Give some examples of everyday vibrating objpyq2ipa t*f 70ects. Which exhibit SHM, at least approx7q pfpyta2i*0imately?

Is the acceleration of a simplep f 97mnthkhe748lf e1 harmonic oscillator ever zero? If so, where?

Explain why the motion of a piston in an automobile engine is apprmw4, dvm:l.h6p g-e kaoximately simple hae:p v,ml6.dh 4mkwa-g rmonic.

Real springs have mass. Wilypxv+/3l d3x g5yi9o ol the true period and frequency be larger or smaller than given by the equations for a mass oscillating on the end of an idealized masslessvg/l px93odi5y3x+ yo spring? Explain.

How could you double the maximum speed of a simp7f.4 u)kpzdjn le harmonic oscillator (SHO)?

A 5.0-kg trout is attached to twwt 1a,ivavm9jx(/ ;da(e-g bhe hook of a vertical spring scale, and then is released. Describe the scale reading as aavv(/,mw(9j x 1gdtabw-;eai function of time.

If a pendulum clock is accurate at seppk;.6m 2 u*hmyxv1kp.wy m 9ea level, will it gain or lose time when taken to high alti6pxu*m.k hv 9.myep m2wy k1;ptude? Why?

A tire swing hanging from a branch reaches nearly to the grw)b;-are ( if4ijnf u)ound (Fig. 11–48). How could you estimate the height of the branch using only a sti in (f-ue)wbraj 4f;)opwatch?

Why can you make water slosh back and forth in a pan only if you shake tjot9znp ., pj rtfh;.*he pan at a certaj*.,prn9 ; pzthjf.o tin frequency?

Give several everydat+ -yh9e n1mpmy examples of resonance.

Is a rattle in a car ever a resonance phenomenon? Expla4v i4b9f6zvhwpuj2d 5in.

Is the frequency of a simple periodic wave equal to the frequency of ittqu do)dza ia6w6 ,(;os source? Why or ;azqwidod6)o t,( 6a uwhy not?

Explain the difference between the speed of a transverse wave traveling down94m m 1obqadc6 a cord boc64qa md91mand the speed of a tiny piece of the cord.

Why do the strings used for the lowest-frequency notes on a piano normae+yl.s-nwe bbg/ 4sc9 lly have wire wrapped aroe4ns+ 9c.eg/bsw l-byund them?

What kind of waves do you think willl82e hkljbb/ al n;x,8 travel down a horizontal metal rod if you strike its end (a) vertically from a8l;l 2k lxeb/aj8h, bnbove and (b) horizontally parallel to its length?

Since the density of air decreases with an incny cinq au5; 7ng421n6eu1y jfrease 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 qj 7;n14y6a2fe51 yuni ngncutemperature?

Give two reasons why circular water waves decrease in amplitude /)nr09ag ih f,edf; o+vdvv5 tas they travel away from the s5ov)h0v v;efrfd+,nd i/atg 9ource.

Two linear waves have the same ampdr;+ 5,-weeqrwo bq 4tlitude and speed, and otherwise are identical, except one has half the wavelength of the other. Which transmits more energy? By what-ewt;+4q wqdbr re5,o factor?

When a sinusoidal wave crosses the boundary between two sections of cord as vh+cil u2d,iu *ov* 2ein Fig. 11–33, the frequency does no*o ec,22+ihdvuvl iu*t change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there any placek-ntik- -b 0y.7gscues you could touch it wittyck n.-g- biks0-u 7eh a knife blade without disturbing the motion?

When a standing wave exists on a string, the vibrations of incident anh,dy n8q:s-atd reflected ,a :tqdh8sny-waves cancel at the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy w/8)2b q4-y rfgnbai3x7px xm las being transmitted from one place to another, how might we de3xbi4 -)mqpn ax/7bf8g2x ylr termine whether the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is th-5 6 ,fb 7wsedeic9hhqe total distance it travels in onehs qee, w5-bhdf 6i7c9 period?    m

  An elastic cord is 6(p6a/dycsv,nqkrwu1 f qx 2 n8 -*w.fa5 cm long when a weight of 75 N hangs from it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” constant k of this elastic cord p,sq2-f .d cwu*(f/wnavq x861yrkan?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg drivervwx-ks)jpi+l(3cx / 4gl9smf gets into the driver’s seat. If the car goes )gxw -i3l+4(/pfcsk xlvs9m j 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 4n5 aasg8f f2rb7 aez,hangs from it. (a) What is the sp2bgs7nf8 z4e,a ara5f ring 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 pg6p2ya3ny vg1a0r;v of 3.0 Hz when a mass of 0.60 kg is hung n01p23a yr6 g;yvpvag from it. What is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position bfzqkvq+a,.qn* brx4iu* 8)j x of the mass in Fig. 11–2 at times t = 0*qi, r*zfujn+8 4v)axkqbbq. ,t = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

  A small fly of mass 0.25 g is caught in a spider’s web. The web vibrates y0nts 3,u;hnv4rp7x x predominately 3 ruxyts 4;7nxn,pvh0 with 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 ofi3;t3 l npbq2z 0.88 Hz. When an addi;lzq23b n tpi3tional 680-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 of a spring vibrates 3.0 times per second wd rprui7k6z-at 4/w0rith an amplitude of pr7 /4-ta6r 0ur izdkw0.13 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 a SHO half the maxim w;6o 4/kxn4vddzvkzc0 sf0) 2ifm+awum value?d+)0mvwofif2wa ; dzk640 /vk zncxs4$\approx$    A

A mass attached to the end of a sfu5ym9 z uhwy8+ r65l ;vm( qdjs)zkl3pring 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 c1fh2 lsc(17ykimgwog* zc-*)alu: v vertical spring 0.315 m. If the spring is stretched an ag1h*)72sk: om*- wlc(vuc yi za1f glcdditional 0.130 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 to a spring with spring stiff8 vx(2 kmifhrbu w8e0gz +n:q/ness constant k = 280 N/m and is executing simple harmonic motion. When t 2e w+z:iufq0nmgxh(8r 8/vb khe object is 0.020 m from its equilibrium position, it is moving with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compress the spring of a toy popgun- .jy4 tdnhx-qyiu,z0 mj;qqtccf0kqb2q 3 7 5 0.200 m to “load” a 0.180-kg ball. With what speed will the ball leave the gun? q4j n3my;xfu2tc.q0 q7 bqczhd0-kjyt5-i q,    m/s

  A mass sitting on a horizontal, frictionless surface is attached to one end+p;-wyfzdvffb7 s ;* o of a spring; the other end is fixed to a wall. 3.0 J of wobzff +v;;w*o fp 7ds-yrk 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 = 0.45cos6.91icg y l :1p4ro3asbu4t where x is in m3i :c bo19ps 4aygrul1eters and t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equilibrium is th:mzcn+1y y ik,e energy of a SHO half KE and half PE?1,yc miz:ky+n ±    A

  If one vibration has 7.0 times the energy of 8nbnc ro3 8w*la second, but their frequencies and masses are the same, what i rnbnwol3 88c*s the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hansfsinn .o7 zlg ; b/a00on7f3eging light spring once every 0.65 s. 37o nebf0g/as . nzo07s i;fnl
(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 vertical springs (/pkv cnaqoaa8j/ 7y:, each with spring stiffness constant k (Fig. 11–49). What will be the fja/p / qoank7:8a(v ycrequency of vibration?

  A 300-g mass vibrates according to the equation w8x1m9 hw9t imx = 0.38sin6.5t where x is in meters and thw1 99 wtmixm8 is in seconds. Determine
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows two examples of SHM, labeled A and B. For each,bgi + )ak3 aa-lo3h*of 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 endisu4ej;6mbnm mzk w v72bk6/+ of a horizontal spring (k = 124 N/m) is struck by a hammer, which gi 46/bk6bm miwk7v;z2e m sju+nves 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 vibrates with aa 5lx6e,lxik9kn8 a+on amplitude of 28.0 cm when 0.260 kg hano6,xa 95ekallx+ 8in kgs from it. The mass passes through the equilibrium point (x=0) with positive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two springs, with spring stiffness consta,-u xt5m*nrtmnts $k_1$ 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 fix( xhx7g5m 7,xh gdwl2fed horizontal spring whose s 7xdxm(wglf,h5x 2 h7gpring 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 ma2cqjl,-y bq (tss 65.0 kg jumps from a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate theyqc,t 2( q-blj 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 exacug- g*ve iy+7*1wcgw 6 d13vva:q aawitly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum mb xqko ( l7:n*n3dhfza0am.* be if it is to make exactly one swing per second?b fxz(:oh nlk 7 mda.**3nma0q (That is, one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on Mars, wherenjhnh24nab/ ,roh *lc bvj,v 8pp()l4 the acceleration of gravity is about 0.37 that o/lpan(nn *cljo ,2v vh4b)8hr hp4b j,n Earth?    s

  What is the period of a simple pendulum 80 cm long 1lk9gb7mu, lr
(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 pendujgnv dsi 2wkt5-+(e0(k uk.jclum bob has a mass of 365 grams, and it isit(uk-.+ec j20s kwvg(jn5 kd 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 ; z.w wl:je:nka length of 0.9930 m. If the clock loses half a minute per day, how should you adjust the length lnk ze;:w jw:.of the pendulum? shortened by    mm.

Derive a formula for the maximum speed 1; tfcm ,nm99c 5gyrzzf 52wci$v_{max}$ 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 ;qqwmhtd:-dxft *s 6 (bnr,9u frequency of 2.5 Hz. At it is released from resr-u(fw nd 9d6q*q: bt,h m;sxtt starting at an angle of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests pass the bow of his anchored boat evf+cwvmi h0/i/ery 3.0 s. He measures the distance between two creivf +/ h0cwim/sts 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 wr e2(*mq gmcp;:doot21l(ng r 9 y:uamba- )dlith a speed of 343 m/s How far apart are the wave crests (compressionyuonc:ql9mob-d2 r( a(1;agrpg :*dlt m2e)ms)?    m

  (a) AM radio signals have l2m di8lx(x7mfrequencies between 550 kHz and 1600 kHz (kilohertz) am78 l ixxmd2l(nd travel 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 longitudinal waver r*u*n) x*br+zjqk p/s in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one is*zh.cq1;gkw4vex4 rt7 r;d.c9 (cnbm-eu gqh twice as dense as the other. In wge(m1 .7;tcrw-dnvrq 4h.c4;qcebh9 k u *z gxhich rod will the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between t71oexq22s jz nhjy8)mh ez6yz5e 1b4) e1 lkfjwo supports 28 m apart. If the tension in the cord is 150 N, how long will it takjyn)4me8byh 11jsxqe71 )5ez2f o2lj z 6ehkze a pulse to travel from one support to the other?    s

  A ski gondola is connected to the top of a hill byml 4,ev0wei ,m a steel cable of length 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and sends a wave pulse along the cabl, evew,lm0 i4me. 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. He hiqauce)f2 pa9.u; nxua u:g3 8ears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is the ocean at thi;a8ia2 u3gu9nqpce)x ufu:. as point?    m

  P and S waves from an earthquake1s-julbor5whify: 1 -l 0v,rl travel at different speeds, and this difference helps in locating the earthquake “epicenter” (where the disu rhs:li5v10f--bow1jryl, l turbance 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 by a sinusoidtnu8nh. u0 zp*5,m irhgr9. noal transverse wave. Assuming a frequr. tn8i gu5,* .umohr9nz n0hpency 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 yj s bqv)r2+)39swd xdamplitudes, of an earthquake P wave passing through the Earthx2 v)b +9swry d)dqsj3 and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake w-72kenc ; xgkpave passing through the Earth is measured to be 7k-2 gpek;cn x$ 2\times10^{6 }J/m^2$ at a distance of 48 km from the source.
(a) What was its intensity when it passed a point only 1.0 km from the source?(round to one decimal place)$\approx$    $ \times10^{9 }W/m^2$
(b) At what rate did energy pass through an area of $5m^2$ at 1.0 km?    $ \times10^{10 }W$

  Two earthquake waves of the same frequency travel through the :pbw wcpkee2qv3 k8le5x. 1,qsame portion of the Earth, but one is carrying twice the energy. What is the ratio of the amplitudes oepec123l:wwpqb e.k58 qxkv ,f the two waves?   

  Two waves traveling along a stretched string have the same frequency, but l4gm+nirkk/c8 i q/kkrr;(1qone transports three times the power of i 41k/+rm(iq/kngl ; kkqcrr8the other. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is obsesijr+vzt+8l8 *t-q ii3;t ohz r an+s5rved to move up and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave ra +*3rt;viqnt z5jslo8 h zsii+-8t+ passes. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in F3gl7f n r5wj-,id k,gjig. 11–52 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 jr,7li wfnk ,5 -3dggjmoment the pulses pass each other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrat xc6 mwdmn3nh+ -bzu)4es at 440 Hz as its fundamental frequency, what are the frequencies of the first hn3d)c+nw6m- zumx b4four 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 w z u kxz6s11/3dnhaj+jbi8rz .ill it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of the1j3+jhs8 zx.nkz z1rdau/bi 6 string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops r+ h.s8smq1bw4 8cy3z +bxt x y9bsmp;at a frequency of 280 Hz. Name at least three other frequb+ss sh mbxcw.yx81pyqt849 mr b+;3zencies at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the frequency of standing waves ijk 5w3ihy(d p-s 475 Hz, how far apart are two adjacent node ( jh3wky5pid-s?   m

  If two successive overtones of a vibrating string ara m :qh86jjjk1ko(nq2 e 280 Hz and 350 Hz, what is the frequency of the fundamental? 2q6johj1 8nkm: qjk(a   Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distance fro *9ltd:01ndfcbn 6bz espr- h/m the bridge to the support post is L = 62cm and the string is under 10sbp9:b6c*lz ftnd h -/dner 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 i3s3c 9vpde i ,i7p/axys measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequencc3es 39di7ia , pp/yvxy?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is 4l7jm/2emep 7yj f lb*supposed to vibrate at 200 Hz, but it is measured to vibrate atfb4lm*7 /yle p2m7jej 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 atmj g0dvv+f*)c *7 nrvttached to a small-amplitude mechanical 60-Hz vibrator. The string’s mass per unit lvn+jm d*7v)gvrt0c f*ength 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 str()vovvtmg *ul23-u9 pomgp w7)qgd,l ing may be adjusted by moving the pulley. If the hanging mass m is fixed ol*2 7p9p)- qgv uvmvwm(gd,u)og 3t lat 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 jwwac vl( :09oq 03khxsust the right frequency, the water alternately rises x0qa0 lch39wskwv(:o and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundary with;pjf l-uk:dj +i+p9cgin the Earth between two kinds of material. If it approaches the boundary at an incident angle of 4k+f liu-jpcg+ p :;dj97 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach a8 (, vtpc2jv;wjusley9u:rw(n underwater “shelf” where the velocity changes from 2.8 m/s to 2.1 m/s If the inci(9,tvl e; v w(uwjs28jp cu:rydent wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air whenav4/c1r /*tt+1 scvd;mw/ zbi :avjxs it hits a layer of cold, dense air. If the sound wave hits + vcd/1t/taxc;a * / 1smvbrvzswij:4the 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 7lthr eq9q(o (strikes a boundary between two types of rock at a 38 o(re(h79qt ql$^{\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. According to the user’s manuj6vd(aj/e :h yal, the dish has (va:/e 6djyjh to be pointed in the direction of the satellite, but an error of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 250 km and velocity 750 km/h /b;qww3 fu+jv travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approxima+w /fujvq;b3wtely 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 constant of 550 kN/m F6u5+khvne: di0a gry9ind 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: Use e9gdvhka 6+ r5i y:nu0conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 1-e)ii( v8fcl6 3yxp ub,k8a(c idu*nq 8 m below, which stretches the net 1.1 m. Assume that the net behaves ld)( f vi,xb8 p*8k-eylacui(3in6 cuqike 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 xv3 ij-:dx-ei, mb wqdxzj5.. freely hanging spring. The mass then falls 33 cm be-xx,-eqvw5 :bj.diz d m.xji3fore it stops and begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a spefvjb9a2sv3y 9 u dpk. c6fy69med of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring. 6m dv sv y9pb9k96aj3cffuy2 stiffness constant of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of coffee (diameter 8 cm) at just the right pace o u)cyl2w -*yr bcm1-fgc0d9mlf about 1 step per second, the coffee 2rg)9y-l dbycc1mfc*- u mlw0sloshes 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 center of a lkqqdpr7i,- sbe:4ip . -v0 toqx;n0f33-rpm phonograph record have a w;-0vti 0 p-,n: rqqsleoq. fx47bidkpavelength of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according m0 kvp 3(ta2i+ koi4xwto the equation x=0.650cos7.40t where x is in meters and t in second 3iti(4mpowv2k0+kx as. 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 witil* +g8dmoo eg.fiv/2vna 5d 4h frequency f. What is its frequency if it accelerates ag gfo+ nv.od*e m854a/ d2livit 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on/ xa6l;3jc1it t5krhb the raft, it sinks 4.0 cm deeper it6 trl/hj bak1ci5 3x;nto 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 uwu3oy*oyls40y vgtah*js8/82d ji 8 are tuned to play at 392 Hz (G) and 440 Hz (A).iv yuh8tgy2/3ausl4oj w dj0*8ys*8o
(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 stretcd 5s gnm mxolvike-7da/ p2((1hed 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 m7vpmolkad s/ n(5x-1g(e2i dboth sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency o effnlfjo1yt5) d t6r.6c+ko3f 264 Hz, and the tip of each prong moves 1.8 mm to either side of center. Calcula)e1dkrfn6 fyfottl6+o .j3c5te
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates wc2 ka -mxqr8)yith simple harmonic motion of frequency 1.5 cycles per second. What is the maximum amp8)acmy- 2k xrqlitude 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” kaj0 p --d ycp*w;*imbend 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 end0m* ;-i*-pc b wjpadky fixed and the other free.

  A “seconds” pendulum has a period oxy - kcnt5h0s dq m(gm)a8h-1hf exactly 2.000 s — each one-way swing takes m1-08sy(dm5 qxh k ga-)th nch1.000 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 spring can oscillate in the verfga-j 1 yzy8q)tical direction or can swing as a pendulum of small amplitude, but not both at the 1qfy)a y- j8gzsame 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 stretcs*eld q8yqu ce: 5*4lmcvt*7y hed under a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at the opposite end. Where wis y d:em7eq*yc*5l8l tq4*ucvll the two pulses first meet?    m

A block of mass M is sus 744oy iwjx3ynpended from a ceiling by a spring with spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillations that will allow the penny to just stay on top of the block? (Assu ox jy3w47niy4me $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel y .qmi1uj d6r+crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the c.61du +yjrqm iar bouncing at the end of the cable. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate akf9iq+ec8mzm d4 d: w9s shown in Fig. 11–58 (which also gives the dimensions of the block). You push it sideways as shown, and then you let go: cwemi9d9m dq +kz4f8. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this vibration, given that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz