Give some examples of everyday vibrating objects. Which exhibi5j0tdx)i hf9 w3a6ji nt SHM, at least approximatelx0f 6i5 hdainjw j93)ty?

Is the acceleration of a simple harmonic oscillator ever zero? If so, where?nq : ugjl29n9y

Explain why the motion of a piston in an automobile engine is at9j8z gat1aa .pproximately simplej 81g.a9 azatt harmonic.

Real springs have mass. Will the true period and frev.dif,alq2 .z quency be larger or smaller than given by the equations for a mass oscillating on the end of an idealized massless spring? qi,dvafl.2z. Explain.

How could you double4jn pxh0 0rs)j the maximum speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook l)o8 t aty1 v)-5+jd xs1llnxe th.qo7of a vertical spring scale, and then is released. Describe the scale reading as a function of to1lyn.+h)l)q58j7satxxo vt dt1e- lime.

If a pendulum clock is as 03cu a-kcv.pccurate at sea level, will it gain or lose time when taken to high altitu.c cvpks0au3-de? Why?

A tire swing hanging from a branch reaches nearly to the ground (F,2j8 86rxqbd mij3cceig. 11–48). How could you estimrbj x36ji8cm 2,de8qc ate the height of the branch using only a stopwatch?

Why can you make water slosh back and forth in a pan only if you shake the pa8 mt4y( sesze/wgq* 4hn at a certain frequency?h*/m4s tygq4z(we es 8

Give several everyday examplespure+ f5j2dcna,--zwlus + y0 of resonance.

Is a rattle in a car ever a resonance phenomlz1m,0fxn k h*gqtz /,enon? Explain.

Is the frequency of a simple periodic wave equal tx8jsw qt*) 6 h2rnzc3bo the frequency of its source? )wb h2 8t* jxqz6rcns3Why or why not?

Explain the difference between the speed of a transverse wave traveling dowb4bwuzz1 vamr(k0i7 - n a cord and the speed of a tiny piece of the corwzmb-b 1r a740vu(z kid.

Why do the strings used for the lowest-frequej.r;*u1lk r ud 4)fw5 gq-tfnrncy notes on a piano normally have wire wrapped nf;1)r jtrwk.-g dl54u*frq uaround them?

What kind of waves do you think will travel down a - apq )(tm 4zm5beqg9 .j4mnxyhorizontal metal rod if you strike its end (a) vertically from above and (b) horizontally paralleln5qp-xmb9j4 qgazm e 4(t y).m to its length?

Since the density of air decreases with an increase in temperature, bu hy4/oakryyhq 7029pft the bulk modulus B is nearly independent of temperature, how would you expect the syyqo 4ypk07h 9 rf/h2apeed of sound waves in air to vary with temperature?

Give two reasons why circular wa* bcf d:+yd,- ygscvq+ter waves decrease in amplitude as they travel away fr *yvccfqd,s y+ b+-g:dom the source.

Two linear waves have the same amplitu)k9g(v1 e2ohvqujms 6l)xw x9de and speed, and otherwise are identical, except one has half the wavelength of the other. 9e2j)x k)gxqhlv wv6(9 uo1smWhich transmits more energy? By what factor?

When a sinusoidal wave crosses the bou+6. 0l2 9dx7s3jonyh fk9vao qj:vvhtndary between two sections of cord as in Fig. 11–33, the frequency does not ch2f 0t.d3n7skvj6 hjqh+o99yv ov: lxaange (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there any places )dny*i du9i(j ue7zck6,ota) you could touch it with a kn uk)ct a6ydij79z*,eo(ni )duife blade without disturbing the motion?

When a standing wave exists on a string, the vibrations of incident and rej ghy;.badw7 .flected h7.;yd.wba jg waves cancel at the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was -ovg9yf)grk r-5sgn/3a*tl2 gybz 9d being transmitted from one place to another, how might we determine whetgsny3f trl9 a vgd)*9yog-rb-/5z gk2her the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the total diqfct,-zb u-nv. dx3,mstance it travels in one permx,-.fvu-d ,nq 3b ztciod?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it but i .pvca9b.p.lzs 85 cm long when a weight of 180 N hangs from it. What is the “c.palb z.p .v9spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress g gqbaxzxkkp+09m .3sqp2-+ b 5.0 mm when its 68-kg driver gets into the drib0+.g gqxpsa9k 2zx+p mq 3-kbver’s seat. If the car goes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stret +*vhw:bqc :acches 3.6 cm when a 2.7-kg fish hangs from it. (a) What is the spring stiffness consahcb*:cqw +:v tant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a frequency of 3.0 Hz when a mass of 0joo(sl 08 ln09ku/ev f-bmk2y.60 kg is hung from it. Whal 2kfbkyvnls-/( 8m09oju0oe t is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mj 3th96m2bnfob mc*6 tass in Fig. 11–2 at times t =*96bf3njcthtmo 62 bm 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 mb,qbr5y .6pf pe h-t/0.25 g is caught in a spider’s web. The web vibrates predominately with a frequency of 4.0 Hz/.-q 6hb5fpe,mbtp y r.
(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 freq;elw(z 2jq fzhy,/i s 2d)yrk2uency of 0.88 Hz. When an additional 680-g mass is added to mks2(d zjfz2/)i2we,hlq yr y;, the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a77z) )kv pk 75csxh4 6)mgzbfbil p)fo spring vibrates 3.0 times per second with an amplitude of 0.13 m.kgm))b)74 fs)k57zhp6bv xp7izo f lc 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 tk8m-ho 9xhwjv1+tmx 3he speed of a SHO half the maximum value?jh 9kxwvtm3xm +oh- 18$\approx$    A

A mass attached to the end of a spring r.c0ka 8 hjdr9hr1x p;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 stretcs)8c7s; )c, kjgcfj cmkz6ev :hed an additional 0.130 m and released, how long does it take to reach the (new) equilibrium position a)vg67cz ec8j km,:sfk;j s) ccgain?    s

  An object with mass 3.0 kg is attached to a spring with k ohb5adz7 66ktx f(g;spring stiffness constant k = 280 k;k7oz6tdx 5af6 (ghb N/m and is executing simple harmonic 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 compr8iqtqa--rh 7 v*pzezk) .gh+kess the spring of a toy popgun 0.200 m to “load” a 0.180-kg bal pzkz +reht-qh)vk7 ga*-iq.8l. With what speed will the ball leave the gun?    m/s

  A mass sitting on a g( xhq ij4h/,-wprp2gm3-8 hfoda4sfhorizontal, frictionless 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 released from rest with the spring compressed, the jg-q3h i(4a shff4h w 2r-8dx,go /mppmass 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 = 0.45cos6.4t where x is iq3ik rh/-u:i x mk)9lcn meters and/il hu -rkx3ki)c9:mq 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 t3p3ga5t xy5k 8tgoo ,c8:g gypqi38fihe energy of a SHO half KE and half PE?c8y ,85g 33p yfot qx8ikgo3gp g:a5ti ±    A

  If one vibration has 7.0 times the energy of a second, but their fkjny 50l,p* rd(d e9rxrequencies and masses are the samerpledrx5d9 jy ,0*n k(, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging liu*im, xbqm kqf:y/(1p ght spring once every 0.65 sufmm,i/xkb( *1q: pyq.
(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 parallelbhsjpg- tf0p*fh5v h44q/w:i vertical springs, each with spring stiffw ht fjibghpvsq-5f4/0h4*:p ness constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equ nlrs-t;)23jf8bp gojation x = 0.38sin6.5t where x is in meters and t is in seconds. Determin jg bj 3s8l-ton;p2rf)e
(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 exampl3nswxu fp3c2bahk9;-oi q 1, zoouo2/ es of 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 horizonrlai ibcj f:863ib0x 8tal spring (k = 124 N/m) is struck by a hammer, which gives tbjrx883i c:a0biil f6he 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 stiffness constant 305 N/m6ssf.r4rqbtq- km5d. vibrates with an amplitude of 28.0 cm when 0.260 kg ha.t qs kqbrsf6-5. m4rdngs 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 springqctf-ki 1w/z mix2-be82 u7mv,wn gh.s, 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 attacheft ;eys6(mlm;y5 vv.wd to a fixed horizontal spring whose spring stiffness constant is e;sml.vw(m yfy; 5t6v $ 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 6lc,2 x wf( l3s9 jp,rqk90cnwi5.0 kg jumps from a high bridge. After reaching his lowessfx, l9i2ww3 09(nc kc,pqljrt 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 exn.* c*de/p 5/hody qpemqas :8actly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly oned8aju i;ts9az )b3.k (ax.scx swing per second? (That is, one complete vibration tk)s8axdca3a;s ( xz.itju. 9bakes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on Mars, where 01f *khsx4 a9zl6v rczthe acceleration of gravity is about 0.37 that on Earth? f6sv1*0ar zk 4lxhz9c    s

  What is the period of a simple pendulum 80 cm long c ,.5gml)c vyk
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulumq n: u5+k0aja)xry p0t is 0.760 m, the pendulum bob has a mass of 365 grams, and it is released at an angle of 12.0 yu)0axjptq5 :an+rk 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 c5 0cn9 ;4+e:c8qclasj nw neevlock loses half a minute per day, how should you adjust the length of the p09en +wc48 je;ev nl5c qcans:endulum? shortened by    mm.

