Give some examples of everyday vibrating objects. Which exhibit SHM, at leastge*+l y o4;up/e6m;jl i si /iw.dz9et approximately. *ui /tsp ol6lj9;e;/z 4+iedigyewm ?

Is the acceleration *u6h u atv4tz. r6u hca2a+ 6,iq3qyyxof a simple harmonic oscillator ever zero? If so, where?

Explain why the moti.cujcg3zw/d+ on of a piston in an automobile engine is approximately simple harmon3jz.gcwc + u/dic.

Real springs have mass)e8r*z1lb 8z0;b 0f)5 kjc yanoixzuw. Will the true period and frequency be larger or smaller than given by the equations for a mass oscillating on the end of an ideak5)i0zz8ncl x*zey0or1a 8j;u b wf)blized massless spring? Explain.

How could you double the maximum s-,7b5 ahkdq sh-; wdxmp.l(mrpeed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical s n17 n z,9e4imyn5htvypring scale, and then is released. Describe the scale reading as a function of t7,nt9n4yv5 im1y zne hime.

If a pendulum clock is accurate at sea level, will it gain or csv4iuh/wj . 4lose time when taken 4ihv/ 4wj c.suto high altitude? Why?

A tire swing hanging from a branch reaches n;wksm9g9a7+vbs z r3l7(4eimj5m / ixspdy *jearly to the ground (Fig. 11–48). How couldaj m3j+syiixz( rp45;wsm79d lme9k s7 v/*gb you estimate the height of the branch using only a stopwatch?

Why can you make water slosh back nu(i1(h fe /lwand forth in a pan only if you shake the pan at a certainwnf 1ui(e (l/h frequency?

Give several everyday exam00has1+nxlgky( b a7uples of resonance.

Is a rattle in a car ever a resonance pheuc. 7ehn i0s1mnomenon? Explain.

Is the frequency of a s6-l6ufe1u8z5v* q l;fow1le tdae: fj imple periodic wave equal to the frequency of its source? Why ofq -fu t ld6z5lfe1ja v6: o18e;we*lur why not?

Explain the difference between the speed of amb fp cr-+7sq; transverse wave traveling down a cord and the speed of a tiny piece of the c+f-qbr cp;7 msord.

Why do the strings used for the lowest-frequency notes on a pianog 0vdlxvac --xf :s/)gcat*z1.h , day normally have wire wrapped around them?:*a.yc/a ddh0t --zc f)xvas, 1lgxvg

What kind of waves do you think will travel down a horizontal metal rod if y/oo7q4+b atf you strike its end 7 o 4qab+yfto/(a) vertically from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase in temperature, but ty9 ol:keuk ou42-3yh ohe bulk modulus B y9-oyo2 lk ok3:u4hueis nearly independent of temperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water 32epkjtdpuo 3-wmc *8waves decrease in amplitude as they travel away from the source.2dcp 3op3tujw* e-8km

Two linear waves have the same am8q fbjs-qr5 -xplitude and speed, and otherwise are identical, except one has half the wave5b - xs8qjrq-flength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sections o u: ntla aqjfj1z6.1z2ol1q-wf cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocity do 1qztzlu q-161a.2wl fojaj :nchange). Explain why.

If a string is vibrating in three segments, arr vj1v fc45k8re there any places you could touch it with a knife blade without disturbingv jrf4kcv51r8 the motion?

When a standing wave exists on a stri 5iiufstl1n *o:q is0;ng, the vibrations of incident and reflected waves cancel at the nodes. Does this mean thf*ltis 0s1 qi u5i:n;oat energy was destroyed? Explain.

If we knew that energy was being xj,2*q oi0 grs*euzx;/5ohxw tso2r: transmitted from one place to another, how might we determine whether the energy was being carried by p0rx* j stx o*2i/ ,o;rh5s2zwouqg:exarticles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the total disk1yz iu 8x,.qgtance it travels in 8zqk u.ygi,x1 one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it k+)z7p5diz qi shsy87but is 85 cm long when a weight of 180 N hangs from sdi qzi5yz+)ps7 8hk7it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg c .g-thu m8onz2wua(c vm:i06k ar compress 5.0 mm when its 68-kg driver gets into the driver’s seat. If the car goes over a bump, what will be t2.nciatgu :mz mv8(wh6ko -u0he frequency of vibrations?$\approx$    Hz

  A fisherman’s scale streerj5xqn 6 1-kdtches 3.6 cm when a 2.7-kg fish hangs from it. (a) What is the spring stiffness constant en51rq 6dkjx- $\approx$    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 0.60 kg is *uv0n ybfl )7tbl)m (xhung from it. What is its frequency if only 0.m7ulvf *n x)bbyl0)(t38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. 11–2 at titi e re6,fzvo5) 6;lt; vehpj.h81f bimes t = e f;otz)61le5b h8r.ve j, pv 6tih;if0,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 h30yqmk8,j.ldu zkqg.mp( .u is caught in a spider’s web. The web vibrates predominately with a fr3qk,.u8(hk .mzlgjupm0 .q dy equency 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 spring vibrates with 8w0rtvdb.c0 g c/ ipdg*p+ um7a frequency of 0.88 Hz. When an additiona0c7wc*pbi /pgt .d 0mv+u8 grdl 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 af(v mx1 +z4(ctnx6do f spring vibrates 3.0 times per second with an amplitude of 0.13 f4zo6n(vx + m(t1xfd cm. Determine
(a) the velocity when it passes the equilibrium point,$\approx$    m/s(round to one decimal place)
(b) the velocity when it is 0.10 m from equilibrium, $\approx$ ±    m/s(round to one decimal place)
(c) the total energy of the system,$\approx$    J(round to one decimal place)
(d) the equation describing the motion of the mass, assuming that x was a maximum at x = (0.13π)cos(  πt)

  At what displacement from equilibrium is the speed of a SHO half the maximum val l0po fu4*lw-auef-*uo4lwlp a0?$\approx$    A

A mass attached to the end of a spring is stretc+edz/puqrmpo 7uh31(+ cs: zmhed 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 iz0*l s .+ncuzstretched an additional 0.130 m and released, how long .zu*lis 0+znc does it take to reach the (new) equilibrium position again?    s

  An object with mass zo+4bhm 2rd 8z3.0 kg is attached to a spring with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is moving o8+b4mz2dhz r 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 thb9ca/svoh / qpac 95.se spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With wh/hqs9ocavc9/.a s b p5at speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to one en1ftlyz (vt, clk ts8;o0s i-y:d of a spring; the other end it t;fovz-l01cly ,:ss8 iytk(s fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, the mass experiences a maximum acceleration of 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates according to th y ))i5ljf e+rjdo1c1ie equation x = 0.45cos6.4t where x is in meters and t is jlciy)5f1de)o jr i1+ 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 Sn: o.mnq/ c0 sd6 srx*t5f) u0yqm6phjHO half KE and half PEtu/s0q)0mhd:nyx6os 5nm 6*rf. jc qp ? ±    A

  If one vibration has 7.0 times the energy ovb7o zgry yd6wgbh,a s).:o(+55h rvkf a second, but their frequencies and masses are the same, what is the ratio of theyy gwz:h)oob.5gbdr,sv( h6r5v7 k+ a ir amplitudes?   

  A 2.00-kg pumpkin oscillates from a verge l vf03;eryt.0j zv6tically hanging light spring once every 0.65 svt30z0ely6ej v r.f; g.
(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 sup6 yq.i6o nxe5gported by two identical parallel vertical springs, each w yi6xo65 .gqenith spring stiffness constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38vamou 94hvr 22sin6.5t where x is in meters and t is in seconds. Determiva2 4umh2 ovr9ne
(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 S, vb1zgg:.gw guk )c,qHM, 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 (zd*q jx4y:a5 h v/lgpspring (k = 124 N/m) is struck by a hammer, which gives ag:4*d5 lphy/xq v (jzthe 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/m vibrates with an amplinzu ,cuv44vo 1tude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) with positive veloc1no 44zucvv, uity 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 stifpy:4vjlrl6r 4+m (fznfness 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 horizon0:3cyq 4t pywctal spring whose spring stiffycwp qc0y:34tness 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 ma :l2qr8q rxfk5ss 65.0 kg jumps from a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the unstretched length of the b58lkrr :2qfx qungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrat/gs zdgr )g27uions in exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simpl laix-twdl,dt: c7 q6r iqz49.e pendulum be if it is to make exactly one swing per second? (rt9zi:4 d6-q caiwqx7ll t d.,That is, one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its peri;dxbc* )q* b0:ell- vcp1qyu xod on Mars, where the acceleration of gravity is about 0.37 that on Eartx*:lc*pqv q ;bxel)y1-d u0bc h?    s

  What is the period oelifpi(h0yn4g,h .*t qf,,irhce,d( f a simple pendulum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple penduluk ae7t q(b-3vlm is 0.760 m, the pendulum bob has a mass of 365 grams, and it is released at an angle t-k veqa(3bl7of 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 ham (h:io6ku8cg o.cbh*cd9:iis a length of 0.9930 m. If the clock loses half a minute per day, how should you adjust *ud(c896ghb:oicm : ihic ko.the length of the pendulum? shortened by    mm.

Derive a formula for the maximum spe o-yoqn)31 lrf-n9bfted $v_{max}$ 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 i whjs*y5ai 9/vt is released from rea* 5vjhs/wy9i st starting 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 crestsd hg.cgok(at5md -2v 18vj sk( pass the bow of his anchored boat every 3.0 ( hsvd(.avggkm2k 851d oj-cts. He 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 *4pk154bp cxxqq,eykw18, lhcc)ub f a frequency of 262 Hz and travels with a speed of 343 m/s How far apart are the wav y ep,44qc8cbb q5flkux1 1hp,*x )kcwe crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1 qbxsmqu;e2g 0 ,a*id6600 kHz (kilohertz) and travel with a speed of q26ibm g*0x;seaq, d u$ 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 longitudinaa,puyjn.mmzky9r7d.t9 n:kyoy 25 q 9h0l d- yl 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 as d+2ae;*q6ohhc joxry;; 7fssyense as the other. In which rod will the speed of longio6;y; *qsaor+7f x h ch;jeys2tudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apart. If the tensfmq4 u15wdl sb- bro/0ui6bz3 ion in the cord bq1umd-l 5r0/ bbzi64u osfw3 is 150 N, how long will it take a pulse to travel from one support to the other?    s

  A ski gondola is conneoa2 :u-nac /fzvh.l0 w+ 6usincted to the top of a hill by a steel cable of length 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and sends a wave pulvf-/ a2uhlnw+:i u n0so6z.acse 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 shipv: .orek, n9fjiv 8j0q just below the surface of the sea. He hears the echo of the wave reflected from j:8 ojr veknfq.v0i9, 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 differ;(oy,xz:x mpkent speeds, and this difference helps in locating the earthquake “epicenter” (where the disp, kxxzm(y :;oturbance 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 surfa( q+mrl*tj8ngce wave 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 wit+r ml* j(q8gnth the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensitaup* q (jatg(o b3,buwhl00 q5+3vgsqies, and (b) the amplitudes, of an earthquake P wave passing through the Earth and detected at two points 10 km and 20 km from the sourc gqlo+g(3u *00hwaqvq5( ,bjbua s3pte?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is mea 9kmut9yekv 1)sured to be 9u e91mtkvy)k$ 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 sazwso n5b0wp-(6o0u ait s*g3eme frequency travel through the same portion of the Earth, but one is carrying twice the energy. What0 ba6o-3p0o (sw swtu5einz *g is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same frequency, but one 2wufg x cd+--9bezsz8transports three times the power of the other. What f uszxdbwze- +8-9g c2is the ratio of the amplitudes of the two waves?   

  A bug on the surface ofy6z lpk nh.c4 razz)aq a;864q a pond is observed to move up and down a total vertical distance of 6.0 cm, from thehyl8z.a arq ;a)p6644kncqzz 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 avl2n aw)c.,ee re moving toward each other. (a) Sketch the s,v ele.)wc an2hape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the 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 itsyurc+ kdz.m. ,hxri +( fundamental frequency, what are the frequenci,crxd+.h .zku (i +yrmes 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 unfihwyru1gk )k z4 23e4*hmrqif/+v2bbi ngered. At what frequency will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirdskhr u/44 q ig2i*y1fw+em2z3hvbb)rk of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequency5penvto* 5 ju4g91 h gfe)f kzt/tr1r2 of 280 Hz. Name at leastttzvh1ng 5kte5 o4/g*u91)rfrj 2fpe 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) f3f 9fkfad6s is 92m/s If the frequency of standing waves is 475 Hz, how far apart are two adjacef3)aks fdf9f 6nt nodes?   m

  If two successive overtones of a vibrat p-ql;;sgo2tfuf2 )5-qsh(ff y8d xxjing string are 280 Hz and 350 Hz, what is the fgylhq)ffj - 5;oxxus s2(fp-;t2f 8dqrequency of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. Thvjmh37 j/ zg;x9w x/kce 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 fundav7h9 xg/kzj3 x;cm/jwmental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, but it is measur;7su*vo sxitl0syl:1) wnuh/ ed to vibrate at 205 Hz. By what percent should the tension in the string be changed to clo;xs /u0v1:susi*hw y7 nl)t orrect the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibra 54 n/o j .i/swajlx,)y3hhkptte at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the stri4. k5t3jnwpsohljay,i/h )x/ ng be changed to correct the frequency? decreased by    %

  One end of a horizontal string is ai,w82 a8dde bkh 6r5anttached to a small-amplitude mechanical 60-Hz vibrator. The string’s56bakw iha2, dre8n8 d mass per unit length is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of the string may be adjusted by moving the pulley)rf4 vh2jl 4qh. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying L b4rhhfv jlq )24etween 10 cm and 1.5 m?   

  When you slosh the water back and forthn*.t zzj zd7y5 in a tub at just the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave 7 5y.zn *dzjtzin 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 stizo5;:x pd; 4,89.jb h;a folca )yswrn0 imbcrikes a boundary within the Earth between two kinds of material. If it approaches the boundary at an incident angle ofb0a yi4mb ;ohw )8i.j9,;zlr; sfdo :5apcn cx 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “shelf” where the velopw a2jd9eve cg i 28rz39e-au9city changes from 2.8 m/s to 2.1 m/s If the incident wave crests ma8pw-9ejgdr z929u ve i3ca2aeke a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air when it hits a layer of cold, dense ai*l4/)i grzne hr. If the sound wave hits the cold air interface at elh*/) 4zrgnian 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 lzt: -82y1 ehp;btplnq,wn-o between two types of rock at a l-nptwnb h2e8 qot-p;l1y,z:38 $^{\circ} $ angle. As the wave crosses the boundary, the specific gravity of the rock changes from 3.6 to 2.8. Assuming that the elastic modulus is the same for both types of rock, determine the angle of refraction.    $^{\circ} $

  A satellite dish is about 0.5 m in diametejz.o93 ao m6jpr. According to the user’s manual, the dish has to be pointed in the direction of the satellite, but an error of about 2 .mj9zoa j36po $^{\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 acrobk7 kozq xze+.)-; 5ml v+iyvme3 xbm3ss the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safet-mxilx.+3qze +37 5z);kmev my vbkb oy? (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 has a spring stiffness constant of)b*3k, woirk a 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (a) biwakr*,ok3pproximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a f*rg mr 8i vm-r6 zr8fl6qo3/jfire net 18 m below, which stretches the net 1.1 m. Assume that th*f z3rimrj /8mvf-8lqg6 r or6e 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 hanging spring. Thealrg+(e g2wj(3; lcfd mass then falls 33 cm before it stops and begins to rise. What il2j(r+ fgga(c3;l weds the frequency of the oscillation?    Hz

  A 950-kg car strikes lr:i8x ouh z8nn2(1y fa huge spring at a speed of 22 m/s (Fig. 11–54), compressing the sprinxlh z18iyr f2n 8(nou:g 5.0 m. (a) What is the spring stiffness 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 coffee (diameter 8 cm) at just the right pace of 5o mvlexes rz:uf+ 7n2)o6f m3about 1 step per second, the coffee slos+oofxmsr:v3 zl67 fe umn2 )5ehes 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 centa*ctg o ea(jc,tcs8/+er of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will* , 8cs/ajgtoe c(tac+ be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates accordis/3(; rnuc m:-o;yt lx4d cpkong to the equation x=0.650cos7.40t where x is in meters and t in seconds.m(r ;-xl 4tu ;ocyo3p dnc/k:s 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 it ru0e43;nyc1-o mjdi0xw -d a f16pvcvs frequency if it accelerates at 0.50g (a) upw 1pcd;w - j03e 4nacrmu1vid0-ofyx v6ard,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lakrrk.4st-w( jdi;)gdu e. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, .rjdrd 4g;t-( wiusk)the raft vibrates for a while.
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a musical instrument are tuned to play at 392 Hz (G) a rf-)n-pc i ryyd,;6mvso/x- gnd 440 Hz (A). v y-yn/xr 6rmf s)-o-d ,pcgi;
(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 thmj r v)sb.bjc9v7zo,gk)+2 koe stretched two-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the waveleng sor) kgkvo+j9b.m,2c b7 )zjvths 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 aetl:92 l okbn2 frequency of 264 Hz, and the tip of each prong moves 1.8 mm to eith2l:btnke9l o2 er 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 simw izb:su(0* ngple harmonic motion of frequency 1.5 cycles per second. What is the maximum amnbu *0s:zg(w iplitude with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that end yqn+d-ht1 sx5v37 r**zkd cufis attached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with one end fixed and the other f3+sh*7 dzd1u-f qcr v5tyk*nxree.

  A “seconds” pendulum has a periodo n 4gzmc23dzfrj9 e:9 of exactly 2.000 s — each one-way swing takes 1.000 s. n j4 cd2og:9f3zzerm9
(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 ix(qdi i/:+ rtstes9 3sn the vertical direction or can swing as a pendulum of small amplitude, but dqsrt3ie: s/+xti9s( not both at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontal swings, and by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

  A block with mass $M=5.0\mathrm{kg}$ rests on a frictionless table and is attached by a horizontal spring $\begin{pmatrix}k=130\mathrm{N/m}\end{pmatrix}$ to a wall. A second block, of mass $m=1.25\mathrm{kg}$ rests on top of M. The coefficient of static friction between the two blocks is 0.30. What is the maximum possible amplitude of oscillation such that m will not slip off M?    m

  A 10.0-m-long wire of mass 123 g is stretched under a tension of 255 N. A pulse wbh4m hiwm.z4 vjc7d x u/1l14is generated at one end, and 20.0 ms later a second pulse is generated at the opposite end. Where will the two pulses h7vb4mw4lud xcim1/1h.4 w z jfirst meet?    m

A block of mass M is suspended from a ceiling by a spring witfi+k z c,it24g7b6eieh spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillati6 ,eic4iz2ebgi7 +tfkons that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kgw ;5qw )iv-id*g:.stsa cp0t);yemzv car at the junkyard. The steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. What is the period os:ecz) ).;gtw w ;tv *yimadiv5 0q-spf the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. c+,mq9*x0yw vu 87obldm)s xh11–58 (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.m xyl8+m9cvwdqox0b,) sh u*7 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