u+b6qg q2 Hz (G) and 440 Hz (A)gsqbky861(g8qn s(ui2x uk6fl+q(np.
(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 sk( n*l6 inywovu)bm( hm.c *y1tretched two-part cord of Fig. 11–33. Determine a formula (a) for the ratio wlo1yvn )icb6hkn.(m y*u* (mof 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. 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 /q3wn);brqt i+syc zn )gxxxfd7*:;y, and the tip of each prong moves 1.8 mm to either side of center.nqw3 qrixz/ ) ynx fdgtxc b:)*;;7s+y 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 r83 yt + bkdsa)d(j: tdeo8wp(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 tht 8d3 8:yo bd)dt(wjr( +kpsaeere (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 to a ring that uw*avu hi qo20n+ v64xxto y9 :/hx1aacan slide without friction on a vertical pole (Fig. 11–57). Determine the wavhwuo n4 a0uy:x6q2*v+9hxvaxoi/ t1aelengths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of e jqnxminm6 -t) -h15xe4pxdj4xactly 2.000 s — each one-way swing takes 1.000 s. xthd4 15xn jenm6i4p) qmxj--
(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 os+9b qq2 q n-vu owuku4u 589+bvrmhi;lcillate 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 q bbu+i ;n+9k h9uwrq5vmvu-o8luq42 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 stretched6ul nlslp6mfg)l6*x,3;x ot w under a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at tx xs6lm6 ,lluto*png3 wl)6f;he opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spring with spring stiffnese3y jtp 9ps*:xeh(l d fe;p)t1s constant k. A pennspe1xttf (;j:dl)hy epp * 9e3y of 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 cwb kf:l;3psn 2rane cable is 22 m long and has a diameter of 6.4 mm. A breeze starfw skb:l ;n2p3ts 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 Fiqlp*6/ty(v rb 7dbk i: u)5qtjg. 11–58 (which also gives the dimensions of the block). You push it sibk7 t) ivu/j6d br(5qp:q*tlydeways 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 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