Derive a formula for the maximum e-1 o0 fub 28u,-xqb(hehcgbxspeed $v_{max}$ 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. Atys 493 cuo7zjib(lw, p it is released from rest start4jc( p3lsuw7 y,o biz9ing 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 anchore.q5hc supz,xjkz-f :- d boat every 3.0 s. He measures the distance h5x -,-q ups.czz jk:fbetween 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 withwi391eq o5yag a speed of 343 m/s How far apart are the wave crests (comp1i9oe a yg5q3wressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and kqd4 dk,ido3t6qvb5 fibc:7 01600 kHz (kilohertz) and travel with a speed of:b7,kkbdcdvi5qo3 60if dq4 t $ 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 em2*q z q*x8vvof longitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one is twice av -9mmoz6 cusw2 oz0,ks dense as the other. In which roduoz-zm9kc ,sv 06w2om will the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between r1i) 0l, utwvah9w ye)af86zctwo 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 othe9it0u86aw h1,c fvwe za)l)ryr?    s

  A ski gondola is connected to the top of a hill by a steel cable of length 620 p :r (,)db;9hggj o j,:qkttdrm 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 ojtrbpj g,(t,; gk 9)rdhq:d: is observed that it took 16 s for the pulse to return.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

  A sailor strikes the side of his ship just below the surface of the sea.jfqksa4a.81 sp * 2qhmzt0 -vb He hears the echo of the wave reflected from the oceanm q4qj th2*v.1bsf z8aap0 sk- 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 speetex m;(q.zbi7 ax2iq19 k* zkfds, and this difference helps in locating the earthquake “epicenter” (where the 1 fx 2q(z* 7atieq;9z .kkxmibdisturbance 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 bq nv7n)- nu:vzc72zb xy a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical 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 aunz b z)x:v-n2qn7 vc7cceleration a>g]    m

  What is the ratio of (a) the intensitiexxpjer30 0bvou-s,/ s k9hx -lxo u;+es, and (b) the amplitudes, of an earthquake P wave passing through the Ebrxu- -vx30kuxjs;s+hex, e p9 0o/olarth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wavlcfek34 n9va (e passing through the Earth is measured to be 3 fc a(e9ln4vk$ 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 fre3 fu*uy/;ugrtquency travel through the same portion of the Earth, but one is carrying twice the energy. What is/r *uutg;yuf 3 the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same ydxgk l4 k2b8+frequency, but one transports three times the power of the other. What is the ratio of the amplitudes of the two wy8 x gb4k2lkd+aves?   

  A bug on the surface of a pond is observed to move uzc7n0 ss79c7wpjq:te p and down a total vertical distanceesj7 0q7cnt7:9 wzcps 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 KE change?   

The two pulses shown in Fig. 11–52 are moving toward each other. (a) 3u/bwrez5,v 9t qq0lo qo (l.lSketch 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. 11–36owzq3, l(/l.be9 t qr0ovl5qua, 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 67 j0p + gt61hnqstduzm 5lk3has its fundamental frequency, what are the frequencies of the firsthlq hktt6p7 +n15u6jg 0zd3sm four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz whe n1z0p3 vv7)eg;ad 1 -e1pgz7q3gdy( vdlhu sdn unfingered. At what frequency will it vib1 pdd ;v37hde a0vgs g1vyen p-z(q3dg)1u 7zlrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string rek5 ,4kf vh/ aby1o5v3r3 by9b ag;kgydsonates in four loops at a frequency of 280 Hz. Name at least three other frequencies at which it wiao;a4g /kbvgdv 1b9 5 f3,yb3yk 5khryll resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s-z fslwcm1y/1; rw el/kx, -fx If the frequency of standing waves is 475 Hz, /c-xw/ ,fsewf1ml l 1-;ry kxzhow far apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280x t4rmzazf4zns8xxtbza *g5/-.6 (fy Hz and 350 Hz, what is the frequency of the fundamenz/tmf 6x a saz *-ygb5zzf4x8r x4t.n(tal?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distance fxgui)(vn asq78w- qo4rom 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 ove ag(s7unx )vo-q q4wi8rtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, but it isd:iu9yzsx)m lgr -0/ m measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?So the three frequencies are, zs-0lgr/y9ud:mm)i x    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vxy l bu*lqrh(rhi6pcd 73 5,d7ibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what pe7ir(7p 6*hxhdrlu5d 3bl, y cqrcent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontaljh2 j 1ks:iiow(b*fc0 string is attached to a small-amplitude mechanical 60-Hz vibrator. The string’s mass per unit le0:oi(sc k 2 ijhf*1bjwngth 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 r6 ef6eed 6rx:moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying L between 10 cm d6re :eerf6x 6and 1.5 m?   

  When you slosh the water back and forth in a tub at just thunk*m* :f gixvu2 fu79.3g wcge 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 the watg2f*u*cux3 f 7. g9kiuvmwgn :er wave?    m/s

  An earthquake P wave travel--v brkbr7) d-,nrq/pgiytz , ing at k.0 km/s strikes a boundary within the Earth between two kinds of material. If it approaches the boundary at an incident angle of 4gdkbp rbr,/v7inyr-) -ztq,-7 $^{\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 vel;2+:vlyxqg4xw bpjd e -(fra :nbav* /ocity changes from 2.8 m/s to 2.1 m/s If the incident wave crests make +* :q/ dl vjpbb4:we;xaa( -gyx2vnrfa 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in nyo4yj0* +xed u(dxr1 warm air when it hits a layer of cold, dense air. If the sound wave hits the cold air i+j4*x x1uy(ynr0eo ddnterface 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 bei1 21 -hmx-,z -vvcku-wbep gj8ppfntk:( i0utween two types of rock at ap-b tuf0mv- inwg , (hpkuvj 21-:x8pez cki-1 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 a5,es)fuq ifst-8v-9 jf ips 2ovx)c/g 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 /fq) tf pjvui),s9vg o5xci28-s fe-sof 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 Pacxv;2pb so()jjy io x**ific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of svobpxxij)(*;* o y2j them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness constant of 550 kN/m Findq*ol zf +5gv;l the maximum compression of the bumper if the car, with ;*fv+5l ogl qzmass 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 fir) , ry7 xk:c6.zlbsuhpe net 18 m below, which stretches the necx.7 6,shl bk:zpyru)t 1.1 m. Assume that the net behaves like 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 h 37y) wc,jvta22f myxtanging spring. The mass then falls 33 cm before it stops and begins to risevc2mfayt72 yjx,)3tw . What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 11–54), comabuwe cfijld6jv+ w:j6 .9(4 upressing the spring 5.0 m. (a) What is the spring stiff9 wjj (ewvuf aj:bc6u6.d +4liness constant of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of co3jze ( )*6y kv1tqzukoffee (diameter 8 cm) at just the right pace of about 1 step p y3e1ztov (qk6u kzj)*er 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 a 33-rpm phonograag+ibvy3 ,geptm7 txp6 v81k(ph record e6a k(tpmyv ipxt1g bv8,3+g7have a wavelength of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibratesy . 6 h9tmgu1(nddrf+l according to the equation x=0.650cos7.40t where x is in meters and t in se(.1 yhg ml6+dftn9u drconds. 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 irpt :c* cfz7 4dd,4gupf it accel gdd 474*cpf zrtpc:u,erates at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floa rn*a,x0- ; tjybe)jhlts on a lake. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the wate;0yt,lx- )najbrh*je r. 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 musicaw6qsz2-s6 dgj l instrument are tuned to play at 392 Hz (G) and 440 Hz (A2 6jw qsgs-6zd).
(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 the6jjts* m;fb8 e stretched two-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the; e6fms8bj* jt 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 freque(srb+u8i cd :uv;nhwj2s7 y0i ncy of 264 Hz, and the tip of each prong moves 1.8 mm to either side of centey wu0ncri7j+(2h8sub ;:ds vir. 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 harmon*w c) ekrd.6ct4f+(g bo jq7stviq: 4yic motion of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact wito( jgywq :v*eitf ctr+s .6bq 7c)d44kh the board during the oscillation?

A string can have a “free” end if u4hulf 8s b)6tthat end is attached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the uth86) l4fsb uwavelengths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — hmw b0r9n7snh: 1pgfolp3;i0 each one-way swing takes 1.000 f10 grm0nhh7i:os 3blp pwn9;s.
(a) What is the length of a seconds pendulum in Austin, Texas, where $g=9.793\mathrm{m/s}^{2}$    m
(b) If the pendulum is moved to Paris, where $g=9.809\mathrm{m/s}^{2}$ by how many millimeters must we lengthen the pendulum?    mm
(c) What would be the length of a seconds pendulum on the Moon, where $g=1.62\mathrm{m/s}^{2}$    m

A mass hanging from a spring can oscillate in the ver0:o1vp6 zg qi i p6tdxz1pzb/.tical direction or can swing as a pendulum of small 0z :z tqp11bivgdp6i p6.zo x/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: 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 stretchc)t sj;o5)fvbssl( pi9w q+l 3ed under a tension of 255 N. A pulse is generatvcps3j) +fls;)b (o5iws9q l ted at one end, and 20.0 ms later a second pulse is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is st.4jj/ 6mh cetuspended from a ceiling by a spring with spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscjec m /4tjt6.hillations 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 junkya cqu2d vpzt yr;6kr3,2rd. The steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the endv,6r2 cz qyu3; pdtr2k of the cable. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (which also givesiojqi;0uqr:. o e:5.wl l4hxl1mue u - 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 u eojqwlo15q.rl-;0x hemi::uuil.4of 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