Give some examples of ev h9)q5 sk3cwjeeryday vibrating objects. Which exhibit SHM, at least app39 5kej w)shqcroximately?

Is the acceleration of a simple harmonic oscillator ever-ea6b- mk1i qb zero? If so, where?

Explain why the motion of a piston in an aut 0pgw cz7v5r*.w; +v mo2idv 2wa2wbfkomobile engine is approximately simp5fdam bz0 v7o wwv wk.rp22;gvwc2*i+ le harmonic.

Real springs have mass. Will the trx5 wf j 3p4*8h1bf; ink3ducbiue period and frequency be larger or smaller than given by the equations forw4b 38cd*p3ui 1ffn jb;5xikh a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simplrr( ptqa 4p f1aoa nbovpz7;n 4ups1q.8 n3*7ae harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the y t/xy nvx b:mk+()dr+hook of a vertical spring scale, and then is released. Describe the scale reading as a function of timb: mxyd+k (trxv+ y/)ne.

If a pendulum clock is accurate at sea level, will it gain or lose time whemw) semvkr k25pqcc2 j 1/yp+9 y2-zjrn taken to high altitwqepjcjsp 1v)/9ymz- +cmk y2rk2 r52ude? Why?

A tire swing hanging from a branch reaches nearly to the ground (Fig. 11 wex4vi3j)3pv.tn p s/–48). How could you estimate the heiejpvi pv t xw3s.3/)4nght of the branch using only a stopwatch?

Why can you make water slosh back and forth in a pan b l 3rcy,jm.uv ::. sgez77jl2m cqeg7only if you shake the pan at a cert ms:7b ccmu2gjzeqglr : jl7,.3ye.v7ain frequency?

Give several everyday d 4f4q9y) * ymvobvzc)examples of resonance.

Is a rattle in a car ever a resonance phenomen7hkctz asu+ b4d65xrsna- q;)on? Explain.

Is the frequency of a simple periodic wave equal to the frequency of its : fk;b1c s +ttvyxwct xoa*:45source? Why or why b1cy5+:k;v oxw cx:*t attfs4not?

Explain the difference between the speed of a transverse wave travelin uqv;qe sc8 x ih/rcpoq***8k)g down a cord and the speed of a tiny piece of )qseox pcr8*vq8* hcu;k/* iq the cord.

Why do the strings used for the lowest-frequency notes on a piano normally ha)k u,f i2b msnk3cg w.b7g7;dvve wi ,v nkb7d 7 su;gwg2b)imfc.k3re wrapped around them?

What kind of waves do you think will travel down a horizon)kd o12*sskw e9st*n9 5rcjgptal metal rod if you strike its end (a) vertically from abovej2s9g1cs)*9k* to ewpkr d s5n and (b) horizontally parallel to its length?

Since the density of air decreases wi y zpw5c *i3/r(oyyru2th an increase in temperature, but the bulk moduluc2 3yo/w (zryr5 y*ipus B is 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 waves decrease in ad; )9+pugqwsbmplitude as they travel away fr); 9bduwgsq+pom the source.

Two linear waves have the same amplitude and speed, and otherwise;4q( ee5ahd 5m2oho pw;rs9vd are identical, except one has half the wavelength of the other. Which transmits more enermdd5;p; a ersoohwh ev45q 29(gy? By what factor?

When a sinusoidal wave crosses the boundary between two sections of cord as in Fo7;h 8om ygy;sywoc 27*gz2) az+qoj uig. 11–33, the frequency does not change (although the wavelength and ve yum oz27hqj*7g ;+ oy;82 oscowy)zgalocity do change). Explain why.

If a string is vibrating in three segments, are there any p k0lmi:.o(4xvl2t ygklaces you could touch it with(okl ymx20ikg t4l.v : a knife blade without disturbing the motion?

When a standing wave e6 ie)g m+-ibdgxists on a string, the vibrations of incident and reflected waves cance) m+dg g6iei-bl at the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one place 4vt+p:u ft/(qr.bf; w0c poyxto another, how might we determine whether the energy was being carried by particles (material bodies) or by wave vtx f;+c/q0(ppr.4yubf wo:ts?

  If a particle undergoes w f5k c8j:se1hSHM with amplitude 0.18 m, what is the total distance itec5 js1f8: wkh travels in one period?    m

  An elastic cord is 65 cm long when 5l tu3/v,vb.qoyj6iea weight of 75 N hangs from it but is 85 cm long when a weight of 180 u5i.6 j/y3ot qbvlev,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 driver get:+ -rgqvy/a2k6ek(y h zpzc5xs into the driver’s seat. If the car goes over a bump, what will be the fr k: yc5y+6zv2 gq-(/r eaxkpzhequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hankr8 i4z u k:m *i*qwzvq u+i0zdbm798vgs from it. (a) What is the spring stiffness co:vz+u8r uqi40 wmb*kik 7 i8zqmz*9vdnstant $\approx$    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 +an( xdxi)*g kHz when a mass of 0.60 kg is hung from it. What is its frequency if only 0.38 kg hangs from ii (kdx)a ng+*xt?    Hz

Construct a Table in*+g5oeayz9fckm ; zg 5dicating the position x of the mass in Fig. 11–2 at times t z;f +ky5coae* g9gzm 5= 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 vibra6-xst/ 7sywgxl;hpcq p) a:m 4tes predominately with a frequency o)yla s467ppxtm x :q/h;g- scwf 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 frequency of 0.88 Hzkl. 0xmi1ewm:ds 6m/w. When an additional 680-g mass is added to m, the frequency is 0.60 Hz. Whsm0eimkw :wdx 16/ .mlat is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per se;*-pf/u ve i63l,7 t q0oqp8qahoxr ykcond with an amplitude of 0.13u o k/p03qy7 hqe6o; txr*a ifqpvl,-8 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 equilibrium is the spea u/v;uvxe+k)u, bml )ed of a SHO half the maximum value;u/) vb vlm+) uaxe,uk?$\approx$    A

A mass attached to the end of a spring is stretched 4 fqb/dhl ;nc(7br *ira 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 sprz; sil g0ij-5bing is stretched an additional 0.130 m and released, how long does it take to rejz0ii5s;bg l -ach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attfn8jeh1w6s 6xy0 z 4gdached to a spring with spring stiffness constant k = 280 N/m and is ex1sw6j0e f6ngd48 zyhxecuting simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is moving with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compress*4 ta /lawyz.,: :52xxnlbpqaiskx (fq t8pa2 the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will tf/ ab.82pzax,xt w:k* ys5tpa2l ixn4(l q:qahe ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to*ceg0n low-po i7:q 8u 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 compresseenop u c08-:7og ilqw*d, the mass experiences a maximum acceleration of 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates according to the equation x = 0.45cose /.l 4hxu*tul6.4t where x is in meters*t4ux.lelu h/ 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 hai(kngm-y ta4)g +bwuxs e+g.- lf PE? )gm igw nb xa-u+ekyt(.g-4s +±    A

  If one vibration has 7.0 times the energy of a sl/al 1v/9al k3bmnb v)7 x*oiuecond, but their frequencies and masses are the same, what is the ratio of their amplbvv)oul*k/9l mbn 3la/7 xa i1itudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light spring oncixyr, :q0m3j;*an/kl0o xwo u e every 0.0un* ,rixow/xl;:0am yjko q 365 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 4t cmp7s.tp g odcstpt5q(;3- by two identical parallel vertical springs, each with spring stiffness constant pdgcp5tp.(stq sttm -;7o3 c4 k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x =tqu3 05vo2ebir7xvm/ 0.38sin6.5t where x is in meters and t is 0rt x/v v7b5qui2m3 eoin 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 Brn1lhxgz ( 0jd6 k 8p.dm)g.gn. For each, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on the end of a horizontal spring (k = 124 N/m) is s 3i.pssh66gnhv nyl)q/rrn ,o l11:g mtruck by a hammer, which gives the mass an initial speed of 2.96m/s Deteirmsy:hph ,n6n )g3s g.61o q1/nr lvlrmine
(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-;dfevy. dz mstdeeg3 -.gn )c69d(je with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passe-dds vdj ; mete3.ge(c9fdn.yg)-ez 6s 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 constants nsy3l fjeh7cxfm e9p2l t; -.a(+.wzy$k_1$ 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 gskoe:0t/+ vm a 0.600-kg block attached to a fixed horizontal spring whose spr:est0ogmk/ +ving stiffness 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 j 4 .a2ey-ndsy.tqa-m mumps 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 tsn-t a-.qmm 2da.4yyehe unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrations in excc*/ilal n;,dwr2-f kactly 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:libz5k nd2;i7 umiw. one swing per second? (That is, one complete vibration takes exactly 2.0 s.)kz7i;ldwmui:25n . bi    m

  A pendulum has a period of 0.80 s on Earth. What is its period on qlxr3 5nhaq-: Mars, where the acceleration of gravity is about 0.37 th3:alnr 5x-qq hat on Earth?    s

  What is the period of a simple pendulum 80 cm long gi zxy7qb- ;6b
(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 pendulum bob has a m)jpxe(kypz*9 qseef 7 n5b 3v8ass of 365 grams, and it is rb ( 35ksvp)zxfee 8*7njq9ye peleased at an angle of 12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’s pendulum has a length of 0.9930 m. If the clock losno6hic+sos wwc3)5u ua0 (ad3es half a minute per day, how should you ad n0c3us 3 aao wo5sdhc)w(6i+ujust the length of the pendulum? shortened by    mm.

Derive a formula for the maximum speqmlspi-1 fyy (.-scj2 ed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at aus b znq.a6zu- :1 lgi8;j*e dcmtt y-gr(6/ba frequency of 2.5 Hz. At it is released from rest starting at an angle of6 qte- yud/-sbaj6r cgg(bl*:m ;u .i tan1zz8 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests pass the bow of his anchored boat e*vpdw:e3 dq8 / agqh.kvery 3.0 s. He measures the distance between two crests to be 6.5 m. How fast are the waves travelv:d 3 8gh.kwadq /peq*ing?    m/s

  A sound wave in air has a frequencfkmlgs,2des+n9 /sy ) y of 262 Hz and travels with a speed of 343 m/s How far apart are the wave crests (compr,d/em g)yn 2f+ks lss9essions)?    m

  (a) AM radio signals j3 8dopp (u:.p e*wtmahave frequencies between 550 kHz and 1600 kHz (kilohertz) and travel with a spepum* :8ewdpp ( j3o.taed 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 wpto+ 83b 5yyyicbw fai4p)03taves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one is twiczpgzymz f(u8e;h 6.9fe as dense as the other.z 8z6(eg;fzypf muh.9 In which rod will the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apart.+;renkvk c9w) If the tension in the cord is 150 N, how long will it take a pulse to travce+ )kkv9nr;wel from one support to the other?    s

  A ski gondola is connected to the top of a hill by a steel cable of lenk9w m/cw i ,isysmx*tb,0f( 7ctac(u3gth 620 m and d 0i3ctm x u,tm ,fs9*ykcc(i baw(sw/7iameter 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 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 4/,rcp ogc*idc2p0evsea. He hears the echo of the wave reflected from the ocean floor dicvp 4icd/2*c g,epr0orectly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at differentgtk; cpt5ui;b07o) yy speeds, and this difference helps in locating the earthquake “epicenter” (where the disturbance to);ycot7;p5gk0 yubit ok place).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced surface wave can be approximated by a 7 mgh1cvlzp;, 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 ac 1zhvl,7mg;p>g]    m

  What is the ratio of (a) the intensities, anz9pjl(prz+/zg9 0rb pd (b) the amplitudes, of an earthquake P wave passing through the z( +90j l9zzgr rbpp/pEarth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an eakk5/,rbxl: sez ):7ny old-esrthquake wave passing through the Earth is measured to be k7n,-r/:o)s ld 5lks xbee :zy$ 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:3dusav qr d;.w;g6muf the Earth, but one is carrying twice the energy.u6g u;v; d3.d ars:mqw What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a strt **pa/ nfzcf1me2 9eretched string have the same frequency, but one transports three times the power of the other. What is the ratio of the amplitudes of the two wav2aer*czf*9f m/e1pnt es?   

  A bug on the surface of a pond is observed 4qz.d0wj- f5 aly:(kvo8k dzito 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 maxzkv(.djq4:lif 5d aykw 0zo-8 imum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each other. 3cgrzy fb39f;:4a0od df eoi3vt0eo 0(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,tf: o03e;ofd3 g v0byoc 90drzfe a34i 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 frequency, whav5t 3 4zu,x(:mc (byyhefw o*.7jb sext are the (cz4 7exsfhuo 3j*yxw.beybv( m5:,tfrequencies of the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates atz,1dd2q bu:)r-q 2qxdr7z )7o jlnkkn 294 Hz when unfingered. At what frequency will it vibrate if it is fingered one-third of the way down from tdxnd 1qkdnlz 2 zj-))rub or7q :2,kq7he end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequenc:vvw 2s m-ecf2y of 280 Hz. Name at least three other frequencies at which it will resonev :2 vwc2sfm-ate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If thj4bpnd( +vg8he frequency of standing waves is 475 Hz, how far apart are twoghvdn8 (pj4b+ adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz an29wtnwl;lnr . d 350 Hz, what is the frequency of the f nwt 2w;l.l9rnundamental?    Hz

  A guitar string is 90 cm l(+3xb5wc wer2 5ttbh2dyt wg9ong 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 arert h bw(95bdc3 +egywt 2t2w5x the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar a;z- j/q thkp(string is supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?So the three kh /a-pt;jz (qfrequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar stribu967 fkkf0d *6pphfw ng is supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency? dewk 67*fubpdp0f fhk69creased by    %

  One end of a horizontal string qe 6 7ng500h osxd3ljalr(d6jis attached to a small-amplitude mechanical 60-Hz vibrator. The string’s mass per unit length 5l0nhrdj(egqd60 a67 jo3 xslis $3.9 \times10^{ -4}$ 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 8ol-3cy 3kdrf pulley. If the hanging mass m is 3dyrk8-3 lofcfixed at 0.080 kg, how many different standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at just theo r2 uu9m s)zns2)vcc7 right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the speed of the water waveo9scv22 uz)us7nr) mc ?    m/s

  An earthquake P wave traveling at k.0 :znz8df:hx.jkm/s strikes a boundary within the Earth between two kinds of material. If it approaches the boundary at an inci8n:jfdxh z.:z dent 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 the velocity fzg ov1 g:mb*o,;rxhk-c3q) kchanges from 2.8 m/s to 2.1 m/s If the incident wave crests make a 3;o,m)k*zv:kgo g1fbqc- r x3h4$^{\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 g * e.+9 t.rj vfepjyi5;wtn3sof cold, dense air. If the sound wave hits the cold a.5ti. wre*3nspv9; fjjey+tgir 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 b h .2crfmz:sq*q58k broundary between two types of rock at a scq*hq8rrmk bf2:5z. 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 diameter. Av*4:jl4iox uz ccording to the user’s manual, the dish has to be pointed in the direction of the satellite, but an error of abjvz*4lx i4:o uout 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 travel3iih. nkrhmvuj w3.; *unc:v,s across 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 safety? (In the absence of knowledge hjncw*imi vv ..u3k 3nh;:r,uand 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 hw4yf t x98r7 su5xcu5550 kN/m Find the mau5u49r c5 xtfw7yhs x8ximum compression of the bumper if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m below, which stretches k 2xl/qpy7nm8* 8rwbithe net 1.1 m. Assume that the net behaves like k/ ri8b8p72q*m lwyxna 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 sf g+.w/n, sjpyg:vfq1c:f-q npring. The mass then falls 33 cm before it stops and begins to rise. What is the:-/1:nwq f,sjgf p f .gqc+ynv frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed73tpagdypo ./ a, dqf5 of 22 m/s (Fig. 11–54), compressing the sprinadp,.q 5yp ogt3 da/7fg 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 cc2 r*f9uhzbt wab4x )0up of coffee (diameter 8 cm) at just the right pace of about 1 step per second, the coffee sloshes more and more until a ux 94b*2rbfh 0)zwtceventually it starts to spill over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the center of a 33-rpm phonog s )r2gmabf)fh (/*q 9dpubae1raph record have a wavelength of 1.70 mm. What will be the frequency of the soundbm2)df9sg 1br)upaf*ha ( q e/ emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t wher s;pv 1ui*vt44guddv/e x is in meters and t in seconds. Determiuvid 4v4 v;1spd/gt u*ne
(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 freqa+*. u8 fz ):qshbwfuewfb2,y)c1 9icb syj2 huency f. What is its frequency if it accelerates at 0.50g sbi.ca +w1yyj cs)bfe2*,q)uu wh :29bf h8 zf(a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man s qyzvac61s0m(tands on the raft, it sinks 4.0 cm deeper into the water. When he steps off (61za vyscmq0, 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 3o5 k2huaz uav 7mn96gtuned to play at 392 Hz (G) and 440 Hz (A9gk2 a56nvzumaho3 7u ).
(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 co723-qjz g2epywbvhuym* 0k * crd 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 sec0qeg b2v -cy7uh*p kjw 3m*zy2tions. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 26ze x kh3u2-aa;q:mf1 s0b5a da4 Hz, and the tip of each prong moves 1.8 mm to either side of center. Chs3k q1;ad52eazamubf0: - ax alculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simple harmonic motion of frequency 1.5 cycl:j mw;ws)hvy67v-h(add d 1c rtlo 7(i f7q4xles per second. What is the maximum amplirf-(6i )l4q7dwdwla1: do myjchv(vt7 7s;xhtude 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 tha*l 0ugbe+pbj +t end is attached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelenge pub0+*bg+ljths 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-wagw(bik u (k2f,y swing takes 1.000 s. (2k bgwu, kfi(
(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 oscilpngn.845)s6pumf x m ylate in the vertical direction or can swing as a pendulum ms fnx)yu.84pp6g mn5of 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 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 tenx5 +ud9g+ g9hn gwndp*sion of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generate nug+g9x+nh d* wgd95pd at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spring with spring stiffnem 9hw1 .t r7ynegpre(zi 3f*+gdv,pe)ss constant k. A penny of mass m is placed on top of the bl.e3e*egnvw)zyp 1p g ,7i(h rr+tm9fdock. What is the maximum amplitude of oscillations that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel crane cables)io1( 8/cq+h iipxr) coww:eiym/ 3q is 22 m long and has a diameter o+3/)pc:h )ioew/(ixrq1i cyiw so q8mf 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 gfwo 9j) to.t5y5fdd)Fig. 11–58 (which also gives the dimensions of the block). You push it sidj 5otf)y .)tgwo9dd f5eways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this vibration, given that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz