Give some examples of everyday vibrating objec5 dej5(ftp/h uj)) givts. Which exhibit SHM, at least approximatjg/dj vf)5i)p(u5ht e ely?

Is the acceleration of a simple harmonic n*,e)rdc lef1 jt,in8 oscillator ever zero? If so, where?

Explain why the motion of a pistonjk krw dab.7)z m0pey31ru:: fyee3q4 in an automobile engine is approximately simplek kqmy zp u:fay .weeer3 4bj073d)1r: harmonic.

Real springs have mass. Will the true period and frequency be larger or smaller j1*r1ld 4yei mba.lp/ -npd)ef.q4hlthan given by the equations for a mass oscillating on the end of an idealized massless spryfr e4 pn.1lb*-.m4i ehllp/dqa 1jd )ing? Explain.

How could you double the maximum speed of a simple harmonic oscillator (SHO0q k zn9u(pypl)*zxl7)?

A 5.0-kg trout is attached to the hook of a v2zfxk y:35klgc-,ko a vc;s:b ertical spring scale, and then is released. Describe the::5;kvlozx3fgycs - kbc2ak , scale reading as a function of time.

If a pendulum clock is accurate at sea level, will it gain or lose time wheg-y0:/ wta 5f)znfzbvn taken to high azt5a- znb)0vyf g:/w fltitude? Why?

A tire swing hanging from a branch reaches nearl ds ge4/,qb3sjlr)(kly to the ground (Fig. 11–48). How couqrb)/js3l gsl4k ,e d(ld you estimate the height of the branch using only a stopwatch?

Why can you make water xb zhho7m)e(9 slosh back and forth in a pan only if you shake the pan at a certaihze oxm9 )(bh7n frequency?

Give several everyday examples of x bgc* u ce60flw6b1nj5gx ,5uresonance.

Is a rattle in a car ever a resonance phenomenon? Explain.owt(mbztb+ 0ks ( au/q7 za7n8

Is the frequency of a simple periodic wave equal to the frequency ofazzk w9ku/21 xm3gb3m8s .ssdsih 1 s1 its source? Why ob39szm1is1 1zkkmga2/ hs wu3ss. x d8r why not?

Explain the difference between the speed of a transverse wave traveling domn3 dxa6ktnuc,va9uplx 56 81wn a cord and the speed ouk vt 16 p,mxx9nn5ad6a8l 3ucf a tiny piece of the cord.

Why do the strings usnjyeqvk am,g*ef 76+w:,gmr *ed for the lowest-frequency notes on a piano normally have wignqm:* egk ,wv67rmye*a ,+fjre wrapped around them?

What kind of waves do you think will travel bx t4o.u5 velrf 9tx-x/;5nnb down a horizontal metal rod if you strike its end (a) vertically from above and (b) horizontally parallel to it ebtxnuv9/t- x.5;5 fnxrl4bos length?

Since the density of air decreases with an increase in tempera5h4 h t9+ gjcwet)zab+ture, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves in air to vary with tempera5+g je4h) 9at+ tbhwczture?

Give two reasons why circular water waves decrease 4 g0vhdcg8 3e mljoa47z06 chxin amplitude as they travel away o70e 40gcgx lhzac43v8hjm6 dfrom the source.

Two linear waves have the same amplitude and speed, and otherwise are 9efs+:s ijst :identical, except one has hali js :s9f+st:ef the wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wa3*dcr8wai+po ve crosses the boundary between two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocityd* 8a3o c+ipwr do change). Explain why.

If a string is vibrating in three segments, are there any places ogw; n3 d:yr; +few.m7etf 8wmyou could touch it with a knife blade without disturbing the mom;+ ny7o:fm 8gd. eftewr3 ;wwtion?

When a standing wave exists on a string, the vibrations ofe ,xuc9la11 sq incident and reflected waves cancel at the nod qcsu,xl911ea es. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmix /gef 5st-kw -hecb0wbrd83/ tted from one place to another, how might we determine whethe-w-k8se5g 3ecbbd// rh0ftwxr the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the total dista +z 3ob: zq6/(jgligyknce it (k3joq6bl/+ yzzg ig:travels in one period?    m

  An elastic cord is 65 cm long when a w kbv*+d yo3-t. fulw:jeight of 75 N hangs from it but is 85 cm long when a weight wf -jtuok*+: lv3 db.yof 180 N hangs from it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mmc(s;i6 1vd 8:ae rdbva when its 68-kg driver gets into the driver’s seat. If the car goes over a bump, what will be the frequency e8(av d1;vd :6is cabrof vibrations?$\approx$    Hz

  A fisherman’s scale streth91-kn x9q 7hwj00fxw 88g9vriqpubr ches 3.6 cm when a 2.7-kg fish hangs from it. (a) What is the spring stiffnegw7 n9qrhv i8 098pxq hbxw0ukfr9j1- ss 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 witwe) qfba d/)t+h a frequency of 3.0 Hz when a mass of 0.60 kg is hung from it. What is itq)wted/af+b) s frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of 4ks7dfhmxb +mzmep(/h4 p: 1u the mass in Fig. 11–2 at times t = 0, zkumb fx:1dphm44/ s +ph(7met = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 vibrbxkqwk)tqf 09.;s4yq ates predominately with a frk s;tk40fwqbq)q 9y.x equency 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 0hk i )i8: wy/yaf+jyf5k(;bgq.88 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 Hz. Wiqkyi:(kyja/w+f )f5g8 bhy;hat is the value of m?    kg

  A 0.60-kg mass at the end otr6oly-f pslwd j u r/(n8-6m)f a spring vibrates 3.0 times per second with an amplitude of 0.13 m. Dete/yu6(8d)6 pfojslr- wlrtn m-rmine
(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 halfir 5af)a .uu,8xk2fhv the maximum value) x8v uaf2r, .5hiuakf?$\approx$    A

A mass attached to the end of a springa41iapns2d0pf(p fbl)x9s420 wyjxq 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 st1yj 0gwr4n 2bewz7 0azretched an additional 0.130 mjzyrnzg4700awe 2b1 w and released, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg ismz0jm t: /h1yc attached to a spring with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equ0 zchmm j:t1y/ilibrium 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 )rdehjt7j( 6oq :o o1e80.0 N to compress the spring of a toy popgun 0.200 m to “load” q t) 6oh1e( 7oojejrd:a 0.180-kg ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontalb8 xkmpl *jt6;a /jh8m, frictionless surface 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 releast6m8j;a/ pmhjkx l 8*bed from rest with the spring compressed, the mass experiences a maximum acceleration of 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates according to the equation x jpo pwiwba9+vld 6/8uai.jb,h f( c (8= 0.45cos6.4t where x is in meters and t i6p(+ha(iwb8jac j ui.,9p 8f/bvd l ows 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 equilibriba(zl2 1 zp:s7vh9 yauy2w 4mzum is the energy of a SHO half KE and half PEl7zzmuy2av:h(19w2y z4spa b ? ±    A

  If one vibration has 7. i6*fxp:kirqqilj ;(( 0 times the energy of a second, but their frequencies and masses are the same, what is the ratio of theil i;fkjqrq(i6: *x(ip r amplitudes?   

  A 2.00-kg pumpkin oscillates from ab 87ybz 5)l rjvi)wvq2 vertically hanging light spring once every 0.65 s85q) wvyvbbl7 j2r z)i.
(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 supp ac0uxud6h)nfa( :jw 5orted by two identical parallel vertical springs, each with spring stiffcu ux6ad(jwa)0 hn5 :fness constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.b0kjco d4;7-3- 0hfduwumf yb38sin6.5t where x is in meters a;dj4 y3douuk f-7 m00 bcbwh-fnd 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 eachag3,he3nxw c 0, 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 a horizontal springdy5f0lwxujyuby * m+s6o 34g+ (k = 124 N/m) is struck by a hammer, which gives the mass3 +xl j5g+u yy*ydusm64wo0fb 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 ciwwt0djro1,79yh gv2qx;2z dg uy l/:onstant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium ,2jxguw7y2 q09oghv lzdt : /;rdy1iwpoint (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 oxe(.cosq0zhd 6l x84two 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 attavd4*xb9izl ;f o7,1 rfzworr 4ched to a fixed horizontal spring whose spring bw ir 4vdorf794x, olz;zf*r1stiffness 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. After reachingp3 uveg*w9 pq6 his lowest point, he oscillates up and down, hitting a low poin*wg3 p qe6vpu9t 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 exactly 60 s. m s-qw3i7s:kh 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 per1q(okhg74f. /fv(jv3pzuq ta 0xaq w)k -wm*w second? (That is, )jw7f.4kvkt qpw( qg a*z1h(vmf 0q3wxa-uo/one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on Mars, whefr t),zt8izpxr)y u:: re the acceleration of gravity is about 0.37 that on Ea)i )turzrx:f:8 y zp,trth?    s

  What is the period of a sq:m.v 8(pe+e9p +ww3nrqp e+5lw3ng4tf d ehlimple pendulum 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.kd bg7eb-b r/q*qat95m q bz)/760 m, the pendulum bob has a mass of 365 grams, a5b 7z*)/- mbqqadqkb9 b/tg rend 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 *uiz*b*dpu1m pendulum has a length of 0.9930 m. If the clock loses half a minute per dp*u* 1dbzu *miay, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the bg.fmu6 vi,a+ n2q pc0maximum 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.; v 86bzbvmb/le /b1ih At it is released from rest starting at an angl8 hbe 6b; mvl1v//bbize 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 4rlwrr6-x 9da3.0 s. He mew9a rrrx-4l 6dasures the distance 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 an l4 lc0/7ospzc 7dm9qnd travels with a speed of 343 m/s How far aparl 40c pn77dcmlq 9/ozst are the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (kilohertz) a8o2d )+i /mqvun24j6wxvz fvynd travel with vfz 46o2v+du2/vy 8q jimw)nxa speed of $ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

  Calculate the speed of longitudinaly0:f azr5izhhkhmj .52s4 ah) 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 tuy/19acib/th)zbg pz)2/q yy wice as dense as the other.zi/yyp/12 hzy)t/9a) uc qgbb In which rod will the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched betrbazd hu:-l (h i6xm ibk;752xween two supports 28 m apart. If the tension in the cord i;:xra(m dz bih65k il7b2hx-us 150 N, how long will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to the bbh8cm5v:g 1q dm :f/ctop of a hill by a steel cable of length 620 m and diameter 1.5 cm. As the gondola comes to the e:1cq:g8d bmc bf h/vm5nd of its run, it bumps into the terminal and sends a wave pulse along the cable. It is observed that it took 16 s for the pulse to return.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

  A sailor strikes the side of his ship just below the surface of the sea. He hear 3).-chp30b lz)wnre f*ebl cr2 hwt1ws the echo of the wave reflected ff0pr3ee hb c)*lbnzw.wtc 3-h w2lr1)rom 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 spe bj29)3xx8slb v 8hcareds, and this difference helps in locating the earthqua) rjx3x sh828bc a9vblke “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 sinusoidal transvecilo, 9:hjean*51ma jrse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that * 9 aio: ja5lnh1e,mcjobjects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplitudes, of u; /m qq,15gs mmqu aj24puca1an earthquake P muua,4qs2um m1 pg/a 5;qq1jc wave passing through the Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is measured to bnib. p, p 7b;t)fb7txae .x; ,f77 nppabtibb)t$ 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 th3e7 i dkqhnkd 3p5yh77e same frequency travel through the same portion of the Earth, but one is7edkd7 3qhy 7i n3hkp5 carrying twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling ah4j t*k k8rwi o:6a0vdlong a stretched string have the same frequency, but one transports hik wo *6j0rkt d:48vathree times the power of the 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 q 2) d/zgpy.gwdown a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm, by what factor does the ggy2)d/z qpw .bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each o4a;iyiivbb/ ;els7fl +; bt*r ther. (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 happeyb;+;vi er*;lb7/ba ti 4fli sned to the energy at this moment?

  If a violin string vibrates at 440 Hz as3/ gx8,y-zm4qf hj0vbv3s mlx x8xx:h its fundamental frequency, what are the frequencies of the first four harm q3h-xxxjb mh 4gyz,x0 vvslm/88x3:fonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At whv-6oh3 t1d(q abz8tk;vcjvr y5svj3+at frequency will it vibrate if it is fingered one-third of the way down from the end? (That is, 5 s-j 6d q3bt;czvyrjv v ko8a+1ht(v3only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequency of l :o zqix,aj1feije:coix;.. a g.i89280 Hz. Name at leasta1c 8xigj9q.,; j li.feo a:iz:oex. i three other frequencies at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the frequency of standing wadpjy 6am *+kd9*j4fqv j(qy6 tves is 47+*j pfq4v6y*k6m y(dat jq9jd5 Hz, how far apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 z+k9m,jz5dcdh z 8d6vHz and 350 Hz, what is the frequency of the fundament mk, ch6+dz85zj9dzvdal?    Hz

  A guitar string is 90 cm long and w4jc s5gybpu( 9hf)po15 (ib ohas a mass of 3.6 g. The distance from the bridge to the support post is L = 62cm and the string is under a tension of 520 N. What arej5( ysu4p9c p 1bfi)h g5o(bow the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrates/n 1z o:nz3vk7glj1i at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changz1okslnvzgn i/7:1 j3ed to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed t +xy:yj 9ioeh1o vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed thi9 e1yxj:oy +o correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-amplitude mechanical 60-H3,/6q egyzr nhz vibra 6 3nzr,eqgyh/tor. 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 du.ej:2 akpkv w97p:t string may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how:ukp 7. 29 adtv:wejkp many different standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at just the rig :0m 3kcqql xrht3* ojfz3f;e/ht frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 qocxm0 lr;k *h3:t/j 3fz q3efHz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at 9tq 2r3m4j w-a.zgkenk.0 km/s strikes a boundary within the Earth between two ki eg4kr9waq-m 3n.tj2znds of material. 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 unoh.p5/ n lrtt7ko( evmb8;dj.+ b5grcderwater “shelf” where the velocity changes from 2.8 m/s to 2.1 m/s If the incide5c7g+ thjoo5e;ld /8 m pbnb(kv.trr.nt wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling i(.p euk kk n ,-wcv9pnch2h2m-n warm air when it hits a layer of cold, dense air. If the sound wave hits the cold air ( -k-nmkc22.uh, cwk hev9 pnpinterface 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 steye3btfi3 (. u(kke;n rikes a boundary between two types of rock at a 38 3tyb3 nu ( ke(;efeik.$^{\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 diamet e 0-(4ef bagvrnoyg+*er. According to the user’s manual, the dish has to be pointed in the dire +ng40f ya(bg ere-*ovction 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 travels0ty )aw48hcit 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, peoplea48hitt )y w0c have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness constant of 550 k8rt hr-l6u8 q j5zoc +5 jm8+qf0dobquN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, 5f86r5uj+m+ -hbl0qooqqj z 8rtd uc8 collides 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 window to a fire neh 3m ve8fxk sn: xg1 /nwvan8a3,;snm9t 18 m below, which stretches the net 1.1 m. Assume that the net behaves liassn /nx1n 3g9 v,3x:kw;8nf8h vamme ke 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 td*mg.ksjir x*80 qxmvq*9/ 0qufx hf 7he end of a freely hanging spring. The mass then falls 33 cm before it stops and beginhf9xq x/m.k0 vxj f0*8*sqrg* im7duq s to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at e *pwphl2e6f n(r -p3ca speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the pcwe-6rpe3lp*h 2( n fspring 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 ofm,wsnt6;k g2 pn7w /aqz3jx:qzt0 ) rm coffee (diameter 8 cm) at just the right pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spillj t3z6xtk 7,annr;/wmw0)2pmsq :qzg over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certaincr, id/vv 7f2n groove 10.8 cm from the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frv7ncvd , 2rif/equency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t where x isfyoxd(15mpb1/ .n qf85aplp s in meters a/yb1o5a .dpfnpx sq15p mf (8lnd 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 i8ud)f0hugcaq 1z 0b6ds its frequency if it accel0uq1ugaz)8f hd0 6d cberates at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands onwlr11crzid5j/z0 l ve jv-nv53 s+gh4 the raft, it sinks 4.0 cm deeper into the water. When he steps djz +ls/4e3-rc vhr1wlzvg jn0v51i5 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 areme xvf1*nm ((z tuned to play at 392 Hz (G) and 440 Hz (A).x v1( z*mmf(ne
(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 ,+i7s4jd-v wgjt;usiqv0u r0stretched two-part cord of Fig. 11–33. Determine a formula (iu;,0vgs04+ri7 jvwsd-jt uq a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in 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 26lmju+h wf5-w,ii h5 j94 Hz, and the tip of each prong moves 1.8 jf h l5,ihum9 ijw+5w-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 simploi0u 3e lal8q.e harmonic motion of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in or8oail e0u 3ql.der 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 i9d7ejdz8 z+s lf that end is attached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string wi d7jsdlzz 8+9eth one end fixed and the other free.

  A “seconds” pendulum has a 0gr:d opht x38period of exactly 2.000 s — each one-way swing takes 1.00xthd:r0 p g38o0 s.
(a) What is the length of a seconds pendulum in Austin, Texas, where $g=9.793\mathrm{m/s}^{2}$    m
(b) If the pendulum is moved to Paris, where $g=9.809\mathrm{m/s}^{2}$ by how many millimeters must we lengthen the pendulum?    mm
(c) What would be the length of a seconds pendulum on the Moon, where $g=1.62\mathrm{m/s}^{2}$    m

A mass hanging from a spring can oscillate in the vertical direction or can swinxdj*x :lm gts,lbd.-ka4g pbq1 1s*4 mg as a pendulum of small amplitude, but not both at the same time. Which one is longe:la,jmqdk-x1b*m4.pbx14g l*ssd tgr, 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 h+spes * v67fg(o7swj123 g 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 pulse*vspgj w6o (sf e+s7h7s first meet?    m

A block of mass M is suspended from a ceiling by a spring with sph g9xw0jn 7aa+ring stiffness constant k. A penahn7x9a0 g+jw ny 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? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel crane cable is 08tp ybu)k7 ws4:wvyk22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. What is the perik0s4b:)8uywyk twv p7od of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello restsj3bo1 k d+(khs on a plate as shown in Fig. 11–58 (which 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 modulus oj1+ ksd3hb(k(Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz