Give some examples of every6+ 7 jcnqpn j;o4;ezkmday vibrating objects. Which exhibit SHM, at least apck7 pz;4on mnj6 e+qj;proximately?

Is the acceleration of a simple harmonic mjjsfq ,8c7r*oscillator ever zero? If so, where?

Explain why the motion of a piston in an automobile engine is approximately sifv n1 -bm gos60gw:sv.mpleg:mf sb. vgwo nv160-s harmonic.

Real springs have mass. Will the true period and frequency be lar: panp+ kw6. a4-ecrcwger or smaller thawe6p .c 4r:+-wpcank an given by the equations for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple harmon.b7x/ -+lqn wqbfr kt 1adl)b paxn-9-ic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring saf i8 (6foc+dmo.w4t rcale, and then is released. Describe the scale 6 8dco+a mri (.owf4tfreading as a function of time.

If a pendulum clock is accurate at sea level, will it gapbi(rr:,pm 7s in or lose time when taken to hisr,mp bi:7pr(gh altitude? Why?

A tire swing hanging from a branch reaches nearly to the ground (Fig. 11–4pim;(46 xpo yg2d lj4v8). How could you estimate the hg4 li(42o;yxv m 6jdppeight of the branch using only a stopwatch?

Why can you make water d)qncw5nue 9/slosh back and forth in a pan only if you shake the pan at /uwedncq )n95a certain frequency?

Give several everyday examples o r-c8,z1dopzm+x h1a 4a7atx9w /mdylf resonance.

Is a rattle in a car ever a resonance phenomenoqt-))yxc ,xcz( )pe +vjd twko.:4zwl n? Explain.

Is the frequency of a simple periodic wave equal to the frequency of italc 4oyj39-y;w i8u eos source? Why or whyc 8wle3o;9 y- auyijo4 not?

Explain the differen( k fpm3ryf,* ,sy(ksw(u yz+gce between the speed of a transverse wave traveling down a cord and the speed of a t*m(y,,w f3f( zkupyr+ks(g ys iny piece of the cord.

Why do the strings used for the lowest-frequency notes on a pianon;ql nb.n.3l5 s)l rzt normally have wirsb.l q rzl. )n5lt3nn;e wrapped around them?

What kind of waves do you think will travel down a horizontal metal rod if *z4y j.yctu;a you strike its end (a) vertically from above and (b) horizontally pa4y zu ca;*jty.rallel to its length?

Since the density of ai* 4t8uns+ x+yeq9wbn bx) bhl+r decreases with an increase in temperature, but the bulk modul++q9 t*yxbleu4 nb)bxh8ws+n us B is nearly independent of temperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease ex ugskxro,4a .f21g (ufh5s 5in amplitude as they travel away fuo (x5 5x,fs1 f.kgserha2g u4rom the source.

Two linear waves have the same amplitude and speed, and otherwis.ad8jwn q ;)khe are identical, except one has half the wavelength of the other. Which transmits more energy? By what .q 8;jnwdhak )factor?

When a sinusoidal wave crosses the boundary between two sectums- dm.c d5c2ex jk/:ions of cord as in Fig. 11–33, the frequency does not change (although jx 25-ck:/cudm eds. mthe wavelength and velocity do change). Explain why.

If a string is vibrating icz* ykcs 9j.ll6p4 q/sn three segments, are there any places you could touch it with a knife blade withoutkjy.s 6lsq4/ 9*cpl zc disturbing the motion?

When a standing wave exists on a string, thed:y .g 7pib,3aeaxg i1 vibrations of incident and reflected waves cancel at the nodes. Doesega ,i1dx.gaip3b:y7 this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one place to another, how mig 2od3pv1m*d csty0 + 9iqzrf*tht we dep+ 32m 0rvodfdt9y*zct1i q*stermine 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 th6e s4 .b6u0oa0 ixk4bdiwspit9 j0ox ;e total distance it travels wktx94i ied 0p.boosausj;4x 0 b i606in one period?    m

  An elastic cord is 65 cm long when a weight o:qj3z5rbtd2yme 5*fx f 75 N hangs from it but is 85 cm long when a weight of 180 N hangs from it. m5y :3zxd brfe5qj*t2 What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg cpx(t s1huh l:q:g5ev.a /akj -xhb72gar compress 5.0 mm when its 68-kg driver gets into the driver’s seat. If the car goes over a bump, what will be x1 jvs h2b/:thqk.-e hapu( axggl5:7 the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs from it. (a)ew 60oc3-t qpg What is the spring stiffc0 3w6 ogp-qteness 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 vibr jjz2klyui+a f ei8bt a 9.yr(iql)4*5ates with a frequency of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency)ai 4k8(y+ 59*2 ry lzl.jie qutifbja if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. 11–2 at times t qm)r 1lb0a59cz 2m dvc= 0,t zca)9 0cqmm5v l21rd b= $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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’+r.w )fkkbwhf ;gyd p/fwq );2s web. The web vibrates predominately with af2w rp)k/ wfqf.k; + whbd)yg; frequency of 4.0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a spring vibrates with a frequency of 0.88 Hz. When ;jn *j7,kbv dhjyw+.pfr/z t ,an additional 680-g mass is added to m, the frequency is 0.60 Hz. What is the valuez7 j. ; /jtj,kvnp+frywd,*bh of m?    kg

  A 0.60-kg mass at the end of a sp(zyqq6mf9b6 xn/ yc(sring vibrates 3.0 times per second with an amplituyf nzb/6x(qy ( smc96qde 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 a SHO half kl4m 5hcd3m w/the maximum valuemh3w 45cdl/km?$\approx$    A

A mass attached to the end of a spring is stretct 2d3/vzr ay:m-)prauonl* ydd+ ,l h9hed 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 0.31a:ls+no (gqv61 wcr3m 0gcd d25 m. If the spring is stretched an additional 0.130 m and released, how long does it take to reach the (new) equilib c3s :o(dwg n2rgvdm+qc0al61 rium position again?    s

  An object with mass 3.0 kg is attached to a spring with sx/fi)+suc vc2pring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium positio/v cf2c)ixs u+n, 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 Nq/: g3z:mim4nmqsf +ux .bfr4h64 xxm to compress the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will the ball leave the gz/ff:r.h x imxmq nb3u+m6s x: gqm444un?    m/s

  A mass sitting on a horizonn(qhv. p lu dpynl-e6a87ch; .tal, frictionless surface is attached to one end of a spring; the other end is fixed to a wall. 3.0 J of work is r6h -;p .nv(pa.ynhl ued lcq78equired 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 ac3jqzyh/;c4v qg,6 bziky.f +acording to the equation x = 0.45cos6.4t where x is in mete/q zf bvygza.+6, jyi4hq3c;krs 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 the energy of a SHO6cu6 j;-lj l7dogbr j6 half KE and half PE?d curjl b6g-jlj;6o76 ±    A

  If one vibration has 7.0 times the ener( 4daca1be3 mvgy of a second, but their frequencies and masses are the same, what is the re3cd b ava(m14atio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a verticirvfo;ato e9k 2o.u m)nel8k o/q 95*eally hanging light spring once every 0.65)m.*v9l9 8 iktefro2/o eku oeo5n ;qa 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 sus ccx zz).)*ngpported by two identical parallel vertical springs, each with spring stiffness constant k (Fig. 11–49nzcc))x z.s*g ). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38si/v-,w id+ ouxun6.5t where x is in meters -d ux,w oi/v+uand 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, what is5lhan9)z 7/sc6s va xm)seb:m
(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 a horizontal springzg3 .w 1rbnm d/m60fqj (k = 124 N/m) is struck by a hammer, w md/fjz nqgm0.r6 1b3which gives the mass an initial speed of 2.96m/s Determine
(a) the period and frequency of the motion,    s    Hz
(b) the amplitude,    m
(c) the maximum acceleration,    $m/s^2$
(d) the position as a function of time, x = (    m)sin(4.08$\pi$t)
(e) the total energy.    J

A vertical spring with spring stif9oor8tb. io: mmy0o uo.: bn+xfness constant 305 N/m vibrates with an amplitude of 28.0 cm wh0:no9bbui. oxo8r.+ o o: mmtyen 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) with positive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to tt2txw*wq8kx3 3u7s t c56b rbhwo 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 attached to a fixed horizontal spring3/2x- q4z83gs eje;gwqg(tve mscp 2f whose spring e 4sgfzgq2 m g 3ec3/x(e2jv;ts-pq8wstiffness 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 high bridge. Afterk92 p7,s-efxhd) yjae q9m u6c 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 unst 7e2huej 6mx, csfy9a)kp9qd -retched 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 +5l y8s.avh duvibrations in exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly one swing pem 1e87sbg2*pjnuys 6gr second? (T sn8pg7 2*umbjg16y eshat is, one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is itz/ty3v-xio(re+evj 3h jb9 e (s period on Mars, where the ac jhir(3e(zeje3 +-9y /vvtoxbceleration of gravity is about 0.37 that on Earth?    s

  What is the period of a simple penn/uh szgqhf 0) r1p25zdulum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 m, the pendulum bob has a mass of 365 giuw79vg i-ba (x xntuqe79w7:nx+ 7hirams, a w77ix (ui+ nnxhg: t99iewbv-77 uqxand it is released at an angle of 12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’s pendulum has a lengtcp:8 f*t,/m pjt*aanc h of 0.9930 m. If the clock loses half a minute per day, how should you adjust the length of the pendulum? shortejf 8at/*pc apnmct,*:ned by    mm.

Derive a formula forvkox a( lv8p./wbh6o.f8 eqluz.wbt);- e( ft the maximum speed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at a frequency of 2.5 Hz. At mf;749 nvt fcl it is released from rest starting at an anf9fmc ;4 v7ltngle 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 every 3.qa rj xovgx86mmw8 y9j0,lv 5t)v/ .az0 s. He measures the /5zo0vr j,lya.)6vvaxtq xm8g mw89 jdistance between two crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with a speed of9t wz *nw/2cenk td6j0m/ as5w 343 m/s How0z*dw9ck tnn2w/ wjms e ta56/ far apart are the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHdvbu;c 8 bp;wor9n4;s z (kilohertz) and r bs4pv9wou n;cb;8d; 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 a2fwbhk(z (u :n-k;sjof longitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one is twice as denje *2;ez,nefbbe( )tnse as the other. In which rod will the speed of longitudinal waves be greater, and by what facte eenfb;b)* ze t(n2j,or?   

  A cord of mass 0.65 kg is stretched between two supports 2* zannab)k,: v vhi3-x8 m apart. If the tension in the cord is 150 N, how long will it take a pulse to b):z vaa-k xn*n,iv3h travel from one support to the other?    s

  A ski gondola is connected to the top o zpy7y)h+ b v1nx;2dgcf a hill by a steel cable of length 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and sends a wave pulse along the cadz vb1pn)c 2+y7;ygh xble. 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 ,+ 7xwrioscn :oce8w7of his ship just below the surface of the sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is the ocean atx crw:,ns+o co7e78w i this point?    m

  P and S waves from an earthquake travel at differenul/g2zyv ;a,pl ,4pq 9,tgdsnt speeds, and this difference helps in locating the earthquake “epicenter” ,9l,gu;tz n d24,/ypgsvlqap (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 cabtfdey8eb0 gai182 )tn be approximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what ampli bafib8 1y)etge0 td82tude 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 amplitudesm uu yh:39gf1r3( nqrui(wd7d, of an earthquake P wave passing through tmd7u(q 9wrdu(: ug1in3yhfr 3he 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 Earth is measured to bek9gu5s y q5fi p5wxwb xx76(x65n:lrt j-gf 6v fvxf5j 5ig5b96pt lk7ynu65rx6 -xsx wqw :(g$ 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 h,nr8s lt wja :dauh(wp;13spi 2k g9/the Earth, but one is carrying twice the energy. What is the ratio of the amplitudes of the twjrsslg(3dhn8wtph au,1pwa:i 29k/ ;o waves?   

  Two waves traveling along a stretched string have the same frequency, but 3+a c) 1gyd7fae -zhdgone transports three times the power of the other. What is the ratio of the amplitudes of the tfed7 yz- +hgga 3)1cadwo waves?   

  A bug on the surface of a pond is observed to move up and down a total ve(y0lrufl jera *7l;d)))dcde rtical distance of 6.0 cm, frord)f)lae)l(de7d *;ycu0 jl rm the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown ijv7;aul t mll(+.oa p f+,:)du)ehr btn Fig. 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 moment the pulses pass each other, the string is straight. What has,;l l.ao+: deal(tupr)mv7j u tf+hb) happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundamental frequency, what are the1,lxydmkj /cpi + *;fn frequencies of the first four harmonics?j+,pd/ n x1*y;lc imkf$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates n b. ,o0ww8djq,tsp g 2/xb4qlat 294 Hz when unfingered. At what frequency will it vibrate if it is fingered one-third of the way down from spb o0xw2 ,,jb/g8 qtq4lwn .dthe end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequency of672kfqps7 ykz j- x0my 280 Hz. Name at least three other fr 7px2qzs06ymk jyk-7fequencies at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string7 fl7kbyhipa,m -4 b3echy6 j/i3 4htt is 92m/s If the frequency of standing waves is 475 Hz, how far apart are two adjl44 mt ye hjk ithip7hy3fb,-b /a7c63acent nodes?   m

  If two successive overtones of a vibratinzq83.r fm67tz w*utz97lx 7 auries(bg string are 280 Hz and 350 Hz, what is the frequeniau *.w83x7m(eb76fzl9 z7 s qrurttzcy of the fundamental?    Hz

  A guitar string is 90 cm long and hwbhixm fu*i. q1t:1.i.;r zg b2pwlz 2as a mass of 3.6 g. The distance from the brib2 r.*.zq .gmhp x iiulw:z2ti; 1b1fwdge to the support post is L = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, but it is bds+o4c kiu.alqz vb(2 e- 0:jmeasured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?So the th2s (4 iqb eblka:0o-.jzc du+vree frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hz, bu2jdi ei:jtb80t it is measured to vibrate at 205 Hz. Bybj :8j dti20ie what percent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attachedtl4 fj90 35zekg/aohg to a small-amplitude mechanical 60-Hz vibrator. Th5l09he gfztjk/ga 4o 3e 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 strin z 6y)vnkq;*apg may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how man zna6;y)qkp*v y different standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at just the rir5nun07vg )5p d9sny 5vpf fx,ght frequency, the water alternately rises an7v5)up,rspy90n55v dxf gnf nd 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 uvmhs +2a:5*,c4ad)t zeindl within the Earth between two kinds of material. If it approaches the boundary at an incidentv tau+za m5)*inel2 d,s:d4hc 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 “shelf0 6 ipx9ffsd9r” where the velocity changes from 2.8 m/s to 2.1 m/s If the incident wave crests make a 39x6 sdpi0 f9fr4$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air whc; h mq*lldl+3en it hits a layer of cold, dense air. If the sound wave hits the cold air interfacel;lc+ mlh3d q* 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 bounh7wr,t6u eftdl l+-k/dary between two types of rock at a 3t-6h, lrdl+ 7uek w/ft8 $^{\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. Aaaat sn289+z uccording to the user’s manual, the dish has to be pointed in the tzau+9aa8ns 2direction 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 travels acroo4t,7hzcu7i+ nkw -upss 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,nh c+zit 7o-pu74 ukw died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing cousq3cml ).3nj (bp1 bx ;p:iyar 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 cb.opb3 mqxp3y n(i1su);jl: with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a wibv,(e t/f9hf* : :oofseoya4hndow to a fire net 18 m below, which stretches the net 1.1 m. Assume o/*a shtf4h:: (bve9yfoeo f ,that the net behaves like a simple spring, and
(a) calculate how much it would stretch if the same person were lying in it.    m
(b) How much would it stretch if the person jumped from 35 m?    m

  A mass m is gently placed on the end of a freely hanging spring. The mass thenq:eg3+ qdb 4r 6x5dk zz:ic2cx falls 33 cm before it stops and begins to rise. What is the frequency of the oscillationr6 3q4kcx:cz:g5iq d2zeb+xd ?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig.m-vpc k :iro13 11–54), compressing the spring 5.0 m. (a) What is the spring stif:-irc om p3vk1fness 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 7srnqje;8m 6z beqe,4 just the right pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over thm ez;e46r7b , qe8sjnqe top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm fromhb(gr70a4vxr lh736hw uea 0u the center of a 33-rpm phonograph record have h7al7huv 6xr3r 4u0 eg a0hw(ba wavelength of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650ed ku( 0/ (()5 wburugeekl.oecos7.40t where x is in meters lk)r.goe5/ we(e ((ukud0b ueand t in 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 i. s9jd+ caaq5nts frequency if it accelera9an +cjqa s.d5tes at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands hiqka1n 0/ ;twvljlv8:ore0krn 6(;qon the raft, it sinks 4.0 cm deeper into the water. When he steps off, the raft vibrates 80qnr jk velkvoq;1(:0iha/;t r n6lwfor 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 instrumento y27kiznou3 ) are tuned to play at 392 Hz (G) and 440 Hz (7y)ku no3oz2i A).
(a) What are the frequencies of the first two overtones for each string? G : $f_2$=    Hz $f_3$=    Hz A : $f_2$=    Hz $f_3$=    Hz
(b) If the two strings have the same length and are under the same tension, what is the ratio of their masses ($m_{\mathrm{G}}/m_{\mathrm{A}}$)   
(c) If the strings instead have the same mass per unit length and are under the same tension, what is the ratio of their lengths($L_{\mathrm{G}}/L_{\mathrm{A}}$)   
(d) If their masses and lengths are the same, what must be the ratio of the tensions in the two strings?   

Consider a sine wave traveling down the stretched two-part hf t,8)wo:5vfgjlb3wy4w 99 a,a ujpx cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section verwjpff: 4o9, ,ha9xajvlug3 t 5w)8 wbysus 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 the tip o9-i u j4:kzsmcf each prong moves 1.8 mm zckju4-m9s: i 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 of frequency 1.5k r,vwabdz ;*; cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact wi;abdzvr,; *kwth the board during the oscillation?

A string can have a “free” end : /hvc/50snlhi7 rm ,mxx0g lgif that end is attached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelenghllvs0x/i/m mh0 n,c:5gx r7gths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 )ohb6*1 +xi efdqut atc/-y2v s — each one-way swing takes 1.000 s. v hbdqc 2/otf6ya*x1 ui -te+)
(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 vertic hg4pq)d4:x( kud, tvsal direction or can swing as a pendulukv:ud() 4d gthqp4x,s m 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 stretcugn 36ao/ 5dffhed under a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a sfao 6u 5d/3nfgecond pulse is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspendedh/j b9cmezoft b *3*,d 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? (Asdb c/ ofet,jm9*z3* hbsume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel crane cable is 2 dy2u, ,yy/l2nmyeix 52 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end ,ydm yyy,22x/eiln5 u 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 (which also h v fckr:8qo /4jz*olykp7ee*dv,o,-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 moduvyq -,/* jopzo,lhrk47o8 d kfe:e*vclus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz