Give some examples of everyday1 l2((ie xwih1m 7ywha vibrating objects. Which exhibit SHM, at least approximateh mxi1a1wi2yhew ((l7 ly?

Is the acceleration of a simple harmonic7 gor:c*d5c kbhvb q/* oscillator ever zero? If so, where?

Explain why the motion of a piston in an automobile engine is a5m dw g;uy5e1kk n67y ljgx3f.pproximately simpl egmyd ;w 651y5gfluk.7x 3kjne harmonic.

Real springs have mass. Will the true period and frequency be larger or s3zq-)lr y -koamaller than given by thl3kz- ro -)yaqe equations for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a s8wz9fggps1 4pbg1 c;q imple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring sab;b.3fqelg6 yycgb( 2v i- h2cale, and then is released. Describe the scale g-glyf 32b6 ;.q v(ae cbhiy2breading as a function of time.

If a pendulum clock is accurate at sea level, will it gain or lose time when takgi1ygrus-wo+ sir+o ,i4b76 ken +uw4+ ii6g-yb7 gr,k1 os osrito high altitude? Why?

A tire swing hanging from a branch reaches nearly to the ground (Fi)y8go sb*x 4qdg. 11–48). How could you estimate the height*bd sy gx)o4q8 of the branch using only a stopwatch?

Why can you make water slosh back and forth in a pan only i5k rn3n xd-37qqc,2i 5vjoqye f you shake the pan at x3kived,j-qnc5oq 7ry35n q2a certain frequency?

Give several everyday eb/pi7 02mr mcw ijau7f;bm)/m xamples of resonance.

Is a rattle in a car ever a resonance phenomenoe pu*om+ b3f,rn? Explain.

Is the frequency of a simple cdoj1 vo. 46x9msnhgf: ctm)+periodic wave equal to the frequency of its source? Wm+cs1 6ooch m tdj4.:gxn9vf)hy or why not?

Explain the difference betw r6kng;zu ay-ne x*5170rk zzbeen the speed of a transverse wave traveling down a cord and z-1a7xk6r r*5n;zekb uz y0gnthe speed of a tiny piece of the cord.

Why do the strings used for the lowest-frequency notes on a piano norma)sxpt0 hg (xwt xwu0k*022ceg lly have e0wh x*tg2xg(2suwk0 ctx p0) wire wrapped around them?

What kind of waves do you think will travel down a horizontal/ 56 yukbrhlbx:r*na, metal rod if you strike its end (a) vertically from above and (b) horizontally parallel ya/buk6:r ,hn bxl*r 5to its length?

Since the density of air ;ge-:l:mvxwtdecreases 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 ai- lxmev:;w:gtr to vary with temperature?

Give two reasons why circular water waves decrease in amplitude as th;jj)x9a w3 /ac a:gzosey travel away from the so;gsx j/w j9ca:az3)aource.

Two linear waves have the same amplitude and speed, and otherwise are ident,8faws ltvp jzqaw33d;x a4;9n zrl69ical, except one has half the wavelength of the other. Which transmits more energy? By whzwva;fjlz4w n aq,t3xslrad3;698p 9at factor?

When a sinusoidal wave crosses the boundary between two sections nsjnl;f.v,v 4of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocity do change). v.,f4 snv;lnjExplain why.

If a string is vibrating in three segments, are there any places you could gk1wm(de 3,atr eti2 j:h*+7g1 vyjfqtouch it with a knife blade withoutm1tvadq e,3f i7ew 2g1tj(+h*j :ygrk disturbing the motion?

When a standing wave exists on a ,ne.wls 2pq x(string, the vibrations of incident and reflected waves cancel at q. lnw,x 2p(esthe nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one place to anoth0e.vx .b* h6 to2 5zwvivatn-uer, how might we determine whether the energy was being carried by particles (material bodies) or by waveswe t5.o0vn6ivz xu-ba2 v.th *?

  If a particle undergoes SHM with a*i(xg)xsfa p2u9t ya+5.ddwz0v l c7hmplitude 0.18 m, what is the total distance it travels in one periodpc2a( fgz+u*d9 i sv5w0t)xh.yd7lax ?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it 6,lzw /poln6 qbut is 85 cm long when a weight of 180 N hangs from it. What is the “springq6wopl6zl/,n ” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compou sq2jfv)g7 9/q.bnrress 5.0 mm when its 68-kg driver gets into the driver’s seat. If the car goes over a bump, what will be the fre9ruvfgnjs7 q)2.q/o b quency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs from mygfm5pj fsq )gv t3i 39kw:-005cskait. (a) What is t gm5 0t :p5ckwgf-)j3vyfkssqa0i 39m he 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 H9q6de 7q- yziji+pm13 phel6 mz when a mass of 0.60 kg is hunp jp1e7q-9y m66i3h + idzlmeqg from it. What is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. 11pcb,ivt+sjl*2 (nz5 p –2 at times t , zstpicj 2bl+(*pv5n= 0,t = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

  A small fly of mass e jtf (98aqi 1:wpb0s-i7aer v0.25 g is caught in a spider’s web. The web vibrates predominately with a frequency 8wq ajpr91- bti:e7as efi0v( 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.nkc 8.-v1 pu 4nolxbo1z qg8x3 When an additional 680-g mass is added to m, the frequency is 0.60 Hz. What is the value of 1q x8 nzc-b.xolu4 kvn8o3g1pm?    kg

  A 0.60-kg mass at the end of a spring vibrates 3..l6.9h0sstk 2i0lrc4rwzsc k 6( yoxh 0 times per second with an amplitude of 0.13 m. Determine ysk46z.r0 9.l ost06(2l xhwshcicrk
(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 ht2q jf6lwd.ttb/;79/oueil:h;sy hz alf the maximum value.f 6h9tbd/z o27; :/ ihlqlyts;j uwet?$\approx$    A

A mass attached to the end7*s+;ibp am/ta 7tzm8 2uwlii of a spring 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 st11ilflspz/w0x7 -egmretched an additional 0.130 m a/isf7 0e1- pwlmz1 gxlnd 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 spq7 k2ccchg+o ok,xh5 -3y di;cring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium positioncg k,o2q+- yk cic5hh7xodc;3, 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 0.200 m to p 6.i)c3j5l ,mu ud vpog mxm7fnx:7(4u/mkza“load” a 0.180-kg ball. With what speed will the ball leave the gun? jd6 3. om 4k c,p57gfiamu7)p(l: nmuuxmxz v/   m/s

  A mass sitting on a horizontal, frictionless surface is attaca9-rpl:2iyt8 x vk*b)idkn +bhed to one end of a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, the mass experiences a maximum acceleratio)b 9 i*p8 ndvk2ayi-+tx l:brkn 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 ih51iyk0gm6a1duhj wc *97kb 7i0mbd= 0.45cos6.4t where x is in meters and t isa y d6j*71d mwicbbkgikh7 5hu01i m90 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 frdt //ff ; :dgcm+ydqp4om equilibrium is the energy of a SHO half KE and half PE4 y pqmd/fdt df:;g/c+? ±    A

  If one vibration has 7.0 times the energy of apq8qsje1/ zrz)*y x/ a second, but their frequencies and masses are the same, what is the ratio of their ampliq 8e/q1) *azyr sxjz/ptudes?   

  A 2.00-kg pumpkin oscillates from a vertically hangingbw :6ya1du*/vw6iq2 m*uny rc light spring once every 0.65w/qd cb2 a m1*iuyy 6*r6uv:nw s.
(a) Write down the equation giving the pumpkin’s position y (+ upward) as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. y = (   m)cos($\frac{2\pi t}{0.65s}$)
(b) How long will it take to get to the equilibrium position for the first time?    s
(c) What will be the pumpkin’s maximum speed?    m/s
(d) What will be its maximum acceleration, and where will that first be attained?   $m/s^2 $

A block of mass m is supported ca) 4/n7xn 4meirsaiauzhb*ifsh- 3bd -+; d- by two identical parallel vertical springs, each with spx +d 3d4 *nas4f-iruei- h- a;)nz/ bcimhsba7ring stiffness constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equh nlf 74slyr-:ation x = 0.38sin6.5t where x is in me 7ynrlhslf-:4ters and t 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,lw8z,20tgvow x0 po s8o86ich what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on the end of acc 3q(or4(ca9fy;sr4 yv)t wi horizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.96m/s Detw4 9(cc3q4 rocsy(ar yfit;v )ermine
(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 vi1/: fimga iw5x)c8b eahc)8hbbrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) with positag5cbmhib )e )a1h/ c xi8f8w:ive 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 springsj 8+ghq-xq +u8st zzh7, 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 attacx7h k*mp)l6j jhed to a fixed horizontal spring whose spring stiffnessm)jk6j7x*h l p 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 withs1h fkkeb/n 55 mass 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 the spring stiffness constant and the unstretched length of the bufb5/ 1 ksen5khngee 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 6ieynb r:+ fsto *gc7 6s/f7e(b0 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make ee2/(*kdcv oy sxactly one swing per second? (That is, one complete vi(okd scv2y* e/bration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. Whatody + ex.adc 5+xia n m/1:o);p9pysrt is its period on Mars, where the acceleration of gravity is about 0.37 that on :o1 9c aipy.ox+r ta+sdnmy);pe/ 5x dEarth?    s

  What is the period of a simple penffu)u r) ,v-qi a (qg;nqb9l8v+9dwwmdulum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 m, the pendus5p+ ,pwkfpb 2f )ek6clum bob has a mass of 365 grams, and it is ,+fek25 )bkpwpcs6fp 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 haslz385bcwswd9.xd v;so3 n 6dc a length of 0.9930 m. If the clock loses half a minute per day, how should yowd xn so9;68 wvdb. l5dsz3cc3u adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximum s)6w3o 6*aoe69sd +ebqb jn msacy2c6zepq: 2 npeed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates; 2ya(xsnph*sq mu+i/ at a frequency of 2.5 Hz. At it is released from rex+s;h aypi(nqum s 2*/st 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 hi9 7kb:z2rlft js anchored boat every 3.0 s. He measures the distance between two crests to be 6.b7 jr92z:flt k5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with a speed otb59qc gqyre f1 dk0n)jv-(e5wk5vr*f 343 m/s How far apart are the wavwr510(dteerk kg*-f qvc)njy9bvq55 e crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz anx g2m53z mwxm1d 1600 kHz (kilohertz) and travel with a spem1gmx2x w 35zmed 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 wav,du26nb)fdhr 6-juites in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have cc t0o1.i;wp othe same elastic modulus, but one is twice as dense as the other. In which rod will the speed of longitudinal waves be grea t;opccowi0. 1ter, and by what factor?   

  A cord of mass 0.65 k)ato6l;wz w3ph x v(z4uc 0ag7g is stretched between two supports 28 m apart. If the tension in the cord is 150 N, how long will it take a pulse to trxc0hg7)vu3laa 4 ;p w zo(6ztwavel from one support to the other?    s

  A ski gondola is connected to the top of a h4jq;naz o pt1;ill by a steel cable of length 620 m and diameter 1.5 cm. As the atqj;npo4;1zgondola 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 siml7b3p-mfuyzo(6 4y wz9ty(a de of his ship just below the surface of the sea. He hears the echo of the wave reflected from the ocean floor directl4lz z7(wu9tb6fy m( -mop3y ayy below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthqheuopx;f7eobop :a6+(s :0ia2c 5vi luake travel at different speeds, and this difference helps in locating the earthquake “e60 iaso:xo pbi7: ; oefv5 plc+haue(2picenter” (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 b56 k ; mse4zxe8.qlwxae approximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which 6qzae 4 kxm;sx.5 lwe8actually 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 :o b)zu5l. (nmmbk rz.(a) the intensities, and (b) the amplitudes, of an earthquake P wave passing through the Earth and detected at two points 10 kun:.okbm.(brlzm)5z m and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through t/tm-maydwr,i t,u )u1he Earth is measured to be tiudamrt/)-uw 1m,y ,$ 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 thror fhfz mk5((q,ugh the same portion of the Earth, but one is carrying twice the energy. What is the ratio of the amplitudes of the two (fmf(qk ,r5hz waves?   

  Two waves traveling along a stretched string have tklx00ua9y3 cyr po*3 bhe same frequency, but one transports three times the power of the opx00 9 al3*r3cbuyky 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 vert7jqoxz fnm5(+ical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the rifx( 5oz q7nmj+pples 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) Sketch the5 l-:zq0fjdbo o /juf3q//k pzaa;/wn sh;fb0oo-j 5fd/ //kan: zq zwjp/lqau 3ape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundament/a/c 1xzr lp,lal frequency, what are the frequencies of the first four h l cpz/,rla/x1armonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what frequeno1gxu5wb;m8tnxzrg mn/-: (o cy will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-tx;u5mwgb/n :t-8n rmg( oz1 xohirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequency of 280 Hz. Naug4sij 01wi6 frh igqh gf)41-me at least three other frequencies at whrhij)i46 gswggi10h4 f -uf1qich it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s146;dt/ 9dgmx 9me pjke7x m8nf2 cshj If the frequency of standing waves is 475 Hz, how fakmhxm2cdedj n996t ;/mg8sf14ep j7x r apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 7-jtjy ,byy q un7g*u9350 Hz, what is the frequency of the fundamental? j,9ytu y77n-jug b* qy   Hz

  A guitar string is 9,-r-anodc6ot 0 cm long and has a mass of 3.6 g. The distance from the bridge to the support post is L = 62cm and the string is u 6a-corno ,d-tnder 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 ade- 01/ pmfltgt 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in t t1dpg e-mfl/0he string be changed to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hz, but it is measured)xgnt a8-zg,f to vibrate at 205 Hz. z) g-n,fa8x gtBy what percent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is ac r; k3y)evt wb mv;kc08fw.jq k1z5k0ttached to a small-amplitude mechanical 60-Hzm wb.j0 wk5 fkt1q 8)revcv;03zckk ;y vibrator. 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 adjusted by moving tzjhx0k d+;.dhhe pulley. If the hanging mass m is fixexhd;j 0dkhz+.d at 0.080 kg, how many different standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back 3(( 6dcxyeg2gul /iqqand forth in a tub at just the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Supposeg((q 3iu/l62gqcx yde 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 :*cletv-y )sfwm xv*2within the Earth between two kinds of material. :v)*l2ct w-x ef*vsmy If it 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 underwatesd1q e0xb/h t(o:p pk izrbw)9d+0(vsr “shelf” where the velocity changes from 2.8 m/s to 2.1 m/s If the incident wave crests vod00((qpdhe /+)z :xs wp 1 b9kstbirmake 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 onlk9y;wr .hc7 f cold, dense air. If the sound wave hits the hln9ckwy. 7r; 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 earthquakaoi m.ign:s(gx)n6hqk 8 u 68tp9;q lie wave strikes a boundary between two types of rock at a gakmn 6iqlpn.8)ghi; s qu8:(96x oit 38 $^{\circ} $ angle. As the wave crosses the boundary, the specific gravity of the rock changes from 3.6 to 2.8. Assuming that the elastic modulus is the same for both types of rock, determine the angle of refraction.    $^{\circ} $

  A satellite dish is about 0.5 m in diameter. According to the use:..zr8 bnh)y ibvx6 tfr’s manual, the dish has to be pointed in the direction of thn.f8i t.b)6 :r xzvyhbe 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 velocittn ay x*6t:z :s))rbg.zjir0c)y :tk my 750 km/h travels across 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 died during tsunamis, some of them attracted to the shore to see stranded fi tzy*nibj)a 0)c6r)z: r.: y:stgxktmshes and boats.)    min

  An energy-absorbing car bumper has a 5ccd;x::u27,i9l gbtwd4gs , l kgazqspring 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 ;c,9 qd4azi2gct, k7 u lxw:blsggd5:mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a winli 4o3;h+g oiodow to a fire net 18 m below, which stretches the net 1.1 m. loo3 iho;ig+4Assume that the net behaves like a simple spring, and
(a) calculate how much it would stretch if the same person were lying in it.    m
(b) How much would it stretch if the person jumped from 35 m?    m

  A mass m is gently placed on the end of a freely hanging spring. Thc9 t7w v(q/mxce mass then falls 33 cm before it stops and begins tm 7c(9q/wv tcxo rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Figkzi) ekuts54+2ya .ch. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffness consus cekt.2+ y) 5hi4kaztant 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 j 9)ykabg 1nc(fb77r0nut3ukeust the right pace of about 1 step per second, the coffee sloshes more and mor9eab3 fcnynu k7ubk(t7 1g 0)re 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 -sn/ab m,2 y i0dax8gl62l ngjthe center of a 33-rpm phonograph reco 8in20ay- lbn/g6 a mdgsxjl,2rd have a wavelength of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according gel c( qyydf1wmw7lqnv9ao5 1/ (;de+to the equation x=0.650cos7.40t where x is in meters and t ye onfvm19c(5+ww(dd yll1qa ;/eq g7in seconds. Determine
(a) the amplitude,    m
(b) the frequency,(round to two decimal place)$\approx$    Hz
(c) the total energy,(round to one decimal place)$\approx$    J
(d) the kinetic energy and potential energy when x=0.260 m.(round to one decimal place) PE$\approx$    J KE =    J

  A simple pendulum oscillates with frequency f. What is its frequency ja/ig/6g+be x s o6jnw n9(d9pif it accelerates at 0.50g (a) jg(p96/n/nw oxa9+6eigbs d j upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on the raft, it 0j; dec38xhh*7 fp)nvvr2klqsinks 4.0 cm deeper into the water. When he dc)2h v q7lxp*8 njv ;0k3ehfrsteps 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 440 Hz yj2 abnz 7og7 /lm5jv i0uh9.pt a2zu,(pvj 509ijl7am,/ 2b ta7. zgu2ozhyunA).
(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 stretched two-part cord of Fighsps9pcfp a2 k8*e / m1/ t*bzit;5yzx. 11–33. Determine a formula (a) for the ratio of the speeds /* bhztp1y8mxf29 /ec tspk 5 ip*;azsof 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 wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and thrlg;h tg /4znanv7 ,p-e tip of each prong moves 1,ng t4z vl/7nhp g-a;r.8 mm to either side 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 o ,e +cabvm.ed5f frequency 1.5 cycles per second. What isvdc5,ma b+ee. the maximum amplitude with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that end is attached to a ring that can slide (6j)vx yvm clrtdyk*4ljlify 1(75r 8 without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with onemx1ity8v4yvrlj6 )rdc((7llf *y 5 jk end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 sa h .wvgtwpru)4d8q ,3 — each one-way swing takes 1.000 s. d3)4 vwgp8aqhur wt,.
(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 oscizs(m o bq6i6 a+0l- mjvl+p(iillate in the vertical direction or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the 0 (6ajm lpii6b +(q-zmolsi v+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 jse;gp(jn5yz29nrzsy - wc l-n tlu06:)h8 tvg is stretched 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 will the two pulses fjuj 62c8yn9-gntn vp)terlw- yz 0:l sh5(s;zirst meet?    m

A block of mass M is suspendqj 7l2bl c5:*wosat 9c 0gpx:wed from a ceiling by a spring with spring stiffness constant k. A penny oc5t2p wjgllqs9 x7:b: ac0ow* f mass m is placed on top of the block. What is the maximum amplitude of oscillations that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car emm-+mi -h-nf.ixr 4k at the junkyard. The steel crane cable is 22 m -mn ehm i+mr.4-fkx-i long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (wh-jjsqg z+3-:zap;5bl5 rxmlz 0 j5oh aich 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, estimate the frequency of this vibration, given that the shear moduaar- :55 jo;jqj5z-mzb gx sp3zlh0l +lus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz