Give some examples of everyday vibrating objects. Which exhibit SHM, atf 7 hs2xtj4*ap q6it,v least approximately?7ifas q* ,tp62 xvjh4t

Is the acceleration of a simple harmonic oscillator ever o7o73fw u o/z58bgc/pjrb 6 /w ua/czzzero? If so, where?

Explain why the motion of a piston in an automobif28csgtgwo, 7 le engine is approximately simple har,cf so2w7gg8 tmonic.

Real springs have mass. Will the true period and frequency be2 *d xkes4ov(l(tol3 n larger or smaller than given by the equationtd23(vl sok e4on l(*xs for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the mocbvf f06p,2 q t5*kxgaximum speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring sca h8+8fzg5 2i jdzkq;gwle, and then is releas+gzg; fjkhq wz5 i28d8ed. Describe the scale reading as a function of time.

If a pendulum clock is accurate at st t997xcuxr 1a3; zy8grxlo4x ea level, will it gain or lose time when taken to high altitudt8xlz1y a99xcg7; 3 oxr ur4xte? Why?

A tire swing hanging g yf et.i*lugbx7t7/( from a branch reaches nearly to the ground (Fig. 11–48). How could you estimate the heiefgi(/uly. 7tb *tgx7 ght of the branch using only a stopwatch?

Why can you make water slosh back and forth in a pan only if you shas)* a1 uceptv9w 5mryc14zj+eke the pan at a certain frequw+z vyceu4*1 msp)t9jea5 c1r ency?

Give several everyday examples of resonance.dbk(oam nv3s9h a9 r11

Is a rattle in a car ever a resonance phenomenon? Explcc 8nhxqmx46v9 f jt0;x.8z0 t fnn3ypain.

Is the frequency of a simple pc6us z)9 pjzd,eriodic wave equal to the frequency of its source? Why or why not,69dp ucjzsz )?

Explain the difference between the speed ofs1 .xc+c9hthmxji, h0 a transverse wave traveling down a cord and the speed of a tiny piece of the cord.m0h9ch ix,hc x1tj.s +

Why do the strings used for the lowest-frequency notes on a piano normally(hq mohe/2q)x brqaf8aad02( have wire wrapped aroundfbq2o)a8 a/xe rh(dq a2hq0m ( them?

What kind of waves do you think will travel down a horizon smwme3a96a (b:8u luy drl47ztal metal rod if you st3l 9dm ezuawr8 (4 yam:sl76burike its end (a) vertically from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase o/(i8lu9 i8xz h2l jqkin temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the speej8o x(hui2q8k9il zl/d of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrebs /plf( df(3nrue*2 nase in amplitude as they travel away from the sf( 3n/(*d2ne lfs rpubource.

Two linear waves have the same amplitude and speed, and/n r/f kzg,utu:udh w kfh,k.-1:.og1-veudo otherwise are identical, except one has half the wavelength of th:,1 ezufu: uh,gkod-f g.h-t 1/v /norku .kwde other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sections of cord as b2g(z6xyf q:yin Fig. 11–33, the frequency does not change (although the wavelength and velocity df2x: gyq6by( zo change). Explain why.

If a string is vibrating in three segments, are there any places you could to6lrz4e zt1u+ouch it with a knife blade without disturbing tt1o rz+lze46uhe motion?

When a standing wave exists on a string, the vibrations of incidentpwnn d,90+s,c zu a(dm and reflected waves cancel at the n(9z ,d+mdwnu,ac sp0 nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one place tfhvk1e 4 dm+8id-dy7io another, how might we determine whether h471ddfv i-mk+ 8eiyd the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the total :4bz6)mddgg:fzuzein-*jqt9 ) o : wgdistance it travels in on:n4 g)qo tzdfidm):-bju:z9z* 6eggwe period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs frov)gvb46bcywhpr80 *dx/4dg dk 4vgo2 m it but is 85 cm long when a weight of 180 N hangs from it. What is the 8 bkg04gv4gyv4/xcbdhwo2d 6*dr)v p “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when us0)z:irp4dpkn6c ey8( zq( wits 68-kg driver gets into the driver’s seat. If the car goes over a buceukr0iqp4 z pwd(zs n:)68y (mp, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs from it. (a)t+icake2tna zh820 w 0 What is the spring stiffness cont8ak0i a0z neh2w2c+tstant $\approx$    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 hut5fb *,uo:m 7zr.ryrnn5b f *jng from in r:jrt5 nrf5o.b u7mf *zb,*yt. What is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position 4i4(k-w s fsy*fqkfd5x of the mass in Fig. 11–2 at times t = i5-fw* qky (f4d4ksfs 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 aq0x(uf h80zv r spider’s web. The web vibrates predominately with a fre0(0vrxuzqf h8 quency 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 vibratesvgdy6nww6)+kk0 q oj. with a frequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is 0.606.k6) g ovynkw+wdq0 j Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per second with an amplc y7t )6hqtydi n2/e8qitude of 0.13 y87e)qntqth 2/idy 6cm. 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 havul) +)xgb)r3p.e -p )pkga rllf the maximum valuebpg. arvk+l)pe)-3gprxl )u)?$\approx$    A

A mass attached to the end of a spring iccc) )xa* vvh:s stretched a distance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretches a vertical spring 0.315 m. If tyifbfj y)*l /.he spring is stretched an additional 0.130 m and released, ho*fyy .fib)jl/ w long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a sz ;8-d- o3f1xp d452eglm;boxy/o2spd qivki pring 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 with a speed fko8 sqp;2 i3vly4zmo;b d-1diedox -g2p 5/xof 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 the spring of a toy popgun 02 f0 8mrsl uxn6gu(*uw.200 m to “load” a 0.180-kg ball. Withgsfm6x w8nr u u0l*(u2 what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attlm )(.7xiq3q t,qzc6hu mx wb+ached to one end of a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring byxiz)(c 7bqmmhlwqu .t x q+3,6 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 the equati,(t2j)w 4pfqy9kz uozon x = 0.45cos6.4t where x is in meters and t is in seconds. zju, 94oyw kz2 pf)(tqDetermine
(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 enecgo6pcj::x wu -w7bsmly 23 9orgy of a SHO half KE and half PE? gl9wouompc c63: s2-j7:xywb ±    A

  If one vibration has 7.0 times the energy of a second, but theiqsy cvdl jr093aft) gjgn7e(4-;g0uhr frequencies and masses are the same, what is the raa- 4hs;93tfljje0nv ugg)7y cr(dqg0 tio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from98kewu p.yyvch d:/k g+v5x.o a vertically hanging light spring once every 0.65 s.v eox. 9kgp y.v5dukhwy c8:/+
(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 identibjco-mtrc7 8nfl2) 1ccal parallel vertical springs, each with spring j8fo1)l2c7rmtc c- bn stiffness constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates a.pntmi3p;fw 1ccording to the equation x = 0.38sin6.5t where x is in meters and t is in secondi3tpmf;w .n p1s. 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 tw ca/3+( xfk wuae :gms1jfd:s/o examples of SHM, labeled A and B. For each, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on the end of a horizontal spring (k = 12 5prvs3h kl2, gheeo6(4 N/m) is struck by a hammer, whr5 hh,egvklo(3s p6 e2ich 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 constant 305 N/m vibrateoh i. x;7 ;rfxx8/s4a1yitfsis with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) with pos. 78fi;/4xsro1f; ia yihtx sxitive 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, ht*jjsso6 0+07o+s:ivb6 cy xql(t id with spring stiffness constants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes a 0.600-kg block attached to a fixed horiv2m 3 -dm2 ;s:1chh5tsb w5rrmr)csmq zontal spring whose ;3b -srr qh m2:5c1mdmtvr2 swhsm)c5spring 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 jumps from a high bridge. After reachinj x*opej-y 6.og 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 j-j xpeo*oy6.m below the level of the bridge. Calculate the spring stiffness constant and the unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrations in exactly 60 s. What is itsl,4w5 w2 gyd )n rkaw,a(-pfmgki( u3d
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is 6js8//ev3jnw2 zt rb uto make exactly one swing per second? (That is,vz8 6w/jebs23n/tuj r one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Eartcttutq fg,tm/fkc1dk/e2:gj4* : vfrtq 2v4+h. What is its period on Mars, where the acceleration of gravity is ab 2fc4fr vj:u2t/,kqet /gf q1:tttd*g+ mk4vcout 0.37 that on Earth?    s

  What is the period of a simple 3dy)0m: ol0xz8s 40 gkrm siripendulum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 m, the pendulum bob has a mass of 365 ewuohr(0+-z y gra youz0(e+-hr wms, and it is released 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 o lm(rw-r2tx 6wf 0.9930 m. If the clock loses half a minute per 2rrmwxlt -w 6(day, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the o( g opjglam-lo.8it r 16p/t pphx;+mr+a-/dmaximum speed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at a frequency of 2.g,j p4x( hbwrx-:z t/n5 Hz. At it is released from rest starting at an angle of 15z,4 : jth(wxprx- /nbg $^{\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 mpji 8r3a hjy4,ur5 c 5pb:+riboat every 3.0 s. He measures the distance between two crests to be 6.5 m. How fast are the wavp45j+h5 aj8p r,c3bmriury :ies traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels .-wdwch v .ka zx+82iquodu./with a speed of 343 m/s How fahq /dukiww dzu xo +.8a2-v..cr apart are the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1ah ri: nw.59rsbs) (pq,wulh*600 kHz (kilohertz) and travel with a speedqa)(sr i h :9s,bwlhu5*.pnrw 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 0r uxr/g5x7xfw 9tux:waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have tf6m o8llje-9u gkz50 phe same elastic modulus, but one is twice as dense as the other. In flkp6m g50zj 9u-8ole 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 apnimsrj; /g7podja5-v zbl 5+. menrpe k39q) (art. If the tension in the cord is 150 N, how long will it take a pulse to travel from ojase k 5on(imb/)ngepzp5+ jrd3.v7m q-l9; rne support to the other?    s

  A ski gondola is connected to the top of a hill by a steel cable of length 6208yzczi; gl; z, m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and sends a wave pulse along the cable. It is observed that it took 16 s foiz ; gcly;zz,8r 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 th* kvx z:.p3, ngt6khzxe surface of the sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is the ocean ax zv:zxt*kkhnp.63, gt this point?    m

  P and S waves from an earthqute:67 nb k*zhfets6 4bake travel at different speeds, and this difference helps in locating the et bzbt4eekh: s67f*6narthquake “epicenter” (where the disturbance took place).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced surface wave can be approximated q,t 4uwsz58g fby a sinusoidal transverse wave. Assumifu t,q8g4z 5swng 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 a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplitudes, dc81)j mog9z/9mb sbxof an earthquake P wave passing through thmj8o/smd 91 9gb )xzbce Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is xj *bvmfa; 9woibs* 7/measured to be oisb9/vj *;fwxa b* m7$ 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)4 2l3ht)rxy qc6oqmy same frequency travel through the same portion of the Earth, but one is carrying twice the energy. What is the ratio of the amplitudes of the two wavyxrt2y43 c)lmh)6 o qqes?   

  Two waves traveling along a stretched string have the same frequen7yfd3*+yq:z b3aa9hfkn w u)pcy, but one transports three times the power of the other. What is the ratifpbu3+3*:hdk)qnzay af wy7 9o of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move up and bs)oo- xqbh; 2down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrb ob-x)qh;os 2ease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52yp;xa :9*dew3 af-tf f are moving toward each other. (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 pass each other, the string is se yf9fap:3 ; fw*-dtaxtraight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundamental tso; hcn7bxj:r8 l97 efrequency, what are the frequencies of the first foo9s ne77;lrjx:hbct 8ur harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what fr i+*awtb +:rdoequency will it vitbi: +wda*o+ rbrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops s4 fy t7 9u*5q3qstpskat a frequency of 280 Hz. Name at least three other frequencies at tssu*py35q qtkf79 s4which 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 frequency of st/rspa/3xo:)2jr yi b3 f tbk3/pn sr:randing waves is 475 Hzrbr)ss3 i/rtrx/on j :a:2b 3ypfkp3 /, how far apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hzxp d2gfi:6y 0c and 350 Hz, what is the frequency of 6 fcpiyg:2xd0 the fundamental?    Hz

  A guitar string is 90 cm long and cm8 7y:3jiccu 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 frequencies of the fundamental and c 3 im:7c8cjuyfirst two overtones?    Hz

  A particular guitar string is supposed to vibrat9cez t2ae8j2 rob)qp:m *om;oe at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be coz:o2mr8 aeq o2cet); bmp*9jhanged to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 2 uoqd1-a39mwo7hyt n :00 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the freqwq:nta79ou m-o3dhy1 uency? decreased by    %

  One end of a horizontal string is attached to a small-am; x:-hnkyfb r-a*py3w y 8fthx*cp ;t/plitude mechanical 60-Hz vibrator. The string’s m ftf; ywky-nr-x :y cb8/p*3x;pah* htass 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 ofu8 ach( *thyd2ske t8o+tn7i + 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 varying L y ott8n(8ek7++ 2udtc sa*hi hbetween 10 cm and 1.5 m?   

  When you slosh the water back an8g/ktx+ f9irf45m lj kd forth 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 pfx kt9m 4jrl5/ 8+fkgiroduce 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 strike (vi-n*ips bwmtisqm;f 9i;.0s a boundary within the Earth between two kinds of material. If it approaches the boundary at sn;*t 90pimsfwmii;-ib(q.van incident angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “shelf” where the velocit9dy)/+n dl2re2dv)k ty /cc ayy changes from 2.8 m/s to 2.1 m/s If the incident wave crests )y )n9at/+2l2yvd yccd/ekdr make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air when it hit8dk )yy k-twr2s a layer of cold, dense air. If the sound wave hits the cold air interface at an angk k8t-y)2dw ryle 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 between two z-go 9 1a/z8o3gcn*/ilcr9buy1 ejwv types of rock at a 3cw1uzz9vn9y a -gr 8goecjol/13/ib* 8 $^{\circ} $ angle. As the wave crosses the boundary, the specific gravity of the rock changes from 3.6 to 2.8. Assuming that the elastic modulus is the same for both types of rock, determine the angle of refraction.    $^{\circ} $

  A satellite dish is about 0.5 m in diameter. Accord x 6)zgg21 :st9xvqpadpfid2s:l (3g ning to the user’s manual, the dish has to be pointed in the direction of the satellite, but an error of aboutp2si zd1(a l xgd 9: xg:q2tnvgp)f36s 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength .ykc3qfzmai+ p8* 2sg o(7xwp250 km and velocity 750 km/h travels across the Pacific Ocean. As it approaches Ha +wo(amc2zp7i g yfk8xqsp3 *.waii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness constaavm lr8/x6+tc kxfu e69tq/1snt 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 (approximately 5 mi/h). [Hint: /1 /x8fum kxtc6r q9s+leav6 tUse conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m below, which s: pk(mjcz8w;xd - fr1q 6sb8rx:2bpmgtretches the net 1.1 m. Assume that the net behaves lx8mb jgp ;(:mr:1- kf wzrd2qs6bxp 8cike 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 hangin 9g)d k64 1v 3q*pbtgu4ihlrdrg spring. The mass then falls 33 cm before it stops and b rdt)1vlpq g4dk r9hi*b4u36gegins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 11–5f07 fnjt4 lby*4), compressing the spring 5.0 m. (a) What is thj*ylb047t nff e 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) atpqh5,rbu 4 ,sdo ecw(9 just the right pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the towo b ud,9hscq5rp4(e, p (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 6rh4 yc/rdkg+tf s-t26.ritjphonograph record have a wavel+6/srg62ttf -ik. rjd cyh4trength of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibratesr:p pnhphwr 6z)ja)87cv77w s according to the equation x=0.650cos7.40t where x is in meters and t in seconds. Determinevzh :w7 )sr76p8p)wjc7r ahpn
(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 wiy:bx+ s..;vymxnaa 8hth frequency f. What is its frequency if it accelerates at 0.50g (a) upwa a.+my x.a8s;ynv:xhbrd,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands oh/ouvxsi. 0(u n the raft, it sinuxsh/(o v .i0uks 4.0 cm deeper 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,vj+u1nai lks s dkffy; 8)1e- are tuned to play at 392 Hz (G) and 440 Hz (A). sj v-1)+dunlaf81,k e skyf ;i
(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 theco ps u uy1; gy6m.u1p4yfsp18 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 iyg46 ps1 sc.1; uf8yypuop 1mun the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of e0adfhuf.4 t8thj6(s264 Hz, and the tip of each prong moves 1.8 mm to either side of center. Ca.djf e thau8(60sfht4 lculate
(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 frequencyghy , k d/s8u3cvtx94n 1.5 cycles per se/gdn su4cvx,y8 9thk 3cond. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that end is attached to a rin6-6:): sukzt rdrzdot g that can slide without friction on a vert 6t6r:r -dod szkt)uz:ical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a pers 4 0evper+v7v1t0pnt+ tq)fmiod of exactly 2.000 s — each one-way swing takes 1.mpr)++4 tnvetf v00s7vt qe1p000 s.
(a) What is the length of a seconds pendulum in Austin, Texas, where $g=9.793\mathrm{m/s}^{2}$    m
(b) If the pendulum is moved to Paris, where $g=9.809\mathrm{m/s}^{2}$ by how many millimeters must we lengthen the pendulum?    mm
(c) What would be the length of a seconds pendulum on the Moon, where $g=1.62\mathrm{m/s}^{2}$    m

A mass hanging from a spring can oscillate in the verx2q 4ejfry-5 6vb fwj)tical direction 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,6)2jv jy4xw-efqrb5f 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 pj (yjaro6tt +m)+ 4(7jx wjmyiulse is generated at one end, and 20.0 ms later a second pulse is generated at the opposite end. Where will the two pulses jo+wj)mxj74ajm+(y irt6y( t first meet?    m

A block of mass M is suspended from a ceiling by a spring with spring st4i7vd3 6q zlwsiffness constant k. A penny of mass m is placed on top of tz3l6 4dwv i7sqhe block. 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 c2nvsb9c 0 z0atlhfe (pe42 nt-able 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 of the bounc b-09c 4n(z a h0vntt2f2elpseing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11;soj d*q 5qj/02xewrwh w3 2uj–58 (which also gives the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, eu5swrdoh 0jw/2wjq xj ;2e*q3stimate 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