Give some examples of everyday vibrating objects. Which exhibit SHM, at lee +u/d)d1ag rmast appreddg+)u1a /r moximately?

Is the acceleration of a simple harmonic oscillatorlusdg-m t-n z3s8t9-f ever zero? If so, where?

Explain why the motion of a piston in an automobile enginev,vo4c(ljr) ugw5xcw *ln 8pw8 o/x.x is approximately simple harugoo) 4v88,wcx jp wx5(vwl.r/c* xnl monic.

Real springs have mass. Will the tr por4b,.ohzi8 k6 . os:1u-w5tlof ilbue period and frequency be larger or smaller than given by the equations for a mas- .hb,zpso4:6k 8rol loi b f15.uiotws oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple harmoox+,ep mmrmwc p wd03d+9 zo14nic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scale, 1-q4f3rtg/p wuohj2qsb0eo*/8czth and then is released. Describe the scale reading as2htqceqz4*sj 3g1b/ u o0th/ pro-f w8 a function of time.

If a pendulum clock is accurate at sea level, will e9a(t5tfu q etycj;04it gain or lose time when taken to high ayt ;j5ea c(uq0tf9te 4ltitude? Why?

A tire swing hanging from a branch reaches nearly to the groun,f 5h1( fuauard (Fig. 11–48). How cou aah 5uru,f(f1ld you estimate the height of the branch using only a stopwatch?

Why can you make water slosh back and forth in a w5-i lqu ouyf)v-s(e5l:r3ak nfcr/8 ik +bk6pan only if you shake the pan at a certain f:i 5-b+ lw k6va uoe3(rk-u)5srn8ly/f cqik frequency?

Give several everyday examples of ren k3jle)w9pn3sonance.

Is a rattle in a car eve/oxc2u4pp e+0i+ l6xhg +gviujy.lh )r a resonance phenomenon? Explain.

Is the frequency of a simple periodic wave equal to the freovzugqqnnb n;4t0w 4wi0.)1;cf *hu vquency of its source? Why or why not wnh40b* wvvc0qu;ti.qonz ;4g1n) fu?

Explain the difference between the sp qu.rh45dpdigbn7 d42hq v( .ieed of a transverse wave traveling down a cord andrqu. 4 qp h(dn2.4iidgh7v5b d the speed of a tiny piece of the cord.

Why do the strings used for the lowest-frequk sk3je) uofr(r (:5awency notes on a piano normally have wire wrapped ar s5 froj(kaw3r:kue()ound them?

What kind of waves do you think will travel down a horizontal metal rodqwpza ./ie -0k if you strike its end (qai-pz w0.e /ka) vertically from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase in te(.8bg)z6ple44j aqk; t;yq bpce 3gh smperature, but the bulk modulus B is nearly independent of ts4) e;bzq4;8g eypcqblg kp (a3j.6htemperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in amplitude as they travel *ugc-k8bl 3n daway from the sourc -blucg8 3d*nke.

Two linear waves have the same amplitude and speed, and oth3mv c sx:ff59xa)t(d herwise are identical, except one has half the wavelength of thhvf( 5) x3fsa9dt:m xce other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between mg,vmj(b37rv two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velg mm 7r3vjbv,(ocity do change). Explain why.

If a string is vibrating in three seg9v xucu-1p) kcments, are there any places you could touch it with a knife bladek) cuv u1-xc9p without disturbing the motion?

When a standing wave exists on a string, the vibrae xfqhe9(qa*g n6t4 z:v-p em*tions of incident and reflected wavezqa9h t*q6g(m- *efx4nvp:ee s cancel at the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy wk y uk8kc0 m 7ckcxjxg;n hv38f96p3*nas being transmitted from one place to another, how might we determine whether the energy was being carried by particles (matj;k86fv0y83 k9nmcknc7 ugxk* hx 3 pcerial bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the total dis4g6r 7p zlf;+kqr 2qdctance it travels in one pericpfl7qrq;gz42+d r6 kod?    m

  An elastic cord is 65 cm long wxu. x noi 6ject/4k5 m66e6psqhen 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 kqexx6.eoj t6ksinu45mp 6 c /6 of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg driver gets into 4 ash /mj 4qq9pbjzb;)the driver’s seat. If the car goes over a bump, what will be the frequency of v /m4qjaj9zhb ;4qp)sb ibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 5(jedx(l5 xrecm when a 2.7-kg fish hangs from it. (a) What is the sp(x xl(d5 ere5jring 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 freque0 6(mw8kytdtyuol ,f 8zj.c n1ncy of 3.0 Hz when a mass of 0.60 kg is hung from it. What n (,m dcyk.tjzw6tlof01y88 u is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. 11–2 at hi5e4rc9m4i hf .mymay 5k( 7ftimes t = 0,aym .iihk 5r 9m7cm4 fe4(hyf5t = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 predozkd;ctj0r k t aze-,9-mina0dk,t;9k rte-jzca z-tely 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 spri-.k hb-lszame6 wl6+ yng vibrates with a frequency of 0.88 Hz. When an additional 680a whl .+ -mkz-66ysble-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 ry/ w2q5uc bt-a spring vibrates 3.0 times per second with an amplitw uy 2qbt/5-rcude of 0.13 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 am 9;za9/cws iv SHO half the maximum valuesvc im9/9z;w a?$\approx$    A

A mass attached to the end of a springo)fg en3 f8r:r 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 spring 0.315 m. If the spring is stretche8rkqrbk-l-wu)7qti f 6-i) jcd an additional 0.130 m and released, how long does it t-kb frc 8j-krq6)tl)- 7q iuiwake to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg mwrz((b t 8j*mis attached to 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, i(m(8mzrjb wt*t 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)7 7c,whejwcst-m5+o xc tg-wb8v+ y l popgun 0.200 m to “load” a 0.180-kg ball. Witw)j8h5et-,-wy x cclbs + mvw+oc7g7th what speed will the ball leave the gun?    m/s

  A mass sitting on a horizdb4u35-:i,s a8hztkbhk4 gd qontal, frictionless surface is attached to one end of a spring; the other end is fixed to a wall. 3.0adz b ukik q8 th4-dgb:hs53,4 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 x isq wfomy8,w 8;z in meters and t is in secowy q 88foz;mw,nds. 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 g mn3,;twgsi/opx: *s is the energy of a SHO half KE and half PE? ± gs/: * nxpw;sogi,t3m   A

  If one vibration has 7.0 aod-qzbg :j-2times the energy of a second, but their frequencies and masses are the same, what is the ratio of theirq2-z job:a -gd amplitudes?   

  A 2.00-kg pumpkin oscilla:r -( lzf2,odwuhz o5ztes from a vertically hanging light spring once every 0.6wu2o- ,f(r5z ho z:dlz5 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 islxq f1w 4j/n)vo;p7 xx supported by two identical parallel vertical springs, each with spring s 7q/4nx1wjfxpo v)lx; tiffness constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according esz*s 43mq+j gto the equation x = 0.38sin6.5t where x is in meters and t is in *jg+ mqs e3z4sseconds. 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 /-8eqpvx jw + w stif))a;du(*eoae5j, 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 y /se)b 2zg*rz rcxlh 8q.x9j3on the end of a horizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an iniz x)*rcb89hjexzr ly32g/ sq.tial 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 den,mzg069 pb with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equili9m neg p6zbd0,brium 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 twopf1l-.vo4 me jalt;1x;bd5zz springs, 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 atovvd2z ml2y)r5 3wzo v6t n,j5tached to a fixed horizontal spring whose springvj2o 65z53doz2m tnl v, rywv) stiffness constant is $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with mass 65.0 kg jumps from a higs5. v4xd5lu hhh bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the ulhu 5d54xh.s vnstretched 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 6se c8gb* l+9ib0 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum bg9a *d3ml3e pcp ,slm/e if it is to make exactly one swing per second? (That is, one complete vibration takes exslg3c *mp39/ eapm ,ldactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on Mars, wher8 r )l ,,)otwhptso6qpi)* vdfe thq*dov)l )sohi6rt8,p, p ftw )e acceleration of gravity is about 0.37 that on Earth?    s

  What is the period of a simple pendtqx6 4x1bebp 1wl v9r;ulum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simplw+p;ccc + dkz*36vgl/z tk3p ce pendulum is 0.760 m, the pendulum bob has a mass of 365 grams, and it/c vpl *k+;36 tzp+d zcw3gcck 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. If the clo )eimtjn t;(;eck loses half a minute per day, how should you adjust the length of the pend ;njeei;(tmt )ulum? shortened by    mm.

Derive a formula for the maximum speedcevu39a. rn zbpq(3 b) $v_{max}$ 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 fromsrk e z.fs p--)+iaf3d rest3pfi f de k+sra-)-z.s 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 an.g p9zhxtw9i )chored boat every 3.0 s.xt9w)9pz gi.h He measures the distance between two crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has q-t* cv m.rv26 e+k ;abvo pi+ceos7.ia frequency of 262 Hz and travels with a speed of 343 m/s How far apar ;e7+*6bq acr -k.ivcvv+.2oi mots pet are the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 16 p(yjx deo-b:6: pxpu400 kHz (kilohertz) and tjuop-yxpx4ep( :b 6: dravel 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 sybae - hy+qqbc1;v*:of longitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modufy fsf uwy:6)p hn l 9+)zm(rzy-ypdf1-*g*snlus, but one is twice as dense as the other. In which rod will the speed of longitudinal waves be greater, and by what -fly( y)z gsn*1 w*f:pms uf6p+zy 9r- ydnhf)factor?   

  A cord of mass 0.65 kg is stretched be ,wbtxbyq.3xpjl8 0l-.f nz7j( om 4;xff6 ryotween two supports 28 m apart. If the tension in the cord is 150 N, how long will it tay,4bfl yox n t3lj.f 0x 6;r-wjf8mq7b o.z(pxke a pulse to travel from one support to the other?    s

  A ski gondola is connect6zg(k j8u0o; bn-, g;xj pha euu4i8kled to the top of a hill by a steel cable of length 620 m and diameter 1.5 ce0ua,-g68hg;l4p u;b(ix8 jkzkn oujm. As the gondola comes to the end of its run, it bumps into the terminal and sends a wave pulse along the cable. It is observed that it took 16 s for the pulse to return.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

  A sailor strikes the side of his ship just bed14fq nfhe p/( 1jee:a9pt) gglow the surface of the sea. He hears the echo of the wave reflected from the ocean floor di eqh :4pe9fafgt/n1j d) epg(1rectly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at different speeds, and7oog j(d*yx r(d85o ba this difference helps in locating the earthquake “epicenter” (where the disturbance toybj(r ox7gd58(ado *ook 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 sinusoidal transvc9g; hppox-c5/ ye 5zberpcoz5y;/- pgc5 9b ehxse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplitudes, of an earthqakc4t z:/.*gj,z ghnzuake P wave passing througgz: h,z4k*/n.zj ct agh the Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Eartyf* h)r,ulhfb w rt;0;h is measured to be )hr;*l,wyt 0hbff ru;$ 2\times10^{6 }J/m^2$ at a distance of 48 km from the source.
(a) What was its intensity when it passed a point only 1.0 km from the source?(round to one decimal place)$\approx$    $ \times10^{9 }W/m^2$
(b) At what rate did energy pass through an area of $5m^2$ at 1.0 km?    $ \times10^{10 }W$

  Two earthquake waves of the same frequency travel through the same portion of ta1lv-2xqtm er67rk. yhe Earth, but one is carryinlr2qar k y.6xe7t-1mv g twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretcheeaxl qp6m+vm03bz/l, d string have the same frequency, but one transports three times the power of the other. What is the ratio of the amplitudes om0apl l ez6 q/b,vmx+3f the two waves?   

  A bug on the surface of a pond is observed topqj 6gkg1fyw) n2)co1 move up and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as2)y 1f1ojgp)wkc 6nqg 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. (a) Ss:) 3lde fptk(ketch 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 dsp :lft(3) ekis straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundamental +i fs)g9h)s*v qkbop+7sg 1jp frequency, what are the frequencies of the first) 1fk7 qgssp+vboi9jhgs) *p+ four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when 1my fogzcgpn( 3a3*lr i0g7 -ounfingered. At what frequency will it vibrate if it is fingered one-third of the way down from the end? (That( ilzgoag1c 3f*m-rpg0n oy73 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 al9d9v.;d oi f ej7*4sjb uxa+gt least three other frequencies at which it will resonaj i4. obx vd 7+afl;u9j9g*dsete. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the freqli ;ini5o,ui:uency of standing waves is 475 Hz, how far apart are two adjacenti:o i5u i;in,l nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 350 Hz, what i.; *mbvy dd-o e4ls0g igtxdje,md7;(s td;do ejyl-m4git dx sdb 0*,.;7ve(g mhe frequency of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 gna ki8foxi )a(fgph,5q e(d,: . The distance from the bridge to the support post is L = 62cm and the string is under a tension qp,kaeg( xf,ofha8i ndi)(5: of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string lmn/m.6z(tytkj 1 fq 8is supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the freqj1.nmztq( /8fm6ly kt uency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supdd(0 x87czonvc0s gd:n3ew 2s posed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tenws3zo 0x :vdce(csn 0nd 7g28dsion in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string f;y)f;pu 2ugrkbr/ujkq: kc+7 nic20 is attached to a small-amplitude mechanical 60-Hz vibrator. Thkfn j:7cgq+/;kr ;ur )c2ukybf i0p2 ue 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 3d;knz0d5c-oq4b )vy( ahe vaadjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, howevk 40hdb3ana)-q 5vdy o(c;z 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 tu 6o1nu5ez 9mruorrb q(ke -/:nb at just the right frequency, the water alternately riso/q kruu9m 5b1o6r nn zer-:e(es 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 within the Earth 9(/vcdln:v): 8yjavio0 kvbh 5 j(cjf between two kinds of material. If y(cj8jc(0bjakh / 5)9fvvd ::o ivvlnit approaches 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 underwater “shsj:eu f +l+fc:elf” where the velocity changes from 2.8 m/s to 2+ esfjlf+ c:u:.1 m/s If the incident wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling b3e4. yc yk4fcin warm air when it hits a layer of cold, dense air. If the sound wave hits the cold air intyy bc4 cf3ek.4erface 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 bouz:7b su4264 p8kuqhrvck 3r xvndary between two types of rock at a 38h6k x v:4uvrsupkzc72b348 rq $^{\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 diameyrn-+9slaqo 7rmekt 5-z8v (x ter. According to the user’s manual, the dish has to be pointed in the dirr smov97-r+-a q k8xty5n(lzeection 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 velocich dq 1f18:4m7cqtbrd ty 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level 8mfd7 th4q cc:b11rdq 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 caa.cfvi ,f 7v5hr bumper has a spring stiffness 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 (approximately 5 mi/h). [Hint: Use c v,h57.a vifcfonservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m below, whin rj1b3ekj1iqt ucd ):b (6mcs r-:q-dch stretches the net 1.1 m. Assume that the net behaves like aj6utq1-(dq)1k :n 3bdrb :cjecri m-s 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 sprin( ypdi4aq:o5k g-(m byl z bm7u4;pc2lg. The mass then falls 33 cm before it stops and begins to rise. What is the frequency of them:uzi o7adp-yb5(l;k 4gy bl qm2cp(4 oscillation?    Hz

  A 950-kg car strikes a n*kf, 7a x 9*(: srokmwfhbp)ehuge spring at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffness constant of the sfw r,9e*) 7*ksfk:pxa boh( mnpring?    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 gr:f7 mu3c g)bx(5wau pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate th57bwu fx:c3(rau g mg)e speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the center of a 33-rpm phonograph p)7v9o5hfso 52ob ldyrecord have a wav5o 52soh yp)9lo fbvd7elength of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates accb,j h:w7*mxwl5m g 0q54-4zj bvh*ugeuu g.dvording to the equation x=0.650cos7.40t where x is in meters and t i e5vhmw*jj7z,:u4mgbugu- vq5g x. l0b 4w dh*n 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 a k7h6zrv3ye 1bf .wt8frequency f. What is its frequency if it accelerates at 0.z ektby w ha6v8f1r.7350g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft float)t;jezf5ogo3y z(g z ,s on a lake. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into to )5(j3otz;fz gzy,eghe 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 tuned to play at e4gni4dfg:0vj7ucr )s9a:mtwlk: t ) 392 Hz (G) and 440 Hz (A). t4nm wsv:tl9 g)ade f0uic gr4::k)j7
(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 stretchedy .9f9kda9s qs1qfwx : 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 wavele.a1 sx:q99f9d ykwsqfngths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequs0hc/h gfx64 vency of 264 Hz, and the tip of each prong moves 1.8 mm to either side of centv0gs f/ x4h6hcer. 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 simplou,mj y5sk3dc tst592e harmonic motion of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board c s59 3cy kj2,tdt5omsuan vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that end is attached to a ring that can 3we0sy4x*xrwuju j3)td +)oua:wef2 slide without friction on a vertical pole (Fig. 11–57). Deteoyuj )*xw a0uds)32:eu rt xejww34f+rmine the wavelengths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum21y 1elg 1pl8 +tcirko has a period of exactly 2.000 s — each one-way swing takes 1.000 slk2eo1g 8prl+1 ity1c .
(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 direction)m0;t, , wvzep7gi0gjs7gv si1pf- sc or can swin fmvgz )s itcsp;v0,g7we0,1i gj p7-sg as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontal swings, 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,j jkutpg:r+k;vgm; 7v3i gb/ N. A pulse is generated at one end, and 20.0 ms later a second pulse is genera+g j/k3b;,pjv;:uv i mg trkg7ted at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spsokq/)(zv /,iwrobj1 rc) ( jjring with spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillazor ,ojb)/wr i)((sjc q/1vjktions 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 cable is z*:l -1lf qfid22 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?f:l1 ilz*q- df [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (whichl7e unj3 uyk.: dz16wb 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 aln: jd7kzwu.ebyu31 6 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