Give some examples of 4i/z5v vwp wm.everyday vibrating objects. Which exhibit SHM, at least approximately?/zim4 vp. wvw5

Is the acceleration of a simple harmonic oscillxe (3mherb:w/ hfd-64wpev9 fator ever zero? If so, where?

Explain why the motion of a piston in an automobile engine is approximately simh x/h:4n4 ap 6dd8yw jxr,irt,ple harmonic8rrdj, ph 6ynh x:a4 idwxt/4,.

Real springs have mass. Will k x6:e su6npwgpf4 4+ mvjk7f3the true period and frequency be larger or smaller than given by the equations for a mass oscillating on the end of an idealized massless sprinnw6p+jusm7: p4ef34x kfvk 6gg? Explain.

How could you double the maximum speed of a simple harmot.zo b1*n cin 8znr rvxme801/nic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spr+dh /g 0ytpta*ing scale, and then is released. Descri attpdy0+ h*/gbe the scale reading as a function of time.

If a pendulum clock is accurate at sea level, lud( 2y6(y8x)5 rpu)z emkdho will it gain or lose time when taken t6dr8(mdz)k u ohl)ex( 2pyy 5uo high altitude? Why?

A tire swing hanging from a branch reaches nearly to the ground (Fig. 11–48). H)cut ved 121k dqy.3oqow couqcq1.vt o 2eydk1ud 3)ld you estimate the height of the branch using only a stopwatch?

Why can you make water slosh back and forth in a pan only if you shake thev 2m :p3.i.*ny wit- sva5h:9sbr hd.vae- zud pan at a certain frequeme.39v.:v -as nhvui:5d ia.br d -zsyt 2hp*wncy?

Give several everyday examples of resrw*/uec z5tuqnywc+ me(1c+ ,ji6z6 eonance.

Is a rattle in a car ever a resonance phe5juzbv+9 suh )2fk ybp:1f 4rpnomenon? Explain.

Is the frequency of a simple periodic wave equal to the frequency of its subvsq - zw-g*+u p(ww3*vhfo7ource? Why or why notfh(+ wq*v-uw-ow zg*uvb s7 p3?

Explain the difference/zbscl fboqbx 9 )(,n: between the speed of a transverse wave traveling down a cord and the speed of a tiny p,x9b bo(snz/qc: f)l biece of the cord.

Why do the strings used for the lowest-frequency notes on a piano normall69e bdz v gvh+ kb2w.)67lnegyy have wire wrapped ybz 6dbh l )92 +6wk7egvv.ngearound them?

What kind of waves do you think will travel down a horizoh ksakvhr. n/yn l*x f7r/46u1s *kwl2ntal metal rod if you strike its end (a) vertically from above and (b) horizontally parallel to its lengkf2*rshl*la k k /xur4nn hs7yv .6w/1th?

Since the density of air decrea92rcq goci96zcc lemg-v) a15 j5cbu5 ses with an increase in temperature, but the bulk modulus B is nearly independenqrje5 acg51mb c9cgu)cl62-c i95 ovz t of temperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why c;dv5 *9oiubog2 frer*ircular water waves decrease in amplitude as they travel a*ioer;rguv*bo25f d9 way from the source.

Two linear waves have theerj4t;km t( :c 0lg0lg same amplitude and speed, and otherwise are identical, except one has half the ;tgk0l cetmj0r4g:l(wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sections of .sd 84p)w4 c scct1popcord as in Fig. 11–3c 4ps.4w t1so dccp8p)3, the frequency does not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there any places you coumr ym4 pv 3h71xi:d0yhld touch 7iv0yxyp:mm3 r h 14dhit with a knife blade without disturbing the motion?

When a standing wave exists on a string, the vibrm+sc3htv8pl -8mmv/,hc 2lgp ations of incident and reflected waves c -pc8tmhm,8chvv2+/l g msp3lancel at the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being 7etc ;jffbe u1kz(4:b transmitted from one place to another, how might we determine whether the energy was being carried by particles (materia4 7bf(uefjcek;: z1tbl bodies) or by waves?

  If a particle undergoes SHM w,e6gz9akeiy ,)bbl 5with amplitude 0.18 m, what is the total distance it travels in one period? 9e,w y glkbezai,6)5b   m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it but i.fqm bg(f*cu vc 0j0v+m3ie7y s 85 cm long when a weight of 180 N hangs from it. What is the “spring” constant k of this elastic cord? cu m*qvfi(. vbc07ym3fj0+ eg   N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg d s o+ v x5m;-siykw.c(b:c:mdkriver gets into the driver’s seat. If the car goes over a bump, what will be the frequency:(xcms wdb sv o5ymck: -.;k+i of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.:8g9t/+q ajcd axyd3l.n) froae;2a f6 cm when a 2.7-kg fish hangs from it. (a) What is the spring 8. /e3dg9 2acfxn;yqr:dot f aaa+j)lstiffness 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 vibrate wghg+7yd+l 9fs with a frequency of 3.0 Hz when a mass of 0.60 kg is hung from it. What g+ +9lyg wf7dhis its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicatitt8eq, r8+z abkbjd+i.nn (3cng the position x of the mass in Fig. 11–2 at times t = 0.b3 tdi+a8+kb8tj nz erc(,qn,t = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

  A small fly of mass 0.25 g is caught in a spider’s web. The web vibrate8k na9sj2) vzss predominately with a frequency of 4.0 Hz.j2s)9vk8 nzsa
(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. m5a58fg4n vx)1 jexsz88 Hz. When an additional 680-g maszjx5 ngx 4m5va s1f8e)s is added to m, the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per second wi+ yncoboaf-en 8. 1uy1th an amplitude of 0.13 m. Determine 1 yao.1-e8fyn+ bncuo
(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 th y;pe0)s g)npu)azu.x e speed of a SHO half the maximum valpe);gx0uyn)uz.)pa sue?$\approx$    A

A mass attached to the end of a spring is stretch-mb+f7hc v-g( gg-qaxh) gv2 xed 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 stre+m 2eprci rwj l. 21f;5vhbya/tches a vertical spring 0.315 m. If the spring is stretched an additional 0.130 m and released, how long does it take to reach the (new) eqabvlfje r+2 2;.c /rh1wyi5p muilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with spring sti :qtyq /6+v3hr qvr95mhc ya,jsq:0vfffness constant k = 280 N/m and is executing simple harmonic motion. When the obvfc: vyh mt95q yh3q +:q0a/6vrqj,srject is 0.020 m from its equilibrium position, it is moving with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to coajp;z ( mk2ldfp8a5 o0mpress the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will the ball leave the gun?f0z5pa; mop8 (d2ljka    m/s

  A mass sitting on a horizontal, frictionless surf( x5 pflts jw.8utd6u7ace is attached 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 exj56tdu(u87p fwx lts.periences 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 . q7ftytmxo2gec) lqp): 8. sqis in meters and t is in seconds. D):.cpmo t ye gqfs82x tq.)lq7etermine
(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 fro2ur+n1darg fp )4ei l.pj.9zom equilibrium is the energy of a SHO half KE and half PE? ±+jfgp.id19po ena l rz.)ru 42    A

  If one vibration has 7.0 times the energy of a second, but their frequencies 4,5oyp x5a2y ke,shiu and masses are the samey5oex, p 5as,i y4huk2, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin osci.rjuy7qkc 9u6+w q xze)w8uo ,llates from a vertically hanging light spring once every 0.65 j qwu r),kwc6y+u8q.euz 79 oxs.
(a) Write down the equation giving the pumpkin’s position y (+ upward) as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. y = (   m)cos($\frac{2\pi t}{0.65s}$)
(b) How long will it take to get to the equilibrium position for the first time?    s
(c) What will be the pumpkin’s maximum speed?    m/s
(d) What will be its maximum acceleration, and where will that first be attained?   $m/s^2 $

A block of mass m is supported by two identical parallelje8mdgl a 2889t2inff vertical springs, each with spring stiffness consfnm afe8 8jtil 9d2g82tant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates accorddtq ,zajr*:oz 6e:1o nq(n mf1ing to the equation x = 0.38sin6.5t where x is in met *a o1nzeq,6zr o1:fjtm(nqd :ers 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,/ oj:gg3h0/b) t2fvl0cb ihuo labeled A and B. For each, 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 ) c5quw 4cqtl/a horizontal spring (k = 124 N/m) is struck by a c 4uc)qw5/t lqhammer, which 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 stiffness j8 s)nz:u gakg1 ,c:njconstant 305 N/m vibrates with an amplitude of 28anjg ck81 z::,jnug)s.0 cm when 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 two springs, z gm-q-d 0xkgf 4k1gh(rjc 23vwith 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 hor2qdjaq hos 3.8izontal spring whose spring stiffness const8dasj.hq o32q ant 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. After reaca2.un. ep y/mqhing his lowest .np2.ye / uamqpoint, 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 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 exactlymhkg y8er 6u x1 5n1dvq.e 6yns27vy3k 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 oj55 q t53 ud:lnjsrsf0ne swing per second? (That is, one complete vibration takes exactlyjn st5j55 30 :qdsflur 2.0 s.)    m

  A pendulum has a peribh6nq4piw( s0 k*a c,fynu* z9od of 0.80 s on Earth. What is its period on Mars, where the accelercwnf**bs z 4ai6huky(q0 ,n p9ation of gravity is about 0.37 that on Earth?    s

  What is the period of a simple pendulum 80 cm lih n83:.bxwxpong
(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 365jyovj i ro4i,7 l4a7 .8xm,dng grams, and it isimvxlja4oy , g47r o .ijd8,n7 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 cloc -ens ,v + v9hx)rn7t d6hci2gt,nfu5ik loses half a minute per day, how should younf),i- ht+e9 vdxsru 2,5vitchgn n76 adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximhkd( *y)tdxjt /tj -ul4t/nk-um 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 oscill)0hi gsqhzz8 hou g(66-m/ hfjates at a frequency of 2.5 Hz. At it is released from rest starting at an anggh- (h)sm8hqzg oif 0z u6/j6hle 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 anchoredn1- 1wnxc .*lat t1c rgx+q- j32gfjwg boat every 3.0 s. He measures the distance between two crests to be 6.5 m. H3+-.tg cn nr*gfqc -gx lt112xw aj1jwow fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travelc:i7:vrw+k9cudug p + s with a speed of 343 m/s How far apart are thc+v+rg7 i:up9:cu kwde wave crests (compressions)?    m

  (a) AM radio signals have fq3:alt 2m3 pe1naw/jg requencies between 550 kHz and 1600 kHz (kilohertz) and travel with a speed1twnm33pe/g:l jaq2 a 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 ooh s:(9 4ihhzwf 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 4f2m9zy; as rris twice as dense as the other.z;sm24r r9fya In which rod will the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is str 1)g1 ugiqxi;detched between two supports 28 m apart. If the tension in the cord is 150 N, how long will it take a pulse to travel from one support xgiu) d11 gq;ito the other?    s

  A ski gondola is connected to the top of a hill by a steel cable of nn 8(oymqp,hv 3zav2/ length 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminaq8zn 3ah(v2/ ,yovn pml 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 below the surface of the4di-.td4lat jr e126smz1fkj sea. He hears the echo of the wave reflected frt11- k4md.2se f4dliazjjr 6tom the ocean floor directly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at different speeds, andjdfr8+y, 1 xyd this difference helpsx+ ,rd yjyf8d1 in locating the earthquake “epicenter” (where the disturbance took place).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced surface wave can be approximated by a sinuj)v -. jfoq1hmsoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually i.mj o1vqh-fj)nclude 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,w-nwp u7e sc 7.yz3:ed and (b) the amplitudes, of an earthquake P wave passing through the Earth and detected at two points 10 km and 20 kzu7.s-yw3: d cnew ep7m from the source?(a)    (b)   

  The intensity of an .zgiw cnq8 q7-earthquake wave passing through the Earth is measured to be qc7 i 8gnwq-z.$ 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 o+ b07t m:w.qg(4v/ 7zdm whuav;vwg vqf the Earth, but one is carrying twice the energy. What is t w m7h.u +7gvvg:m/;b4z( qtv awqd0wvhe ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched strinjf/hxg;xa-/cyo* gd 7 g have the same frequency, but one transports three times the power of -;xxc7g /f jago* /yhdthe other. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is ob8kgc7pk* cohqu67p / zserved to move up and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease to 4h7p*gu86 cpqc/kok z7.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving towa8a higm +1chxhg:ok4f+nj1/ix;oq i 7rd 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. 11jkmh1 4 hxo gcii;1+a7/fig8+hqno :x–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 ojq *hn if7*5kyqtv h -- o(98qadcps:440 Hz as its fundamental frequency, what are the frequencies of -si5* qjo -cha( pfq *8 9k:7otyvqdnhthe first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what fredc( ,jv(;p vkoquency will it vibrate if it is fingered one-third of the way down from the en (p ok,(;vcjdvd? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four lo6;.j;t7s x ejqgcruv2 ops at a frequency of 280 Hz. Name at least three other frequencitq;7x6u. vg r;c s2jejes at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the89y0(un*andq w 0gqk9igl/ k m frequency of standing waves is 47 y d( l*gu89ka09nq0/qgnwmik5 Hz, how far apart are two adjacent nodes?   m

  If two successive ovex(.h t rwtv;o;7osm/ajcql 8,rtones of a vibrating string are 280 Hz and 350 Hz, what is the frequency s7tv.rhqo wj(/c, t8;l o;xmaof the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distanzc/8dn5 iib yz8/ (kaxce from the bridge to the support post is L = 62cm and the st5b (y88xac/iznidz /kring 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 measur ,bs:lmd+ n6yced to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?Snsml by:+dc, 6o the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hz, j0 6)0l,v,pf(hnwwhco4ik hh d4u0ambut it is measured to vibrate at 205 Hz. Bypnj4hh( ,f wv6 0wh0ckm)u lidoh4,0 a what percent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attache(4c)rbdfan8fwsz* (z d to a small-amplitude mechanical 60-Hz vibrator. The string’s f(*(8crfsa 4zb nw )zdmass 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 tqj,6*m v.d .cj:cnzazhe string may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many ,najzz:cdq .6v jcm* .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 twk8b3 i8uzq6b he right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a wk683z ibq8bustanding 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 trat2 dk 9c,;dtlhveling at k.0 km/s strikes a boundary within the Earth between two kinds of material. If it approaches the boundary at an incident angle th, ldkd92t ;cof 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 “shelf” ro-f/ kq+icou0x ma27where the velocity changes from 2.8 m/s to 2.1 m/s If the incident wave crests make a 34q07i+m-crouofxk 2/ a $^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling inig.9 ze 3qqpj- warm air when it hits a layer of cold, dense air. If the sound wave hits the cold air interface at an angle of 2ezgi-3q9. jpq5$^{\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 boundary between two types of rock atspi z sa3xof3 .aq 0z;tw-2d(g a 38 .3z;q oztsaxsd3a -gwpfi20 ($^{\circ} $ angle. As the wave crosses the boundary, the specific gravity of the rock changes from 3.6 to 2.8. Assuming that the elastic modulus is the same for both types of rock, determine the angle of refraction.    $^{\circ} $

  A satellite dish is about 0.5 m in diameter. According to the user’s my v iefj0upnl): :h*,lanual, the dish has to be pointed in the direction of the satellite, but u*h :ypf: ev)lil,n0jan 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 across the Pacific +t6 vf) pbzei:e3 bm:zOcean. 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 sho +vp z: 3mbfe)z:i6btere to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a sps)su 6i6y8:ppm(pe rpring 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/h8 6 p():puyeps pri6sm). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fir1 de0us584dwn4o-g spd1o) njlrk+yy e net 18 m below, which stretches the net 1.1-)41gwd 8 yo lj1 eonny54krpudds0+s m. Assume 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 /a ki6rn-aiu0 the end of a freely hanging spring. The mass then falls 33 cm before it stops and begins toun- a0i/k 6iar rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fin a,f7mfst1x98 q/ikvg. 11–54), compressing the spring 5.0 m. (a) What is the springfxiv1kq fa n,9ms7t/8 stiffness constant of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of coffee (diamzs4wept5da 04 57ib7 jpd;/u2xpgmje eter 8 cm) at just the right 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 the speed of waves inj7piem/;pz swbad5 54 up42exj td0g7 the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the center of a 33-rpm 0llhf y bjr+)jws //;,tqwyl +phonograph record have a wavelength of 1.70 mm. What will be the frequency of the sound emitted?+b fjyq tlwwr+//s0 ly)jl; ,h    Hz

  A 2.00-kg mass vibrates,gk2 jww shu+-* o-jbd according to the equation x=0.650cos7.40t where x is in meters and t in seconds. Determinbdowjh- ,gs2wu*+k-j e
(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 frequencyjs uan,f,tp29 mtv43 / rhntj5 f. What is its frequency if it accelerates at 0.50g (amp,4n9rnjstvja 2 u35 ,tfht/ ) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-v ee0,bih/6 h0bo kw44;cqwgckg man stands on the raft, it sinks 4.0 cm deeper into the ;h 00vwi6be4 4k/whogc,cb qewater. 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 toct9-d4lslx8 i q7u vg2 play at 392 Hz (G) and 440 Hz (Ac ud v98ts247l-lqgi x).
(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 twjqt j x5gebgu:/62zh3gp 6 h3raveling down the stretched two-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wavg/2jutx h:g6 e zbp6 jqgw3h53e 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 the tip of each prong tuc w *,kgt9oqligt46 1 cgw kvwg*,;+moves 1,ww,kgg+wc tivg4o kt9cg;l *tu*6q1.8 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 wit6sig6eg 5nf*d ds6 f c3p7qa9 )*allamh simple harmonic motion of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebbf*nei l6cl)ddqs g 66357gf9a*ps maale 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 isaz1w6yns;: mz94wi7lwg-zz b attached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with one egnbzs iy wz:ww 1z9z6alm74;-nd fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 spo)j wc5ne q*4 — each one-way swing takes 1.000 s. eqo c w)jp54*n
(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 vertiq-j4o)h;g p n h1ffvj8cal direction or can swing as a pendulum of small am;jv8o fjhq 4-gfp1 h)nplitude, 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 N. A pusoraa e)5r82oed9a61, k nrr qlse is generated at one end, and 20.0 ms later a second pulse is generated at the opposite end.oorrr5d81 ns ea 9r), kqa6ae2 Where will the two pulses first meet?    m

A block of mass M is suspended froo(yp -9 5bdcemm 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 te 59c p(-omdbyhat 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 isj2ig3lq )bf3 s 22 m long andql3sgij)2b f3 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 (w8fyrfolume 7vr74 8xi:v27zz hich 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 vi m y:zeuxvz2l8v7 7ifr7f 84robration, given that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz