Give some examples of everyday vibrating objects. Which exhibit S4v5dp-kf f 8offds(8 q7q4 wepHM, at least approximatelyfdsf784pe-k4ffqpd8o5 q v( w?

Is the acceleration of a simple harmonic oscillator ever i:3 h .6a b(r(*xdjn-gnu.xavratc6 nzero? If so, where?

Explain why the motion of a piston in an automobile engine iu/p; k1uq;u. wz; tiwkxxjs9z;h m1z*s approximately simpl/u zk ;utwx; uswhmj9z pq* zikx;1.1;e harmonic.

Real springs have mass. W cz45y)3ly 9prbyu)at ill the true period and frequency be larger or smaller than given by the equations for a mass oscillating on the end of an idealized massless spring5y3t))uz ayr b yp9c4l? Explain.

How could you double the maximum71i :a/iqjgd u speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scale, acc9kfj( (.s tknd then is released. Describe the scale reading as a functict9j( k.fck s(on of time.

If a pendulum clock is accurate at sea/d55 vym*suzt level, will it gain or lose time when taken to /s5 y*m5z vduthigh altitude? Why?

A tire swing hanging from a branch reaches nearly to,m 4wh+y:1wd m hd7pwx .qrm3k the ground (Fig. 11–48). How could you estimate the height of the branc:+ mh31.md,wh7rkdpm wy 4xqwh using only a stopwatch?

Why can you make water slosh back and forthr3fvq(jw u:s5f.kjun su. 1 n8 in a pan only if you shake the pan at.kf5 : 8jwvunfr sj1 qs3.uu(n a certain frequency?

Give several everyday examples of resonank 2zx1ugv7f:t7gj7+ l qh.loice.

Is a rattle in a car ever a resonance phenome6htp wmsv dmk8t-7 k--non? Explain.

Is the frequency of a simple periodic wave equal to the frequency of itsi6 ( zx wpnimrmd7; ;y4h8ja*e source? Why or w7wihz(m;;inr* ame j 64 8dxyphy not?

Explain the difference bnf42mbp r*. k3nrbfdg5ix0 1x99 vo ebetween the speed of a transverse wave traveling down a cord and the speed of a tin0 erkbfd.if5g*9rvxn 12opm3 nbb9x 4 y piece of the cord.

Why do the strings used for zu ;/jm(8gp,pksq a6athe lowest-frequency notes on a piano normally have wire wrapped around themuzmq,a6k;ppg/( ja 8s?

What kind of waves do you think will travel down a ho6y3(ud(cz (q.+sq/i qn yozd srizontal metal rod if you strike its end (a) vertically from above and (b) horizontally parallel td + 3y.(sn6qszi zcq(qo (uyd/o its length?

Since the density of aiishs(a8hpr4 i+p,+ i*nz7wd ir decreases with an increase in temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the speeda+sip*8(r hi4nwp+s,d 7i hiz of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrz /-zhcr rv.a611bm sfease in amplitude as they travel away from-z s / fcazb.r1r1hvm6 the source.

Two linear waves have the same amplitude anolny+* 0ax(bxd speed, and otherwise are identical, exc+a (x0*ybnol xept one has half the wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses tu9h mq-wa,m 9lhe boundary between two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocity do change). Explain why.m-mwu9hq,la 9

If a string is vibrating in three segments, are there any places you cou7mn:osy,ysvx5ie k 4z1. u-* ijau0v tld touch it with a knife blade without distu4yn,5sia0 7i sxt -1vy.e*kmouvj z:urbing the motion?

When a standing wave exists jx988yqznst-on a string, the vibrations of incident and reflected waves cancel at the nodes. Does this mean thytxzj n9sq 88-at energy was destroyed? Explain.

If we knew that energy was being transmittedv)la7 - kng,an from one place to another, how might we determine whether the energy was being carried by n)v 7alkn,a-gparticles (material bodies) or by waves?

  If a particle undergoes SHM with amp p2yflao,x6)b 4r2ts mlitude 0.18 m, what is the total distance it travels a fbx462pl),2mr otsy in one period?    m

  An elastic cord is 65 cm long when a weight of 7 - (:vl,; d)l 2nwzkh1ywgftjf5 N hangs from it but is 85 cm long when a weight of 180 N hangs fromz flwn1ghdw:lk)-; 2(f,tvyj it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car comw *mqs j68sq)fpress 5.0 mm when its 68-kg driver gets into the driver’s seat. If the car goes over a bump, what wiw)q*m6 jfqs8 sll be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs from itrsds56 ,mtd 9315ncoxa q tg-g. (a) What is sog t -6qact5dd5 mn,9r31 sgxthe spring stiffness 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 :yv2oay62sqow,p 1 uvfrequency of 3.0 Hz when a mass of 0.60 kg is hung from it. uvyw26yqo sovp:a, 12What is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of tf,i+f0/3 v)p-t o)qdyd kbvlehe mass in Fig. 11–2 at times t d y qfe,l)f +t3dpiv)o/ b0-vk= 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 vibr8 ,n.ae:/w m qb ,*cucsy buidx.+nyy;ates predominately with n amnuisx*. yby/c;w.e,y d8c+ub:q , a frequency of 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 sprin :adt2n pvj2vb7f 61xig vibrates with a frequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 Hz. What is t vbxa vd ijtpnf671:22he value of m?    kg

  A 0.60-kg mass at the end of a spring vi6u c5tssgwm3. brates 3.0 times per second with an amplitudeu.s5mscwg6 t3 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 from equilibriu6 w.c8f8orsr,tb xkc 8m is the speed of a SHO half the maximum valxbo .wr8,ft8s6 c8krcue?$\approx$    A

A mass attached to the end f(utbj g37+7kz yq ed4of a spring is stretched a distance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretches a vertical spring 0. gn+ :4cc-75ogjexksk315 m. If the spring is stretched an additi57ex: -gc nk+ck4 ojgsonal 0.130 m and released, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is at+ufmsqc5 7eqs3g )t3w tached to a spring with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 u)sf 3g 53t7+wsecqmq 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 to5mekncv hqzo3 -3f 94n compress the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will the ball nq-hem94 zcfvo3 k3n5 leave the gun?    m/s

  A mass sitting on a horizontal, frictionlelepej-5 k s,4yss 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 mass s,lye54j-pke 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 whereba( /gjykt 5:lb4zr gq 7df;/z x is in meters and t is in secondsagjlz f;rz/kt7 4gdq/5b(: by. 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 half PEkghh7 god9 j:6t kmxw/a.jmnmt941d1g kkjt:da.x6g9hh71d oj m/t 4n1 9mwm? ±    A

  If one vibration has 7.0 times the energy of a second, but their frequerdrlcrwq+(ln;2k ,w , ncies and masses are the same, w;2 (wcl rw,nldr, q+rkhat is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillat9r3j89y8yd rb i4g+v2/nzk uw7y kjktes from a vertically hanging light spring once every 0.6j8ry2rn 4j /i+wkk butyz8gv9d73 9ky5 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 supc iug28r0inbpvmp67* ported by two identical parallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What will be 0 *m8prc2bgpnui76i vthe frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0 hysar . nymu/s-y: )n*5p5+vpx qy0dw.38sin6.5t where x is in meters and t iryywqv: phd0/n* nps ).5xyu- 5a+y mss in seconds. Determine
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows two examples of SHM, labeled A and B. For ea jno:b*voakq;(m5gm : ch, 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 ontv tra4)/- q6h f mxon)v/:8 yaq4apzv the end of a horizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial speedvzroa8taq f / /4vt) ayvhn6x)q:p4-m 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 se;mck5et: (wp; 2g.lk ,obt xhm+m;we8gs a7lpring stiffness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) with positive velocity :mw m h.g ,(t;mk5o8gx;ap wb llc+kte2e;es 7at
(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, y(z zsy v vlkk)5ks,rj.*j2 -lwith 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 eb7kvp/b p ,u0a 0.600-kg block attached to a fixed horizontal spring whose spring stiffne 0/ vpb7kubep,ss 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 jum/r6)* jotklmzar t;kk. bn/n3ps from a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes tkzntrt/lrn)jok3*.b/ m ka 6 ;o 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 vibrad vk+2zc, sndy0 o*u9wtions in exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly one swing per secondi 8exsrqfspr(:2jz,,? (That is, one complete vibration takes exactly 2.0i,q2:( xf,sejz 8sprr s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period onyp5d2abwc twb,l*zm 4c;h8 o, Mars, where the acceleration of gravity is about 0.37 that on Earth?; cl2p5 8ohc d4bbaw*tyw,zm ,    s

  What is the period of a simple pviu3hgymwmlp, ( (pfh-oi-,pf yz-+ * endulum 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 pendu;f18ey: 3 02 ztoknth;excrb zlum bob has a mass of 365 grams, and it is released at an angle 8nfzhy0zx ck1;:tt o2re; b e3of 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 wva.bn+w r 6c0the clock loses half a minutr+ vab60 wn.wce per day, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for thipcz307:nqwv0lf h: s:jx/use maximum speed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at a frequency of 2.5 Hz. At it is rele lxex )9s(lf6cased from rest starting at an angl(9 ecllxs6 )fxe 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 wavej3,z;r f 6ywtw crests pass the bow of his anchored boat every 3.0 s. He measures the distance between two crests to be 6.5w r;,j6zf 3tyw m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with a speed of 343 m/mc b h+k)cq4b::/jpt*+i vuwfs How far apart are the wave crests (coft)vbipw /b*:4h+ jcc+q:mku mpressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (kilohx i/i4-1mnv7(i 4dewt v(fx ppertz) and travel w mi4i/f(iv-nxwet p vd1(x4p7ith a speed of $ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

  Calculate the speed of longitudinal wavestex8 5x2wxq;9s3awy e in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic*. e rcq7-piz1dv-q0 yllkho8 modulus, but one is twice as dense as the other. In which rod will the speed of longitudinale-q*r7 8c dqk0.v o 1yp-lhzli waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched 1.u0j isw0wbsbetween 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 th i0 bsuwj1w0s.e other?    s

  A ski gondola is connected tgoqfuk v)685 kf.mm b0o the top of a hill by a steel cable of length 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and sends a wave pulse along the cable. It is observed that it took 16 s for t6ku.b05 qf vmg)fko8 mhe 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 hikgye/k0s i/c/d9z ni 4s ship just below the surface of the sea. He hears the 0 yekks/ind4/zig/9c echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at different speeds, and t(+do2) h xnb1bowvp p)6c)l vmhis difference helps in locati(v) )c2 ml 1bpwbvnho6+dpx)ong 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 o 6qtz4p5(so 9 aat-rwwave can be approximated by 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 acceleration sor4t6 wq z5a -ao(t9pa>g]    m

  What is the ratio of (a) the intensities, and (b) the amplitudes;/nzspv uqrt0pi:i+mtwf. 81 , of an earthquake P wave passing through the Earth and detected at two points 10 km and 20 km from the source?(astr+uwim fq zp:;tv0 p ./i18n)    (b)   

  The intensity of an earthquake wave passing through the Earth is measured to beov. d u*:tei/+gwjn*y .gi+y/v *: t wu*odejn$ 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 z+a agq0z9f-ils 54arf the Earth, buarg -sa5z4f9 qa+0izlt one is carrying twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the srhux7wdb :fzk0k1kky8 82 / e04u ollpame frequency, but one transports three times the powe7u0pkwuk1 : /8 20yodfkz8 eklx4 lhrbr of the other. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of aqmu .t7q7b43vgkr- aw pond is observed 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 the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KEum7qbk7av-w4 3 qtr.g change?   

The two pulses shown in Fig. 12/fag2rof jk 81–52 are moving toward each other. (a) Sketch the shape of the string at thk/ja2gfrof8 2 e moment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundamental frequencyv;0qjx97nbw l , what are the frequ9xnj07 wv ;blqencies of the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when uinus:0yc i*d8nfingered. At what frequency will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-th*80u cds n:yiiirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequency of 280 Hz. Name 62wb dn0ya3b /1ae ji0g)b ud*g7tqbgat least three other frequencies at which it will resonate. )qa60bj bbd2ywd geg3t nig/a0 *b71u $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the fr- me*ki+tgp 5zit -:lvequency of standing waves is 475 Hz, how far apart are two adjgmk +5p-:zi ettl-i v*acent nodes?   m

  If two successive ovegk 4.hmv( ukt2rtones of a vibrating string are 280 Hz and 350 Hz, what is the frequen.h2v tmk gu4k(cy of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 m*/ wbbpb2*oc:vz9qu g. The distance from the bridge to the support post is L = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundamental and first two ov / :z2 w*qu9p*bbmovbcertones?    Hz

  A particular guitar string 5)dq6n1i wb+uht - wbiis supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. u )+w-bin6i15q bhdtwBy 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 measujr.nj-d +vy,rred to vibrate at 205 Hz. By what percent should the ten-y+j.r r ndvj,sion in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal strn,ytuv3: 7wgmn.ykmamge-) 3ing is attached to a small-amplitude mechanical 60-Hz vibrator. The stringmunye3nkgyg.,)a-v tm3m7 :w’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 d6k-/d ktwc8 tyo:/8 o;ki r2pybdan;moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standinn;;di-t /b/pck 8ddo rkyw:yko68at2 g 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 .)x zn9)jcwe eat just the right frequency, the water alternately rises and falls at each end, remaiwz )c)e9 .ejnxning 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 water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundary within tp d8fljhk9,y1uy;dwh y5 63as 4 yva*uhe Earth betay1vy, addy43l;k*spu 9 hjwyuf6 h58ween two kinds of material. If it approaches the boundary at an incident angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “shelf” where,0w29 3af qwsc+ae, quuwu/t1bg oqxgxv041u the velocity changes from 2.8 m/s to 2.1 m/s If the incident wave crestsqva0sxfuq0/,o+12au4tw, gu 9w 1wbc e gxq3u make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air when it hits a layer8c 1we:ffjoy5 of cold, dense air. If the sound wave hy8fc5fowej: 1 its 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 earthquakd./uun)xgl9;i 7 lzjse wave strikes a boundary between two types of rock at a 37u zsxg.jud i)l;l9n/8 $^{\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’sbqv8j a6t 6w 8581 ktxh0e )qtk7ibqba manual, the dish has to be pointed in the direction of the satellite, buaxbqht0w1)qat8ebt q 8jb 7k65k68i vt an error of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 250 km and velocity 750 km/h travels across the Pcn.tpom4v3oe c9o )w 3(vq(zu acific 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 )m9334 np e(.ou ovcq(cowvz tabsence 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 4g l (i5 i2vvegep30g-io9sxy)6 whfihas 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 w3g-hy25p9ov i(v6 )iie glefwi4s0xgall 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 bel6fby.tct)wc y ( i :acd91col5ow, which stretches the net 1.1 m. Assume that the net behaves lik1(odc. w:fc )aty 9ctyil65cbe 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 62sb;pf bzqa:on the end of a freely hanging spring. The mass then falls 33 cm before it stops and begins to rise. What iqa2ps :6;bbfzs the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a -he/sei9xb p8vhab/0qh x e- 7speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffness constant of the spring?x8ibehh p79ax0 eqh/v-/b- se    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 cofftvf(15d6x (yi7 eycem0u,hl zee (diameter 8 cm) at just the right pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). me (d5,h(uyvy e7x 6c1tfzl0iEstimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm f+(r7 8yw :qt5loeg hhmrom the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequency of the sound emitted?e5tmhy(7o+ l gh:8wq r    Hz

  A 2.00-kg mass vibrates acco.t 6ew* i+pfkkrding to the equation x=0.650cos7.40t where x is in met p.ie* kf+k6wters 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 ib*;s yzw;yt5u kb8a)a s its frequency if it accelyw ;tkb8)y;5ua a*sbz erates at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on ap;vl86 xlj8kp lake. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the 8 ;p8pv klxl6jwater. 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 instruc 3 axgyr w6r7 l8w7.4cc8muqmment are tuned to play at 392 Hz (G) and 440 Hz (A) 684wwxa .c 7cmymcr3urg8l7q.
(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-pa 7 f;krcqdao1,rt cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength1afk;r 7, cdqo greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the tip of eachm(m-rnsayr 7s9n3 6ix prong moves 1.8 mm to e7 rsmm3 ni6r( s9x-yanither 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 mo1 0fqraz(7tvk2( bhhj / r-kdwfs56mltion 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 con l/w52ks-b(0k1avfhrdj6 (hqrftzm 7 tact with the board during the oscillation?

A string can have a “freeg n0b wf7r8ma1b::w lf” end if that end is attached to a ring that can slide without friction on a vertical pole (Fig.g1:w8b:an mblf0 frw7 11–57). Determine the wavelengths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each one-way swinh,g:3cvp,q lc)uxs:c2rdj+u-h o l a (g takes 1.000 : ,r,)ahol(c 2+3cdxqv -ugpcu:l j shs.
(a) What is the length of a seconds pendulum in Austin, Texas, where $g=9.793\mathrm{m/s}^{2}$    m
(b) If the pendulum is moved to Paris, where $g=9.809\mathrm{m/s}^{2}$ by how many millimeters must we lengthen the pendulum?    mm
(c) What would be the length of a seconds pendulum on the Moon, where $g=1.62\mathrm{m/s}^{2}$    m

A mass hanging from a spring can oscillate in the vertical direction or can swin t+ y94yvqy428 vuz pz(g szzg9fq5reosp9o2.g 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 peri+yug 9qr 5sy8o et99 zov 24yz.s(z2v4zpq pgfod 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 gd;-/e 0i +jdh( csdu 8qg+vmab is stretched under a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at the opposite (b/;ug0+8ed svdda+ mci-jhqend. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spring with spring sx.u h2 pnvgfly326q8ctiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillations x qfv6y8u.gp 23lc 2nhthat 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 stee ;/z:-ppik hkyl crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car i;p:-khpkyz/ 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 5 m4va+( 0 krwzx)1 c-pxcvgwxa plate as shown in Fig. 11–58 (which also gives the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this vibration, given that the x0g )vrv +xkwmcx-pa 51cz(4wshear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz