Give some examples of everyday vibrating objects. Which exhibitjnx sfz)s0* )r(ml 8tn SHM, at least approximately? f*s nj zs0(tnxr8m))l

Is the acceleration of a simple harmonic oscillator ever zerj4i dy+k)t 2teo? If so, where?

Explain why the motion of a piston in an automobilj j9)uyv:4ufso5v1tulz 5: t ue engine is approximately simple harmonic ul)v4t u1usjo:5v9tf yjzu:5.

Real springs have mass;a.c:i8c a,tp1ioha v . Will the true period and frequency be larger or smaller tc.apc :oa8;hi,it1v ahan given by the equations for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of ay/aoh g- *usc. simple harmonic oscillator (SHO)?

A 5.0-kg trout is attac atdcedr2rg k *ro,f5r1kosq+t:2.,phed to the hook of a vertical spring scale, and then is released. Describe the scale readings2c, fr.p: +a2od5,rrr*koeq kt1dtg as a function of time.

If a pendulum clock is at9 i ley2 x)rd:om;4fhvll g*0ccurate at sea level, will it gain or lose time when taken to high altitudedmr;flht9 l:2 v yox )i0l4*eg? Why?

A tire swing hanging from a branch reaches nearly to the ground (Fig. 11–48 80x/cc9maf9shc zv,n). How could you estimate the height of the branch usa n,cv x cs8hm0z9cf/9ing only a stopwatch?

Why can you make water slosh back and msle-5cbfsso *) ol*- forth in a pan only if you shake the pan at a certain fre*ml*bl) e c -sfo-o5ssquency?

Give several everyday e kf 5borne1qgx.6e/44 xr ik5dxamples of resonance.

Is a rattle in a car ever a re)1i9.m pnrmtq sonance phenomenon? Explain.

Is the frequency of a simy(t8cy mx 1qsl0k3 2ysple periodic wave equal to the frequency of its source? Why or why nk0cyytm(y x3s21lq s8ot?

Explain the difference between the speed of a transverst*)3 ea - oao63xcszz:ik2bmd e wave traveling down a cord and the speed of a tiny piece *i6 stodoxa 3z2z: bmce)3ka-of the cord.

Why do the strings used for the lowest-frequency notes on a piano n)p- 0s i taw/ykjkku84ormally have wire wrapped around them?kw/ akk -t0uysj) 48pi

What kind of waves do you think will travel down a horizontal metal n:brve-1az0 ba3;wx2xhkzx +rod if you strike its end (a) vertically from above and (b) horizontally paral2:az-vxxk ra +be zxb10wnh;3lel to its length?

Since the density of air decreases with an increase0a6c-6g i+b f-vn ywzg in temperature, but the bulk modulus B i-v g b+6gny0aw-c f6zis 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 wavi+ 0z emghi m;d3k(z6podee25es decrease in amplitude as they travel away from the sour(+ imzkzh65ede;3ogd m 02i pece.

Two linear waves have the same amplitude and speed, and otherwise are idento-q,lsst 9f hmp58i3cical, ex lo9p,c5mstihq -8fs3cept 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 cord as i2u+v-c / urg 96;dll-clgdyirn Fig. 11–33, the frequency does not change (alth g-6;+gdycl l/2u 9lr-icr dvuough the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, amu4ndsz-ntpxr pag o 7bpt9a:;/y/- b: 5rlh,re there any places you could touch it with a knife blade without disturbing the / or bangb,z -9da hmr7 -;punp4xy/5:slptt :motion?

When a standing wave exists on a st )7mhf v ti(4hpo)dn9,j;jgkgring, the vibrations of incident and reflected waves cancel at the nodes. Does this mean that energ(hp 79hkminjjo )4);gd,vf gty was destroyed? Explain.

If we knew that energy was being transmitted from one place to o ;uscch1 wz(,another, how might we determine whether the energy was being carried byu ,c z(wohc1s; particles (material bodies) or by waves?

  If a particle undergoes SHM w9fgg p7zgp6:h ith amplitude 0.18 m, what is the total distance itg9f p6 phgz:7g travels in one period?    m

  An elastic cord is 65 cm long wye9e2 h5z;bfburnt(ih* 4g m0hen a weight of 75 N hangs from it but is 85 cm long whenm 4u eney0h;gr5*zi9 (fbbt2h a weight of 180 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 gets into - :s m3pnlbax.the driver’s seat. If the car goes over a bump, what will be the frequency of vibrations? .-ms:blnxp3a$\approx$    Hz

  A fisherman’s scale stretches 3uu .rev -,enx+.6 cm when a 2.7-kg fish hangs from it. (a) What is the spring .x,ee-u+ ur vnstiffness constant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a frequency of 3.0 Hz when a f g5) )9wqgr) qdo.ddxmass of 0.60 kg is hung )9) )orqxw5.dddfg gq from it. What is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating theb qa0gwd-osp 1zlru:.6:k*cr,* lbnd position x of the mass in Fig. 11–2 at times t = 0grn:*s akr:u *, plzlod 6.c0d1 qbw-b,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 wevc07 7e9ox d4lkim-ssb. The web vibrates predominately with a frequency of 4s9i-l c 7ek4m 7d0sovx.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 vz)s-smi- x:g u,vy5keibrates with a frequency of 0.88 Hz. When an additional 680ivy m5-kux)e- :sz,g s-g mass is added to m, the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end/v8*dh+bh 7jyfb ve ;x of a spring vibrates 3.0 times per second with an amplitude of 0h ;h x*ejybfv v8bd7+/.13 m. Determine
(a) the velocity when it passes the equilibrium point,$\approx$    m/s(round to one decimal place)
(b) the velocity when it is 0.10 m from equilibrium, $\approx$ ±    m/s(round to one decimal place)
(c) the total energy of the system,$\approx$    J(round to one decimal place)
(d) the equation describing the motion of the mass, assuming that x was a maximum at x = (0.13π)cos(  πt)

  At what displacement from equilibrium is the speed of anwjicza zn,5 a953ze) SHO half the maximum valujn3a5,cz5wa9)e nz ize?$\approx$    A

A mass attached to the end of a spqf9:p ce0l/6v 9kml c )9kwrxsring 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 s2oruurq(vz(-or-r/) cfbxzm 3w-w z6 pring 0.315 m. If the spring is stretched an additional 0./( 2b-r( zc)u- 3urrow zvm6 -fxroqwz130 m and released, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached tkpfc98n ,6ru mp( lfl9o 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 with a spe,pmunf86 9 cfpl(lr k9ed 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 k4yy) u2c yj,q2 as.6*c /q bskd;uvoscompress the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what s)sqk byo,;*ys u c.2yus ajkcd2q4/v6peed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to one enbiln wx szsoaa9h y:4,,5(7cjd of a 9xjbhszn4 wi o5 sc (,la,y7:aspring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, the mass experiences a maximum acceleration of 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates according to the equation x = 0.45cos6.4t where dn4 -j/-hw:,la xc 5 wo:drirfx is in meters and t is in second5j rc4n wl/- ,a x:-wdfrdo:his. Determine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equilibrium is the energy of a SHO half KE and half PEr58jwwj 8vbzs+yy-o f,+t ,ud?dy5zuwtfy8 wr ,jo-, 8++vj bs ±    A

  If one vibration has 7.0 times :6,b)f;xout +c srymz the energy of a second, but their frequencies and masses are )ux+bf,ym6so trzc;: the same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanahb+4 /-:l4cqqla w :; qazxqsging light spring once every 04-sb+;qcx lwaz 4:a qlqahq /:.65 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 6yyt5)a 8d.fgz ;qv xysupported by two identical parallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What will be the frequency ofag;zq ydx6yyf5).vt8 vibration?

  A 300-g mass vibrates according+qk1)fxcxjm 4 to the equation x = 0.38sin6.5t where x is in meters and t is in seconds. Det qxf14c)k+ mxjermine
(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 each, whmkt6i/ip2f g7(m 0ngiciy e: .at 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 ere+x a/q m- r(goye/3rest on the end of a horizontal spring (k = 124 N/m) is struck byy ar/e3r /-mge qxe+o( a hammer, which 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 vif8lm yq;l,+lgbrates with an amplitude of fl mll;gyq,+828.0 cm when 0.260 kg 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 spring/o:4v,/aiyoz81u j e7qxp azys, 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 horizontal spr l+ftjgk* )sw:ing whose spring stiffness constant is +s wjk*gf):lt$ 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 reachinv2xms4 7 wlt0gq) 8oq-f.izyjg his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally com0qzv)xql7 f.2 i jm 4ty-g8oswes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrations in exactly 60 s. What is it28yg y b45fvn6ae.uh is
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make)d83ts0l(q zw.n ubk e(ja-bo exactly one swing per second? (Thb-)odan3qk( z . s(8w0bujl teat is, one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its per : xsyytd:m77p-;bqohiod on Mars, where the acceleration of gravity is ab:osq7 x:m-7bh pt dyy;out 0.37 that on Earth?    s

  What is the period of a simple pendulcngq*1/ itilc2ksv(r-h+ pa 80 qbk3kum 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 hasxq13oa np3+ k*.wayhy a mass of 365 grams, and it is released atwxon+*13yhqa y p.ak3 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. Ifhr1- :f gem pz,.lmf3,e)p y1yw jidx2 the clock loses half a minute per day, how should you adjust the length of the pendulum? srw ,)2py:mfif1lepyh. 1-gx dze3,mjhortened by    mm.

Derive a formula for the maximum speez 9/i-bza0le5 hknll03 v3tz udcd -j(d $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at a frequency of 2.5 Hz. At itc c+j/ c plyb3lunw/7; 80ebev is released from rest starting at an angle of/y/clecw38e; b+ pubcl7jn0v 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 yt(a)0we bkmidn:ba(z4w t ;(boat every 3.0 s. He measures the distance between tb(4zt(0anm i;ewd) ya: (wkb two crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frf 1xk/61cn rnxequency of 262 Hz and travels with a speed of 343 m/s nxf6x 1 /krn1cHow far apart are the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and yxs(2yo 2gs7u 1600 kHz (kilohertz) and trau2(so7ys yg 2xvel with a speed of $ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

  Calculate the speed of longitud: vr 8rxf 28tb 2ooxu78fls+j( 3iqkfwinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic moil 5k15j r5cmtpr:a6d tir+:ydulus, but one is twice as dense as the other. In which rod will the speed of longitudinal waves be greater,t1p yimkic5rr6: 5+5r:jatdl and by what factor?   

  A cord of mass 0.65 kg 8y(b q gmb k8vf4ns;,zis stretched between two supports 28 m apart. If the tension in the cord is 150 N, how long will it takemzvy,(k48 bn bsfgq; 8 a pulse to travel from one support to the other?    s

  A ski gondola is connected to the top of a hill by a sxg6i gdh3iv05m: u4/biqt, gfmi)1b s teel 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 an/: 6m 1tfgi4diqbb), 0ihg3 isxumg5vd 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 sea. y82sv2pma8w +ta2x7 q 8dulyx He hears the echo of the wave reflected from the ocean floor directly below 3.0 s tw7x vax8al+yup28 dym8 22sqlater. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel atfp()e4 xnrfs/w u)r x4x 7iw-m different speeds, and this difference helps in locating the earthquake “epicenter” (where the disturbance took place). ) w4exxwruf4npx )/m(-f 7rsi
(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 tm(o c;1izg-.vw .lsoapproximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitutmv og-(.1isc wzlo.;de 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 ay 7xbp,0nljt+ n earthquake P wave passing through the Earth and detected at two polypbtj + ,7xn0ints 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through th+fmx jzc8oz*9qwg.0 emwo d 2/e Earth is measured to be e9 q2jx d0c*+/ gmmzoww8.fo z$ 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 travyq tm; uw-c(r3el through the same portion of the Earth, but onut(-w3qr ;cmy e is carrying twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretcheoqx3r ;pm6* ltd 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 waves? qo*x;t6r 3lmp  

  A bug on the surface of a +m nrn71: 9*znjkmyxupond is observed to move up and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm, by what factor doe791 zn+y j:r xmnumn*ks the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward eac7fz3pz 48yyjbh 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 straight. What has ha3f8zy4ypb7zj ppened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundamentalsgg-pm* ih f,0 frequency, what are the frequencies of the first four -g hg,0sp*mif harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 -ezm hje9yiom8z4m q7 -bwxa6 ,.oyu2Hz when unfingered. At what frequency will it vibrate if it isbyq7om9 o6az.,8u2yei m- xwe-jh 4zm 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 at a frequency of 280 Hz. Name at l)b r6b 6z)mppqvcwaxll844) p east three other frequencies at which it will rz l8p6 )4m)p)lwcbb v64qpaxresonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a strfz1uj6 j5p;.qkuawd(pn s(02 ybh1zb ing is 92m/s If the frequency of standing waves is 475 Hz, howfu0 2jp z6upjs((1kw;h a . ynb1zdb5q far apart are two adjacent nodes?   m

  If two successive overtones of a vibrating strisdc2 /ve/q i6png are 280 Hz and 350 Hz, what is the frequency o /2qdcs6v ep/if the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distance f (g7lagr;vw9 wrom 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 frla9wvg;gw( 7 irst two overtones?    Hz

  A particular guitar string is supposed to vibrate at 2 w;uh(7vt *:z8 tnmc3fspvh1 x00 Hz, but it is measured to vibrat7fu8twshv(phnm v3 txc;1z: * e at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hz, but it is mb hzoo4 ia5 :ghkg;+c;easured to vibrate ao;gk4oah+bh 5zgc;:i t 205 Hz. By what percent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a.mkw s lzyi-2wf19 fdhx,)3 un small-amplitude mechanical 60-Hz vibrator. The string’s masshsdwux nm 3- i1 9yfkf2,)zlw. per unit length is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of the string may be adjusted by moving the pulley.1 +nlv /vou5dr If the5 l1o/du rvv+n hanging mass m is fixed 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 the right freqkwisu85/gt5- syw q -0s srdp12bi5tuuency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wsi i-p5u85uts/w1 5sybs rd2kt0w-g qave 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 boq)cz8 htvcqs,..3 mwe undary within the Earth between two kinds of material. If it approaches the boundary at an incident angle of 47.evscc )3. w ,8qmtqhz $^{\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 t.7vzk/cn 3uh khe velocity changes from 2.8 m/s to 2.1 m/s If the incident wave cresun hv73kz.kc/ ts make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warmj4 9knc:mz) v)bl qwii;hhi- ko2)a0r air when it hits a layer of cold, dense air. If the sound wave hits ow)ah ) kqkbl-v4i)9hr0;jmii2 :znc the cold air interface at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave strikes a boundary bet-r t0iwrkm3s0ween two types of rock at atkm rri -s030w 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. kz3fmc46rr:tm.e rz21znh9 l According to the user’s manual, the dish has to be pointed in the direction of the satellite, but an errze1kr cr2: ltfz4mmr n9h .3z6or 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 wavelengthd9 tskqdef s8;b48l (u 250 km and velocity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, pe8(ds;eu qld8kf 4st9bople 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 stiffnesr; d h :upm(/ecoe(/cbs 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 (approximatehre: /(pmebc(;o/ cdu ly 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire n8 c-smco4da)d et 18 m below, which stretches the net 1.1 m. d4-s 8cmdaco )Assume that 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 placed on the end of a freely hanging spring. The mass efuhy(1bb+1+oe+f;zy:yi lo5iaglv w i;-p +then falls 33 cm before it stops and begins to rif abeibl1o+ + viw+u+;;flo-zi(g1yyhp e:y5 se. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes aye/ns ;aks16 a huge spring at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffness con 6eysas1ka/;nstant 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 o y;scq3 uu):aif coffee (diameter 8 cm) at just the right pace of about 1 step per second, the coffee sloshes more and qaiusu);c 3:ymore until eventually it starts to spill over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the center of )4k7m8y0ozpl ps km0u a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequz7mk 8okp 4yl0sp0u) mency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according( n )1d qw15csk7zofr dc8d-mh to the equation x=0.650cos7.40t where x is in meters and t inkmrc 7)c1d8o q(sdw1ndf 5h-z seconds. Determine
(a) the amplitude,    m
(b) the frequency,(round to two decimal place)$\approx$    Hz
(c) the total energy,(round to one decimal place)$\approx$    J
(d) the kinetic energy and potential energy when x=0.260 m.(round to one decimal place) PE$\approx$    J KE =    J

  A simple pendulum oscillates with frequency /+ xjfui r)qt-f. What is its frequency if it accelerates at 0.50g (a)u jfi+qt- x/r) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on the h v/5yv 1 vep3+ew/+sywv7 ploraft, it sinks 4.0 cm deeowv/e+/ e1pv + sywpv5yv7l3hper 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 twf vepav zf 97 -b-tza9)3wug0uned to play at 392 Hz (G) and 440 Hz (v93faz-ta7wz b v )fg-upwe09 A).
(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 stretchedela) dr6ht ,4q/ qekjz)5roa - two-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the sam-5 qqa /,oae6 zd )4)tkrrehlje 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 264 Hz, and the tip of each prong m 8oha5aeocq(-oves 1.8 mm to either sidca5ah-(q8oe oe of center. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates wi+o8: es + hynpgons52ith simple harmonic motion of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebbhgss+ip:5n28 +y o oenle 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 attachedo 48:mf8w, jbctjkmq f8j1mbb2gdw3) to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine fkm j8jmb)bb3 g mojt8wq:248f wc1d,the wavelengths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each one- z .lb;gf3-u/5e j ayttjypks07u:4luh9x5xvway swing takes 1lxyzu;sf tuhayb 0p / :k543j5.l t j-xu7ge9v.000 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 sa4+,ugy -mahj;2 mcpax i- js7pring can oscillate in the vertical 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 ap,; 4j7y-j2ua-ag+ mihs mxcperiod 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 tek .ugjmx76 jl zp 58:lq(4ffjonsion of 255 N. A pulse is generated at one end, and 20.0 ms later a second xl 8zu6lpfj:j74o 5kf.q(g mj pulse is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling bx2n/y as-.sroy a spring with spring stiffness constant k. A prs ao-s 2/y.nxenny 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 block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel crane cab,fka* )wttatec1/t vq5kr; i+le 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 bouncing? [Hint: Refer ak r,1ftcv+;*5ttitaq ek/ )wto Table 9–1.]    s

  A block of jello restq *p7dc.jaa. ss on a plate as shown in Fig. 11–58 (which also gives the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrate. In analop. a.d7saqc j*gy 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