Give some examples of e7rjfb(2 evevp(b0jx :veryday vibrating objects. Which exhibit SHM, at least approxibe0(v j xr epfj72:v(bmately?

Is the acceleration of a simple harmonic oscillator ever zeroe,zl2v 9 ttsijj7r6ou3:p-s b ? If so, where?

Explain why the motion of a piston in an automobile engine is approxzmc1;cqi xlmt(3:rh /imately simplehlmm3 (;qzrt 1cx/: ci harmonic.

Real springs have mass. Will the true period aoho(8 )/h xuo6a gttx(nd frequency be larger or smaller than given by the equations for a mass oscillating on the h8 ogu6ot a/x xt)(ho(end of an idealized massless spring? Explain.

How could you double the mazh+b yaz 3 zkl1l:)hs-ximum speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scale, and then is a/ulqvx - kmgsj3k*t7c95d z 6released. Describe the scale reading as a function-c 9v6ql5* m tdks3zxa ug/7jk of time.

If a pendulum clock is accurate at sea level, will it gain or lose time when 9n tailv7pgm mf0(9c7 n5n9 ihtaken to high altitude? Why i(p5 a9th0ncn9g im7mlfn7 v9?

A tire swing hangingy3rcz 4vx bwyf (v1m91n (ax1t from a branch reaches nearly to the ground (Fig. 11–48). How cou rwyty3(4v1xa9 b1n( 1mcxvfzld you estimate the height of the branch using only a stopwatch?

Why can you make water slosh back and forth in a pan only if yow/ z+ (fmy0cs yyg92xau shake the pan a w 0(yc a+m2fysyx9/zgt a certain frequency?

Give several everyday x+umf2ar*+ gidiz3 oug/* +bmexamples of resonance.

Is a rattle in a car ever a resonance p8n x60 ou)ly;l/vfqf0u)aoy qhenomenon? Explain.

Is the frequency of a simple periodic wave equal to the frequency of its s zhjh.yjk33b)k 3 ;ckfource? Why orjh3 ;y c)fk3b 3kjhz.k why not?

Explain the difference between the speed of a transverse wak v8gw wra.m9+ve traveling down a cord and the speed of a tin8m9.kawgw +vry piece of the cord.

Why do the strings used for the lowest-frequency notes on a piano normally hae83p6q yv6zqi ve wire wrapped aroqez668p3 q vyiund them?

What kind of waves do you think will travel do u 0(ke2hxll hq3fhp1/wn a horizontal metal rod if you strike its end (a) vertically from above and (b) /u1hlp e khfh0xl 2q3(horizontally parallel to its length?

Since the density of air dj yzpbf)7q g;jnu*35tecreases with an increase in temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves in air to vary with temperatu fjb5)uq;z*pty7g 3j nre?

Give two reasons why circular water waves decrease in amplitude as they tr4r su.egj; cyw0-j d4navel away from there;.cuj4 y wgds0j n-4 source.

Two linear waves have the same amplitude and speed, and otherwise are ident erdtqxfzgfx7-, ;56 sical, except one has hafeg xf,r-xdt;qz6 s75 lf the wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sections o ;qhg3kv:mr un;.j7j: 0 vx,fsclz1puf cord as in Fig. 11–;1 fugv3mq ,slp;:kcv7 hn rjxu.0zj:33, the frequency does not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, a9 yw;b)m5gky mkv ua25k3od l;6f(e tdre there any places you could touch it with lugy3dk ) m6wk ak5yv(f5ed;2o9bmt;a knife blade without disturbing the motion?

When a standing wave exists on a string, the vibrb s, hy* z)aio6+j2klmations of incident and reflected z oyb2mi6ahjk)+,* lswaves cancel at the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one place to am(bnds)4gu /h nother, how might we determine whether the energy was being carried by particles (material shd/g u(n4)mb bodies) or by waves?

  If a particle undergoes Sm( gh-4dtl 1keHM with amplitude 0.18 m, what is the total distance it travels idhtm kegl(1-4n one period?    m

  An elastic cord is 65 cm hwloe 9 pe 6;yu-56ke/b (bodplong when a weight of 75 N hangs from it but is 85 cm long when a weight of 180 N hangs from it. /ep ue9kwo5 bp6 obye-l(6h;dWhat 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-kgd*v,kcvq9e/m-t t8m b driver gets into the driv 9t-/v*mvcb8kmted ,q er’s seat. If the car goes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs fromay,s5q66qcald t cbl* -k*;zx it. (a) What is the*5lqs q,c*a d6k-b; ca6ylxzt spring stiffness constant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a frequency of 3.0 Hz when a mass of 0.60 kg is8d : 6/ubac 8zjrkgr1z hung from it. What is its frequency if only 0.31dz8a r:8/zrgc6j kub 8 kg hangs from it?    Hz

Construct a Table indicating the posit2zm1tm-g: cf mion x of the mass in Fig. 11–2 at times t = 0,t 2gf:mcm tm1z- = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 g2 zc/p5o4xrfn is caught in a spider’s web. The web vibrates predominately with 24/zpx ron5cf a frequency of 4.0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a spring vibrates with a frequency of 0.88 Hz. When an ad ehlzi9k3 / ,qcdtxn4z +kgh*-ditional 680-g mass is added -qhx e/*zlct9d 3k+g, n4zkihto m, the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per wd:7z pnv44l,1 +60cqjhbo hw +zzdeysecond with an amplitude of 0.13 l nqw7o04yc6+b v h,ze+zph4zjd: 1dw 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 a SHO half the 106xkgu w9wy zldi (3gmaximum valu9l kzwg( 6wgu0dy3i1x e?$\approx$    A

A mass attached to the end of a spring is stretched a 63vi d5nk0 spypj +bg*distance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretches a vertical spring 0.315 m. If the spring is aba(y/*2qo; nb9 tsxw stretched an additional 0.130 m and released, how long does it take to reacht;a/ bbw(q a2syo*9 nx the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring :c lx7bk2r-m c*w-rdk with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object ik rcw ckrmd* -xl-2b:7s 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 the 1 ,a 9bgorov3xda c 0gg- hsd8)rydn(:spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will the ball leave tg,-v3a cbodng:8hrgdr a dy()9 x10 sohe gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to one 5i8v kiy,fz- v ,j(xfyend 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 withy,kiffivxv z8,j5- y( 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 accobx,y+ j6+y cwqrding to the equation x = 0.45cos6.4t where x is in meters and t is in seconds. Determine 6cj, y ++xbqyw
(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 equilibriun2lou 1d4 vnk:(gp5xum is the energy of a SHO half KE and half PE g52lxvk n(up n:14oud? ±    A

  If one vibration has 7.0 times the energy of a second, but their frequench tv/fso/ ,tnti+,kina5 a,*-4qonxbies and masses are the same, what is the ratio of tho,5a - *v n nit+fah/o,txtbnqi4,/ks eir amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light spring once everye 1:xcu x3ncw+l*su,mk7 so ci/8e,rs 0.65 s.3lc +m:cskicxn xuss8, 7*e1 o,uwr/e
(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 identical parallel verticassdu( k s406hol springs, each with spring stiffness constant k (Fig. 11–49). What will be the frequency of vibratio46hsuod0 ks( sn?

  A 300-g mass vibrates according to the equation x xxp1wv+g m9r6= 0.38sin6.5t where x is in meters and t is in sx rwv+m91xgp6 econds. Determine
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows two examples of SHM, labeled A and B. For ez )f.1te8 ipriall )v9ach, 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 e -te)aa7i sih,hgph+9nd of a horizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.96m/s Deta9pah +)e-igt sh 7,ihermine
(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 a,p bworgeh q4;;-b6pstiffness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The m,arwq-pbobeh4 ;p; g6ass 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 sprin509ja:a h,fvxqw;o s bgs, 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 jy.uz63 79zgawm) h mzattached to a fixed horizontal spring whose spring stiffness constant i6za7u)mhwjz9gz3.y m s $ 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 reach x8mh*qivq29 s, zm5gcing his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 2qc9z s,*mvm x i82qgh55.0 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 vibrationr* +j74 jp)k0,r7:yolf3xhkq h evvahs in exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple penb9l:6 +biwli jgd8jk4( d7 yfndulum be if it is to make exactly one swing per second? (That is, one complete vibratiol dlbny6fjbi+78:ik4 g9dw( jn takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its perdw3e.9 7p si.iqhz44ykkmc.diod on Mars, where the accele wqi. e.k k3z44imcpdds.7y9hration of gravity is about 0.37 that on Earth?    s

  What is the period of a simple pendulum 8)+aet lx8 ny.1 kjow-ra3re4z 0 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simp 3 um).dsxk2; wks(cnsle pendulum is 0.760 m, the pendulum bob has a mass of 365 grams, asskw3(m) ;xskn .cud2 nd 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 of 0.9930 m. Ifpo5ml4w8zb*/, j08rh uu y dvk the clock loses half a minute per day, how should you adjust the length of the pendulum? shortened buz8pw8d,k4 0 m hu/5ovl*rjy by    mm.

Derive a formula for the ma;b+l*f vs9c4mid*xx s ximum 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 2.5 Hz. At it is released frogzr.k3 kiwxihe.b; *,m rest starting a. zk 3.i ,hxwbri*g;ket an angle of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests pass the bow of his anchored boat evehllhpyiz-d2,c* 4ukpm. lj- 8e7m, cxry 3.0 s. He measures the distance between two crestl 7ljp phm,-zui 4de8lxm c*.-khy,c2s to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with a sps1( q.i/s- ujangq,qg eed of 343 m/s How far apart n( ,1qu -/asgq.iqs gjare the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 i1-bker2 gb.5cydqn3 qas ./lru-k ( tkHz (kilohertz) and travel with a s31q2se/ ibgdl .-t5rckk a(ybunq.-rpeed 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 waves inbe ,1)8(fc/sk v2tk plxz t)mj
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the sa:6mqduk;v -bgme elastic modulus, but one is twice as dense as the other. In which rod will the speed of longitudinal wakg-:mdu6;v bqves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched betyq.nk ght q6 os n3 +nbf)8p4l/zw5sr0ween two supports 28 m apart. If the tension in the cord is 15sfz) o0l q6hy/g8wrk53 tb.snpq+4nn0 N, how long will it take a pulse to travel from one support to the other?    s

  A ski gondola is connrq 232 cni45e9htcm iiected to the top of a hill by a steel cable of length 620 m and diameter 1.5 cm. As the gondola comes to the end of its run,ein34m 2 c29trih 5qci 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 sh/)x76wkcrh ctip just below the surface of the sea. He hear/6rc) ktc7hw xs the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel )f+;isoxr u-yvc k9+x cx ;z)59y zpdr0jzfx6at different speeds, and this difference helps in locating the earthquake ; zzop5frj); duxck0sr++ y)c9f 96v-xzxyix“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 approximg59v*gntpvyhpxt(a+ 8 *h : hgated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of fr*x59t vn g at+ hgpph:g*8y(hvequencies), 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 i9;x5r2br82 (akbhc3niy,fea sw/ lahw.m w: hntensities, and (b) the amplitudes, of an earthquake P wave passing throuc hsh5w2,; (9 wyk/ 2b8x.amn:bwrf aihlar 3egh the Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthq w4rtk .;het,yuake wave passing through the Earth is measured to be wh .y4 tkre,;t$ 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 frequencgmgr5a d,/pom+ m q96tom.n z7y travel through the same portion of the Earth, but one is carrying twice the energy. What idmmm75g,n .96goamtpor q +/zs the ratio of the amplitudes of the two waves?   

  Two waves traveling along a72/0s8 )0pgu getbe8afjupzf 3czr ,q stretched string have the same frequency, but one transports three times the pow/jp)p237 s a0zc0geuzuqfb88,rtgf eer of the other. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move up and down a total vertical+sgt9 lr) wf.uqy ),xe distance of 6.0 cm, from the lowest tf,9g t+w)) xlu.syqre o the highest point, as a wave passes. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each other. (low,0ete7cl ,o n6h- ha) Sketch the shape of the string at the moment they directly ovet6leho7e ol0cw ,,h -nrlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as mz33 nihu : pfvbf2j((its fundamental frequency, what are the frequencif(mni fh:v3j(z2upb 3es of the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what frequency willndh/ m obxo387 2zrr/u it vibrate if it is fi oudxr /bh7 rz23o8nm/ngered 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 afeydawnm/z:)ws: d;*r+ vx2v frequency of 280 Hz. Name at least three oth:+vns : yvx*r;f2d)zad /ewwmer frequencies at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If th0nh(pc 4 hx .sdh3/xwnop5oc2 e frequency of standing waves is 475 Hz, how far apart are two adjacent nodpd4 0( o5ph nxhhc./2wcno3sxes?   m

  If two successive overtones of a vibrating string are 2e9;h w*d,qh yx4dx .vu80 Hz and 350 Hz, what is the frequency uehxy,9vd ;h*x 4 w.qdof the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The dis; ,ivnc42qbfb,c llh -tance from the bridge to the support post is L = 62cm and the b,n v-;24lh fqblcci, string is under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, but it is measul4np b+u.wss1 9s uc7kred to vibrate at 205 Hz. By what percen s cn7wuu1ls4.psk9+ bt 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 sq- qv7lva,xtk1 ) v3umjexz dqtg358zj:-j i8upposed 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? de:3i xmju8j1)q8 z vagexlz-qdtqj,k7 t- v53v creased by    %

  One end of a horizontal string is attached to a small-amplitude me :n(otg8yvp i jr4;7bichanical 60-Hz vibraton; iog b:r8i t7pvy4(jr. The string’s mass per unit length is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of the string may be b(z 1qvnca rd5j*n1/c adjusted by moving the pulley. If the hanging mas*15n (badvcnjz/ cqr1s 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 b pty,k5hle8mb,iykav;k99- zack and 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 produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. Whatyp9 ymhi- ,k8a, ;tzkle 9vbk5 is the speed of the water wave?    m/s

  An earthquake P wave x/2huidb v88z traveling at k.0 km/s strikes a boundary within the Earth between two kinds of material. If it appro88hx u/z2bd ivaches the boundary at an incident angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwate,tfrh(21r-qwaaok ot hf4 39 .lqa/ dmr “shelf” where the velocity changes from 2.8 m/s to 2.1 m/s If the incident wave creslo f9qta1hfwkr/q-2,r a4ta. o(dh3m ts 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 hits a layer of cold, densepk o-;ix+nb hhs6z3z, air. If th6h ok;s+x z zpih3b-n,e sound wave hits 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 str vg4-ddttufvhr9a , ; 7vr0-naikes a boundary between two types of rock at a 38vfn9-u r0rvgd-taat4, dh;v 7 $^{\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 diamet)f ,5 1)eqc .ywtiugpjer. According to the user’s manual, the dish has to be pointed in the direction of the satellite, but an error of abou.g)5) uwfi yqce1p,tj t 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 travels acrosd: q*lu js en1(cz0g0js 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 and warning, people have die ucl:nz0*e (0djgq sj1d during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring s+zt ct k2p f5opymzf6,;w 9b1ztiffness 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 ;5m9,6w b ozk pyz+c2 t1tpfzfm/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 stj8gu8e znf;j,v z pu2bx*j b1q)*8gd tretches the net 1.1 m. Assume that the net behaves like a simplebbtdf)pz gvju n2u gjj e*8z1 8*,;8xq 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 the9kfsr 8y zp./hfv/tnng j9* ;hed7oi(n falls 33 cm before it ;sdk/iy ft/z(9.8gnjo p e*h9nhrvf7stops and begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge sprp 0e ku eml1g7rri3nbsp ,;whht0u4:)ing at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What iilhg,b) 7 r4; re:w 1uu m3npehp0kt0ss the spring stiffness constant of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of cofb w3h i,yjs8sgn w7t07sq+tz3 fee (diameter 8 cm) at just the right pace of about 1s3 h7j7t 8zgw 3i0q+ybw,s nst step per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the celd 6y*f l .unk4toaq,:vsc, (onter of a 33-rpm phonograph record have a wavelength of 1.70 m* a ,6ulof( 4cv ,qdotsnyl:k.m. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to g)x 1xtw k:jqb8 wmn+*-g daw4the equation x=0.650cos7.40t where x is in meters and t inw:1g4j8b+qxgn td)wk w ax*-m 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 frequency3aywf qt :b /nv9hc1vm12kue/i,pr+ w f. What is its frequency if it accelerates at 0.1 v/1vbcmyw i ,wutq/3 k9en r2a+h:fp50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on the ryg o+py2 c fdjhuodx8qs:v5 2;r-58cwaft, it sinks 4.0 cm deeper into the water. Whe jd df h8q;s8yorx -5w:2 5gcv2+cpoyun he steps off, the raft vibrates for a while.
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a musical instrument are tuned to play at 392 Hz (G) and 440cc,ovwb/ -8zp Hz (A). c8oc,wpb/vz-
(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 ,fxc;poh5/wxp.nfj( ohlb (xj+7 j( kthe stretched two-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wave;xpp(njk xw(bo7+5l ch xj f./fj(h,o length 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 proq7jswg8 j4ce o07 z2a- cjf-c/ 2bmlydng moves 1.8 mm to either 4bj 7g-z cm e/ y2cdo2lqw-7j8f0jscaside of center. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simple harmonic motion of frequen+wf-: pr h,d vagd31vo3uyvv;6 ztu)ccy 1.5 cycles per second. 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 bvuyrzw,c;f 3v) hdg:dtuv 3oa p+6-v1oard during the oscillation?

A string can have a “freec2n a .ks ec)/q2)onpu” end if that end is attached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with one end fixed and the other freeonqp)k.a2) /nue2 c cs.

  A “seconds” pendulum has anz:ik 38 u;mtc period of exactly 2.000 s — each one-way swing takes 1.000 s :8kzm3nic; tu.
(a) What is the length of a seconds pendulum in Austin, Texas, where $g=9.793\mathrm{m/s}^{2}$    m
(b) If the pendulum is moved to Paris, where $g=9.809\mathrm{m/s}^{2}$ by how many millimeters must we lengthen the pendulum?    mm
(c) What would be the length of a seconds pendulum on the Moon, where $g=1.62\mathrm{m/s}^{2}$    m

A mass hanging from a spring can oscillate in the vertical diw ,a;ygqgj .2frection or can swing as a pendulum of small ampljgg;yfaw q2,. itude, 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 tension of 255 to y+;yedx9- fl)rasd2 y dk/3N. A pulse is genex9o;/ s 3efrd)dy2yytka+l-d rated at one end, and 20.0 ms later a second pulse is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended fro*vm,tsw 9 hf9c-;kwdem a ceiling by a spring with spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillations that will allow the penny to just stay on top of 9w*ed mw-cv;hkf ,9stthe block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. Th1 3vu za/ywp(te steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cabp/ ayw3u1 tzv(le. 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 Faj*e/drs+ qz,9sf 0 ja:vlgt;ig. 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 analogy to a mass vibrating on a spring, estimatgs:9e j faq,d zjvl0;/ +tas*re 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