Give some examples of everyday vibrating objects. Which exhibit SHM,oa1nl3f)y )z;gz vl18f7q lio at least appro za 18ilzg);l fvf73)oyn lq1oximately?

Is the acceleration of a simple harmonic oscdtc0 u+3o;vwo pa0wgq d +,;gxillator ever zero? If so, where?

Explain why the motion of a pisfunnw 1+4yy9s4dll+359 a oct :i siwoton in an automobile engine is approximately simple harmon: d 3aof+9o iw scyw9y14+sluinn l4t5ic.

Real springs have mass. Will the cznc(k c2,i da c7xt.tjfi0:r xj)6x 3true period and frequency be larger or smaller than given by the equca 7jk,i6 3x)xcxd2inc ttjzr 0c.f:(ations for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maxim. ,r fcjzris-5um speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook ofn+yf 7fwui .x( a vertical spring scale, and then is released. Describe the scale reading as a function of time (yfu+ 7fwi.xn.

If a pendulum clock is acheuf )n1h4xb w;u5s 3obya2)k curate at sea level, will it gain or lose time when taken to high altituan ;)sf4 k )o3u2w1ue5 bybhhxde? Why?

A tire swing hanging from a branch reaches nedm/ qv7pqsf6n4k5 ::oht y)zparly to the ground (Fig. 11–48). How could you estimate the height of the branch using only a stopwatch?: p k dqp76mvq/ )f:o4zysnt5h

Why can you make water sloshfy0zj/18ad jri/aiar4)m 4at back and forth in a pan only if you shake the pan at a certain dz)1tm/ji48jar0 raa f ayi/4frequency?

Give several everyday examples of resoi/,4dh9z w yrr 10gclqnance.

Is a rattle in a car ever a re zo+7j;4 axzgd)bh f)lsonance phenomenon? Explain.

Is the frequency of a simple periodic wave equal to the frequency of its sourceadps )3nmw .9wjg l1,q? Whdq p j 3a9n1wg)ls,mw.y or why not?

Explain the difference between the speed of a,kj5p3e7 .xgfim s mzfp .y36b transverse wave traveling down a cord and the speedgz 3fp 5jb7 ,6fk3syem. p.mix of a tiny piece of the cord.

Why do the strings used for the lowest-frequency notes on a piawe430phmp z+ f 2w8vxkno normally have wireh8zpvepm0x3+fw42 k w wrapped around them?

What kind of waves do you think will travel down a hor:r:9smxnbg(mo0gp d)izontal metal rod if you strike its end (a) vertically from above and (b) horizontally parallel to its g )0:ngm( psd9xo: rbmlength?

Since the density of air decreases with an increase -nn ea0hjez.s0i(7cn-h sv 6dpmk( (qin temperature, but the bulk modulus B is nearly independent of temperature, how v0eqzjh s nnns( hpc.(kmi0 -a(67d e-would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in amplitude as o xw8eqs// 3k5ocwaecvj5h, (z+0h0 be:f sqbthey travel away from t/w:o,h ae3+0( /e 58hsejbwfzv x0sqc5cqk bohe source.

Two linear waves have the same amplitude and speed, and otherwise a f 9nenfv:,l(ere identical, excepn9 f(vf el,n:et one has half the wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sections of corjb1wgxikx*8-;f8w8 i+xq ofdd as in Fig. 11–33, the frequency does not change (although the wavelength and velocity do chandgfk x;f8*8 q-xo8xi b w1w+ijge). Explain why.

If a string is vibrating in three segments,* qu9). jd r46pyyzckg are there any places you could touch it with a knife blade without disturbing the motcu9k pj.g ydy6q4r) *zion?

When a standing wave exists o zhx3rxi(b)0: loz6vdn a string, the vibrations of incident and reflected waves cancel at the nodes. Does thisolri z vz3:xdx(0b )h6 mean that energy was destroyed? Explain.

If we knew that energy was being transmitted fr- ;cal m51c51 re)ryp wpk.mulom one place to another, how might we determine whether the energy was being carried by particles (matm 1)5klm1pl5 ;pyr-rau .cwecerial bodies) or by waves?

  If a particle undergoes SHM with auw+zt aw5k syi6j505tmplitude 0.18 m, what is the total distance it travel+ak0wyjz 5wis5t6 t5us in one period?    m

  An elastic cord is 65 cm long when a weight of 7:o 7 9lu8vlsci5 N hangs from it but is 85 cm long when a weight of 180voic87 l9lsu: N hangs from it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg drive3kfq6 q0 t)6jjg7hi tvr gets into the driver’s seat. If the car goes over a bump, what will be the frequency06f36)i tgkth7qqjj v of vibrations?$\approx$    Hz

  A fisherman’s scale stretches1hj3e05br7/;o +vvzo* t-vpak a nd(x vryj.y 3.6 cm when a 2.7-kg fish hangs from it. (a) What x+orvhv;- 3/ ea7.nzyj o v5 kyr dat*b1p(0vjis the 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 vibrapkntpg 86s,c) tes with a frequency of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency if only 0.38pg) sn,8kcpt 6 kg hangs from it?    Hz

Construct a Table indicating the position x of thr4icd/e5lp m5 e mass in Fig. 11–2 at times t = 0dec /45ipm lr5,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 caug o5kcm)y j.7w4sp uud 2f;f6izht in a spider’s web. The web vibrates predominately with a frequenc;65mkwzy 7 d u)i ou.fcpj4sf2y 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 a frequm j:c5oye l0/s+w x)oaency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is 0j +x/moec 5oay l:)s0w.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per secon5 +et(jw*zuem2h*9syv2kzk+ : jjtgr d with an amplitude of 0.13k*j9tz* gthrk22 mj:ewyj ( v++ ze5us 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 equilili/ro2 arz zx( v7pk4ka4+e( 4kaotl +brium is the speed of a SHO half the maximum valur +4+a p244r7a(evltao/lkoi(zkk zxe?$\approx$    A

A mass attached to t m42arkua 61irhe end of 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 1eqs;jtcintj/tjm w1+j.1:y spring 0.315 m. If the spring is stretched an additional 0.130 m and released, how long does it take to reach the (new) eq1/ijjs tt ywm1c:q;j n1j +t.euilibrium position again?    s

  An object with mass 3.0 kg i/(4 vs*ku(ul .j :0bein5whu wlnr0zms 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 wui w k4:vw r.sz(jl00uunen /*(bh5mlith 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 ii:t/tq3ykgl;dnk ;6 h1 om3zthe spring of a toy popgun 0.200 m to “load”16t:imh3 n3dlk;qy /;kztio g a 0.180-kg ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached ta;pavp(h*srk6 9;+*eyqryd mo 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 rd6vayr 9q; she;k(ym*+ra p*p est with the spring compressed, the mass experiences a maximum acceleration of 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates according to the e 7;: m;-54 jhxmtftkwfv-hoqiquation x = 0.45cos6.4t where x is in mqtt -h :j;wimh;vm-7f5f 4xok eters and t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equilibrium is the energy of a SHO half KE and halfeg-8 y 4 jzqt897ecl5ig5x qdo PE? ±y-ji z 98col5g 758tegxd4qqe    A

  If one vibration has 7.0 times the energy of a second, but their frequenm h6 /xpxo+ih5x;gj3qcies and masses are the same, what is the ratio of their amplixo;xmp 5 qhgi+3h/xj6tudes?   

  A 2.00-kg pumpkin oscillates fro-c-vbdlx.mw2 m a vertically hanging light spring once every 0.6wbmxl-2. d-cv 5 s.
(a) Write down the equation giving the pumpkin’s position y (+ upward) as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. y = (   m)cos($\frac{2\pi t}{0.65s}$)
(b) How long will it take to get to the equilibrium position for the first time?    s
(c) What will be the pumpkin’s maximum speed?    m/s
(d) What will be its maximum acceleration, and where will that first be attained?   $m/s^2 $

A block of mass m is supported by two identicao*hjj xekl;f 31z5c-zl parallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What will be the frej1kl ;ejo53z hf xcz*-quency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t where+v cb/ttd6apnogh3*2 x is in meters aphb+c*t6tv/odan23 g nd t is 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 eachyf:v g+k56(-ze93potcp v ixc, 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 onw6; * ur+jfkafms3 tm6 the end of a horizontal spring (k = 124 N/m) is struck by a hammer, which tk3;mf+s*6wu6f mrja gives the mass an initial speed of 2.96m/s Determine
(a) the period and frequency of the motion,    s    Hz
(b) the amplitude,    m
(c) the maximum acceleration,    $m/s^2$
(d) the position as a function of time, x = (    m)sin(4.08$\pi$t)
(e) the total energy.    J

A vertical spring with spring stiffness cons0lj f,kkc7zj, tant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 ,lk jjz,k c70fkg hangs 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 springs, with spring stiffness -3 k;zrk dkc*nvbf 6*mconstants $k_1$ 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 53mb xgm;/tqn 8dmck2a 0.600-kg block attached to a fixed horizontal spring whose spring stiffness constan bm/ km8mt;cqd 5x3g2nt is $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with mass 65.0 kg jumps from a high bridge. After rea4smlm+u/iu2f9d d) carzj0.y ching 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 bungee cord.a4mc. ujf+2 s)luyd/9idrz0m
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrations in exactly 60 jle*2i 9v9yfv s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactlybhsin0 )6mld+ one swing per second? (That is, one compl)sdi +nh 06blmete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its p7pi,saz. iess ( c:98a6aihieeriod on Mars, where the acceleration o iia a:ai86s,(9cshzi.es e 7pf gravity is about 0.37 that on Earth?    s

  What is the period of a simple pendulum 80 zug7) etu :3/0+w/ounufpbts8t ug8e6re5r w 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 penduy tqb;ulzy55,q; f 1qvlum bob has a mass of 365 grams, and it is released at a5q;u tq15v yf;y z,bqln angle of 12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clockzacd l+ngfppo,*w q1e 4u1t0;’s pendulum has a length of 0.9930 m. If the clock loses half a minute per day, how should you adjust the length1t1dnqp4awf ,l + 0oe c;gup*z of the pendulum? shortened by    mm.

Derive a formula for thj+5hlrt 8;1ji .h3ck7b e rqiso *ltq(e 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 frea bz m20sne)5*sf ffj4mor,r 0quency of 2.5 Hz. At it is released from res*,m)s rms40raon 0fjf 2 zfbe5t 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 crests pass;8rxivd t e t)p2c0jb- the bow of his anchored boat every 3.0 s. He measures the distance bvtcjpr ;e 08 )btdi-2xetween 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 wiz):o cv pj l06v6rtnlc bg.5*gye,6l uws07b vth a speed of 343 m/s 6b6l5.6j ,gc vt: u07 )bes0*grcn vvp lwzloyHow far apart are the wave crests (compressions)?    m

  (a) AM radio signals have frequencies g.f2+ bx es) x,4fawvjcgn)4a between 550 kHz and 1600 kHz (kilohertz) and travel with a speedg4avn2 fef)c jx g.)4xs,w+ab 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 longitudm r8g ;tc0 /xdruxew03inal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but mm;j6i*xb tf7-v 6uydone is twice as dense as the other. In which rod will the speed of longitudinal v6xmtuj*y; bdimf 6-7waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two suppisbw,jz9lv o :94sp6g rn gl*(orts 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 other? 9l: lg 4o inrs6(bsz,p9* gjvw   s

  A ski gondola is conne/2 falsfi ,e4ucted 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,ailse4/ ffu2 sends a wave pulse along the cable. It is observed that it took 16 s for the pulse to return.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

  A sailor strikes the side of his ship just below the surface of the sev4 ouqztw0a8 5+p pt(sa. He hears the echouvsz oq+pat8pt w(4 05 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 this differewhz;v2ryaejqo5n(h2ru o /; 9 nce helps in locating the earthquake “epicenter” (where therq2/9r ;nvhyo u;ao e5(hwj z2 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 suoyp2u8wsx) w. rface wave can be approximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a m8y.wu o)2sp wxixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplitudes, of an q,ige.:zxqw +;s0bzlf apv( ;earthquake P wave pa:xb,;fzwq(il+qps z. e0 a;g vssing through the Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquai:zcr 7ez47c ske wave passing through the Earth is measured to be z4:r7szcce7 i$ 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 frzjpr7f k-s w*)equency travel through the same portion of the Earth, but one is carrying twice the energy. What is the ratio of the ampljs-frk p)*w 7zitudes of the two waves?   

  Two waves traveling along a stretched str ke(ixharjka)8b/;zo4 v5xyw yop7yj)9.fo3 ing have the same frequency, but one transports three times the powery)(avh.zabw 85/ 4 7ofkpeoox;kxijj3 y9yr) of the other. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move up and down a total )o7.9 6;*hgrn nz )bcwpa1kqfjqcf5 wvertical distance of 6.0 cm, from the lowest to the highest point, as a wave pa pjc*gqkb hw5)6a7n 1fqnzw .fr;o 9c)sses. 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. vxzy6j p .e*7o(z6 h/plkaeo/(a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses /6 al6je z* .v7pyeoo(/zhpxkpass each other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundamental frequency, whj35w:4uez r c;tgv7cp at are the frequencies of the first four harm4 u c7g vw3tzrj:5e;pconics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what fre wid;dwvd xu-87 8bx2xquency will it vibrate if it is fingered one-third of xduw;d8x2wvixb -d78 the way down from the end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string rdr iz:c ;;s)s cwp/0baesonates in four loops at a frequency of 280 Hz. Name at least three other freque:cr d i)s0;cpzws;b /ancies at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the i2 kr.kgqw19.yklae , frequency of standing waves is 475 Hz, how far apart are two .i yl1kk, wkq9ea g.2radjacent nodes?   m

  If two successive overtones g7 jap .b;lnhi:f,j7e of a vibrating string are 280 Hz and 350 Hz, what is the frequencylp ;ib7j :,j.hg7fean of the fundamental?    Hz

  A guitar string is 90 cm lozn(xb ;sv+ rf3bx :ux .(s0rchng and has a mass of 3.6 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 frequencixhu ;b.xxfz s: (0rc+r3sbv(nes of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, but it is p):i+v +tx;wyl q(mz pmeasured to vibrate at 205 Hz. By what perceq)wpz+my(v:i p l+tx ;nt 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 vibrateal3wxm) .s. cin0dp4z at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent sh.c3)xd lasmwiz.0p4 nould the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal sbfh 7q)gih p52s9z8i mtring is attached to a small-amplitude mechanical 60-Hz vibrator. The string’s mass per unit length i biisqg 79 )5pz8h2hmfs $3.9 \times10^{ -4}$ 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 lenv:q/e;lc y 2 0on1jdv:l.gkqn( 6gzckgth of the string may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varyi;z2dgen(c: v6 nqvc1/yjo0:glq.k lkng L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at rb-r5l+vdxv ( just the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the cvl 5(-d +rvxrbenter. 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 bound-v sr 2((kimm:jii.6xd fse8eary within the Earth between tefvm2xi6 k:8ids-. jimrs( (e wo 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 “n5r;jamo k6xfx ;a4woc6 +l zi:s*lp)shelf” where the velocity changes from 2.8 m/s to 2.1 m/s If lx i;pz)*j :as+5rcx anl4k 6;6o fwmothe incident wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm - )q,l x:3atsk+dzu joair when it hits a layer of cold, dense air. If the sound wave hits the cold ad:x- +aku3l),t jszoqir interface at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave strikes a boundary b e lqy86*s5ks/a x. e*zjn.srietween two types of rock at a ys s.el5k*ixzsq8e ./a 6* rjn38 $^{\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. +0k zr:1lztcr According to the user’s manual, the dish has to be pointed in the direction of the satellite, but + ltk1z:zrr0can 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 v.b cuk/-fm vm6elocity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an mm /kvuf-c.6 bunusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring st*3 s t 58dz u5wqfwt7+rhsry1niffness constant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (ayt5st 8s 1z w+r57* wqhrdnu3fpproximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m below, which su)og*axhw lj)ha: bbo w;93o4u.uq+ ytretches the net 1.1 m. Assume that9;) *:+l4o a)h3gxowowubujbha . yuq 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 p- zuv g j1swi,4tj/sly,, sae-jl 6x0klaced on the end of a freely hanging spring. The mass then falls 33 cm before it stops and begins to risetji w-ax zl4js,,jgl-ky/s0v us1 6,e. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge springi6g q2b2jq+twxq xg r3 n))jl- at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the springjr6 j)wgqqxnbq23lt- i2 +)xg 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:. ,(qiqcg2fomhuf ,a 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). Estimate the speed qmcg:.f,uh oq(, f 2aiof waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the center of a 33-rpm 9vq1*3barfs02o*3 vvy yig z aphonograph record have a wavelength of 1.70 mm. What wilfo ygs9vva*av2q1 y33 b*0i rzl be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40tv j0c,b lu:ws: where x is in meters and t in seconds. Detev0,cb:wslju :rmine
(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 itsss.0mdsu1q(su ;;a 5vef g w*m frequency if it accelerates at 0.50gsm1a 5 ; ugdsu0e .(w*smf;sqv (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on tvczkrvus;f4 hv/ -- 2cuhh 7;phe raft, it sinks 4.0 cm duc /f z-c2rp4;s; -vh7kuvv hheeper into the water. When he steps off, the raft vibrates for a while.
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a musical instrument are tuned to play at 392 Hz (Gjumo w 3t2j:8e(vtp.o) and 440 Hz (Aot.ov8pw(t3je: m2 uj ).
(a) What are the frequencies of the first two overtones for each string? G : $f_2$=    Hz $f_3$=    Hz A : $f_2$=    Hz $f_3$=    Hz
(b) If the two strings have the same length and are under the same tension, what is the ratio of their masses ($m_{\mathrm{G}}/m_{\mathrm{A}}$)   
(c) If the strings instead have the same mass per unit length and are under the same tension, what is the ratio of their lengths($L_{\mathrm{G}}/L_{\mathrm{A}}$)   
(d) If their masses and lengths are the same, what must be the ratio of the tensions in the two strings?   

Consider a sine wave traveling down the stretched two-part cord of Fig.:o9-f he4d a+hv1fz4qlyy-w79q ox hi 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 seci 9ofx zah+:o -y7f-hqhd 1l9wyvq 4e4tions. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the tip of each prong movbjjep.asu q yl4*.5vghm652fes 1.8 mm to either side of center.hqbs*e a. u5pjm. 6vjl2y54fg Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simple harmonic motion of frequenaqghv2fp+;)6oq e2iolmk*x; q; djo+cy 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebbleo2 g*qx k6 eo lqd;h+p ;om+v2jfaq;)i placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that end is attached to a ring that can sli/k 2j0lz-ptknx,1+ me /j2exf(hjg iade 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 fnl i(1f 0kgh/,tjezex pjxm2-j+ak2/ ree.

  A “seconds” pendulum has a period of exactly 2.000 s — each one-way swing takebs9r) a;qgk )gs 1.000 q9 )s )arkb;ggs.
(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 di:7by 9g zt.6zqjh f+wlrection or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontal swings, and by what6.tf:79bzqz ljgw+ h y 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 tensim y hjy3 975nhf seyup4n 56-o0mqst 5z5a5ykeon of 255 N. A pulse is generated at oum kshypyhy55mqyt356 a 7 5fn9-s5njeze4o 0ne 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 sub, )u1 )-e)fsyo*t+kengw k hujw5n0 tspended 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 oscillations that will allow the penny to just stay on top of the blockoj5u) ,)gewskwf eu b* 0hytn-knt +)1? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The stees/p c ft-m 0yxxmglfo*,a 2w9w0m7 wq 6lv1/oal crane cable is 22 m long0x1f, g-9l207y f/omaw lsamomq/p* wtxw6 vc and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (which annvs c cq06n;b.s0 vgxng.5 rh7c. m)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 shea c c cns.xngr0.s7h6ma5gvb0;.v nq)nr modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz