Give some examples of everyday vibratinwr jj,)ay-demxk 47fm l8b,a1g objects. Which exhibit SHM, at least appmxl)mr, 7ej aydfb,a k j18w4-roximately?

Is the acceleration of a simple harmonic oscillator epqb;mz-fx13luv:b5m oq 4dl ; xt27csver zero? If so, where?

Explain why the motion of aw)3re:vrty,v7 8weoq piston in an automobile engine is approximately simple e:) owevtrw7 ,r8q 3vyharmonic.

Real springs have mass. Will the true period and frequency be largen-tu-frb8xt3 bt3 m372txoz rr or smaller than given -2 zbotb 3ut-t7t 338nrxmr xfby the equations for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of08 -e1nt;n isc+8w *esqnms koutx(w : a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scale, and then 2movk;t-ygeax av514is released. Des5ytvg-; x ev1km2o4aacribe the scale reading as a function of time.

If a pendulum clock is accurate at sea level, will it b(, /nsmcqe/(wrf4wg gain or lose time when taken to high altitude? Why?4(rw (fnc/ g e/qs,wmb

A tire swing hanging from a branch rekvnzvrr 5-o +(aches nearly to the ground (Fig. 11–48). How could you estimate the height of the branch r5ovnz(vr-k+using only a stopwatch?

Why can you make water slosh back and forth in a pan only if you shakeazxggx y: ;:r. the pan at a certx r: gz;ya.gx:ain frequency?

Give several everydayi1 8obari ;5zg examples of resonance.

Is a rattle in a car ever a resonance phenomenon? Exp jtpp)s 1ety502uibf4/rlh3 09epco flain.

Is the frequency of a simple periodic wave equal to the frequency 9 7f n;6uezqyqof its source? Why orf;nqq6yz7ue 9 why not?

Explain the difference between the speed of a transverse wavet1qn7tezb9h28 f2yd 7 ke7cwq traveling down a cord and thecf728et kb hqe1yd tzn7792wq speed of a tiny piece of the cord.

Why do the strings used for the l.l4n gkl b0 e+6oymkrllc54l:owest-frequency notes on a piano normally have wire wrappegobkk40 n. 6l:llrl4 ycl 5me+d around them?

What kind of waves do you think will oroii ojw61 si9/c7-f travel down a horizontal metal rod if you strike its end (a) vertically from above and (b) horizontally parallel t ijowf ic/oo19 76isr-o its length?

Since the density of air decreases with an incr+l+xyk6, n jukease in temperature, but the bulk modulus B is nearly independent of temperature, how, xk ny+l6jk+u would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease 3t ou*no r4-bubxj7jj:v. y,g in amplitude as they travel away f:g ju3rjxu7*jo4.otbnvy-b , rom the source.

Two linear waves have the same amplitude and speed, and otherwisl(tzj u31jq 4ue are identical, except one has half the wavelength of the other. Which transmits more e ju4ulj3qz1t(nergy? By what factor?

When a sinusoidal wave crosses the boundary bet4cs 4rk 3,dfpyween two sections of cord as in Fig. 11–33, the frequency does not change (althoughy d,f4kpr43cs the wavelength and velocity do change). Explain why.

If a string is vibrating in thre/ve 0x. p+vs-sg j6pjfe segments, are there any places you could touch vv/+xj -f sp 6j.esp0git with a knife blade without disturbing the motion?

When a standing wave exists on a string, the vibrations of incident and mj+ndby k)7 ,zreflected waves cancel at the nodes. Doesz7nmb)k +j d,y this mean that energy was destroyed? Explain.

If we knew that energy was being ;3xhnd +/wc:dz( jsd xtransmitted from one place to another, how might we determine whether the enes d+x;hx z:n/3dwcdj(rgy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the total distand- hn.e/.xvqst1bqp 7ce it travels in one peri1-7 .dxebtq.nhq spv/od?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs fr)a4c wbz-nr))7jwznave1r f4 j v .2ghom it but is 85 cm long when a weight of 180 N hangs from it. What is the “spria)4nwz1rnzj2j)g7hv v)c.bfr a- 4w e ng” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg s 01:q5m.g /sndzzjubpuda;;tsn v *sp 9bt:*driver gets into the driver’s seat. If the car goes over a bump1 psmzssb9/b * :. ;0adupjnqd zt*ust:v;ng5, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs from it. (a) W .r7mzf*ws(o 0 t// prcwo-cwmhat is the spring 7mcro-o(mzrw/ wfs /pt cw0 .*stiffness constant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a frequency of 3.0 Hzs hgn1vmg;3 2t when a mass of 0.60 kg is hung from it. What is its freqg ; ntg3h1mv2suency if only 0.38 kg hangs from it?    Hz

Construct a Table indicaosum)4g .qy*j ting the position x of the mass in Fig. 11–2 at times t q4jos*gmuy) . = 0,t = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

  A small fly of mass 0.25 g is cmfhrdvgka:9c wazu/8 q 8+1,uaught in a spider’s web. The web vibrates predominately with a frequency of1uhakwca8 /+mqruz g9:v df,8 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 sprt)d9wmw63zg7wjo cg - ing vibrates with a frequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is 0.6 7 wcz3towg6m)gd -j9w0 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per mii*fe 0k7ry5:bq g s*ed7+xo 2kcvmp4ye5.y second with an amplitude of 0.13 m. D75meiyey:dpkk +.yc *2xeig5 f*4or7sbq0m vetermine
(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 equ5 aq k8c*n2o( i*kemtcilibrium is the speed of a SHO half the maximum valin *8qc(c*km2ta k5eoue?$\approx$    A

A mass attached to the end of a spr h 0+6h5akxcofing 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 a3fwmbn5;qk , w vertical spring 0.315 m. If the spring is stretchedkb 53mwn, wq;f an additional 0.130 m and released, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3/t h 5y7v2fa luepk*)a.0 kg is 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 e y27pav t5h* )kfua/elquilibrium 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 8y)p85yv. kqpg wx-5vo0.0 N 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 gqy5pgvpvk) 5 8x-yo.w un?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to one endog5l4w;ol .ck umsd8f 9xkd+ , of a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the8w; lfg4c s ,m.k5do+d9lkx ou 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 accordicnq2yoys5 9g:ng to the equation x = 0.45cos6.4t where x is in meters a:qng 5s9yc yo2nd 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 equilibxnjg: p+c9p7f rium is the energy of a SHO half KE and half PE?+79n cgjxp:f p ±    A

  If one vibration has 7.0 times the energy zni*dpj 7,7fx8kg * nhof a second, but their frequencies and masses are the same, what is the rat7 jnk zfdg7*xi*,8phn io of their amplitudes?   

  A 2.00-kg pumpkin oscillates from am*r mf; mp)k(x97 b/xkgcy/-js w1qnn vertically hanging light spring once every 0.65 s. n)gb mqx;9-7*r 1c s/kkwyx / j(mnpfm
(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 parallel vertical kj160rw aw0 jo3s)rjssprings, each with spring stiffness conj1rjk6 0s3ww)sjr 0 aostant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the j4+8ie7 pslr sequation x = 0.38sin6.5t where x is in meters and t is s rie8j slp+74in 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, labeled1 ccu j/ef-r(v 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 *2qwk ) xfp5qs r84s0 89hzxm6 krkdizus:7k tof a horizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed t x ihs8dwz*mr56qu qxk)k2r8fk0:49ksp 7zsof 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 springg baz at3souo3.j1 k+oga p5.yl-g9v4 stiffness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) with poo.o9g kz33 pla. a+ab4s1j-5utgoygvsitive 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, wcerdh,).ai7 :hldw507q l qnwith 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 .nft82a bw8-xi2aui s spring whose spring stif- nxibsw2i82fua at 8.fness 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 ar 3 ca74hovznh+6*fyw high bridge. After reaching his lowest point, he oscillates up and down, hittih vf6 nyh wr3+4aocz7*ng 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 exactly 60 s. What z fkdgk7lhwnh*t33qoccf*.,)i t 6*mis its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum b9 fr 7.1d8jd9xivfhpje if it is to make exactly one swing per second? (That is, one complete vibration tv71did 8rffjxp9j.9h akes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period ,ai g)v0jx2g o varlpqc-g)gr +gu,, ;on Mars, where the accelerati la -a io+j,g), ;rggcuxv,pv0qgr2 g)on of gravity is about 0.37 that on Earth?    s

  What is the period of a simple pendulum 80 cm long v(eob a7h z,;5kriyp6
(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/s6e(p2s9ir jcp zzk 5 of 365 grr(spzpse/25 icjkz9 6 ams, and 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 ,qn0 k5q5wnz(a.cneg4j9ov ehas a length of 0.9930 m. If the clock loses half a minute per day, how(a5gne, 0noj.k4 n95qve qcz w should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the ma8xmr yh)m)l8 jximum 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 it is release terqx4wi*n:x e-y*g) (6qogwd from rest starting at ane e:t)xw r *6ygnw4qig-x(*q o angle of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests pass the bow of his anchored boat every 4.5pa8glt q3kitpln+ c2ub6 p3.0 s. He measures the distance b4 u ptp 2i.p gl56b+knlc38atqetween 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 a55 -5 dj8be ruwh-eved speed of 343 m/s How whd55b- 5eeru-v8e djfar apart are the wave crests (compressions)?    m

  (a) AM radio signals have f l,7 +hjton;1)tx wpe9s mmi+jrequencies between 550 kHz and 1600 kHz (kilohertz) and travel with a speed of n,iptmw+7 e;jmto 9xls+h)j1 $ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

  Calculate the speed of longitudinal waves vvo,m+)+dr* jrv5 u zbr44d xfin
(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 dense as tho,v c u0w(l:d*fk5dpvq xd5;rcs0c m*knw0k 2e other. In which rod will the speed of longitudinal waves be 50*x(0*mc sc f:02ko,vpwuk5kvc d rl qndwd;greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apart. If th ayl0ibol) *l*8atk5/ phqq5b e tension in the cord is 150 N, how long will it take a pulse to trav0pq 8*qob)lt5bi */yllh 5k aael from one support to the other?    s

  A ski gondola is connected too 0-rg-fvu+5kyz u h2w the top of 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 cable. It is obsoyzuf -g-uk2 +r5v wh0erved 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 suhsv cg/kl qw95w, 5cxyv0 *pc(rface of the sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is thep*x5vy9w vlwgks 5,(c0/hcqc ocean at this point?    m

  P and S waves from an earthquake travel at different speeds, and this differenyvivwd :x*.8i ce helps in locating dv:wv x. y*8iithe 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-produceuvzz qm3;(vv ,d surface wave can 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 amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the accezvq;,(3 zvm uvleration a>g]    m

  What is the ratio of (a) the intsssz: * x,,zejensities, and (b) the amplitudes, of an earthquake P wave passing through the Earth and detected at two points 10 km and 20 km from the sos zsjz,x,: s*eurce?(a)    (b)   

  The intensity of an earthquake wave passing throi8 9 uuwsfq3:mugh the Earth is measured to be mfi:s9u38uq w $ 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 samwrj x/ ln2rd9y b,42vue frequency travel through the same portion of the Earth, but onenbr49x,wl2j uv2r y/d is carrying twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the sasst x(7puga02ody4p)+ z- mfrme frequency, but one transports three times the power of the other.f+ zs - 0(tu2d4g)aprm7oxy ps What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move up and down a tfkjdujxolrkmta.6,0bm.c v/ .i-,rl (a- ej-otal 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 thexuit,6.k 0dl cr vm m( ,/o.-fblr-jjjea. -ak bug’s maximum KE change?   

The two pulses shown in Figotm7t2b: *6hyw ype0e. 11–52 are moving toward each other. (a) Sketch the shape of the string a67 ym:oe0h tpb2 *ywett the moment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundamental frequency, what are tfwh )4 8*uko2zgdgb g*he frequen*4b* uhzdggof) k g28wcies of the 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 freqqfj 0khsp4 .g-uency will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of the string vibrates as a stan.fkg 4j0h sp-qding wave.)    Hz

  A particular string resonates in four loops at a frequr.p x9vbs:,wa: xsc:yency of 280 Hz. Name at least three other frequencies ata:,sx: : wr9sx.ybpcv 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 t0n frry6,si7khe frequency of standing waves is 475 Hz, how far apart are two adjacent sy76n irr0 f,knodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 35 x4rc.npce)gw dbss96q hz9;8 0 Hz, what is the frequency of the fh n)pbs 9qerw g9c xcdzs.6;84undamental?    Hz

  A guitar string is 90 cm )u *:9*oehw-ywl kvxkugx 94klong and has a mass of 3.6 g. The distance from the bridge to the support post is L = 62cm y w-luvew4kxuk*k9* 9:oh x)gand 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 vibr): i q9vfhb08wil,r ucate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the furihl9iq),bf :v8w 0crequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hc:0i4i jpufi24mrvb7/9 rw c oz, but it is measured to vi09/i: 4jrrii v74mu cpwfo2bcbrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-amplitude m06kf/ yb rqh,hechanical 60-Hz vibrator. The string’s mass per unit lengtb6f 0h/qk hry,h 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 vp4dn*n6c a g,string may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.08nncg 4,a*v pd60 kg, how many different standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at just the right frequenc ye, :zqsg gi0p56up6u uu dz- 2vmcuaagt/.6)y, the water alternately rises and falls at each end, remaining relatively c.zg g6:5vui qgs6)c p,z/tud ae-ap6yu2um0ualm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundary within mzn.;7w;-1.ep. tiulxpylyq the Earth between two kinds of material. If it approaie71xw ;qn lm.p. u ;-tpylyz.ches 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 underwai0l)buh6scjh/ n8si (ter “shelf” where the velocity changes from 2.8 m/s to 2.1 m/s If the incident wave 6(s cl8 )uii0bhnsj/h crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air when it hits a layer of cold, dense air. Ij;a bx, /jnczj-/ fzd94s7lbif the sound wave hits the cold air interface at an angle of 25; bb-az z 7c/ijnj4xds/j,lf9$^{\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 ofu* as-/zljck5 5aisss0j: i8 x rock at aac5ik 8-j 5sa*xsl usij/sz0: 38 $^{\circ} $ angle. As the wave crosses the boundary, the specific gravity of the rock changes from 3.6 to 2.8. Assuming that the elastic modulus is the same for both types of rock, determine the angle of refraction.    $^{\circ} $

  A satellite dish is about 0.5 m in diameter. According to the user’s q4f8*ps p)/gm9yazn fmanual, the dish has to be pointed in th 8 *m9)q4n yzgppaffs/e direction 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 across the Pacifmgc* l8g/5,gcx :fkspic Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in *f:smg5k, g8lcc x/ gpthe harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stifm 6s+19w+wb5c l yzo1fjx. ylhfness constant of 550 kN/m Find the maximum compression of the bumper if the car, with 1 x .1+h56byj+9m wlzc yofswlmass 1500 kg, 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 from7.9curq v vl)5w;ortyny1+hp a window to a fire net 18 m below, which stretches the net 1.1 m. Assume that the net behaves like a si r9+ pvn 7h.; ywv)cuq1o5tyrlmple 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 freely0nkc 0sb 5t7k1b ,yjufxb2rq. hanging spring. The mass then falls 33 cm before it stops and begins to rise. What i x0bst ub15b0ny,7cjkrfkq 2 .s the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 2vt dsaq zske*2f9 .cn0iqvit yx 0./;)2 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) W9 ; stv ex.zv0k*a0iy si2/f)qtq dn.chat is the spring 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 (diameter 8 cm) at just the right pae2ht7a) g5o hj zcn5k+ce 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 spect7h2jz5koa +hgn) e5ed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the center of a 33-r8h,ypy f2f5qdpm phonograph record have a wavelengthyf8hd 2y q5f,p of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equationkp9 +zlj pz2zoha e93. x=0.650cos7.40t where x is in meters and t in seconds. Deterkzzph 3e j99+a2z opl.mine
(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 cacu7yyb ,dsi1*/ lxr3ii o,4is its frequency if it acceleratebau/r,1ly 4xi37isycd* ci, o s at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft float.i e(4fk*7e/ctk(0fq ihb bi gs on a lake. When a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the raft vibr g.btif (b(kkf/ei7 q4chei 0*ates for a while.
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a musical instrument are tuned to play at 392 Hz (G) and 440 Hz q2/ lab y)9ydx(A). q/yb)9 a2y xld
(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 tr*dzv,n6tf x--dser9t aveling down the stretched two-part cord of Fig. 11–33. Det e9xd*-st6ntfd,-r zvermine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the 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 51z4 eu vz)4j3pvrsrg 264 Hz, and the tip of each prong moves 1.8 mm to eithev3p uz)4v41erzjr gs5r 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 witajlc21nxxii7;pk + h.h simple harmonic motion of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of 1j;kx ii+npl7 xah2.c the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that end is attached to a ring that jl2f0k)n ga48vd0rfi can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with one 2jdv af08i0fg4n rl)kend fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.00av h8i0vhy .kr7 .d*0hmckc:e 0 s — each one-way swing takes 1.0h8keri vv 0ca.d h7ymk*:.0h c00 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 veryn)p1- +uwu*ayg 2h yltical direction or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontal swings, and by what amyh1)uaypl uy2w -*gn+ount? [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 v da7m+agq8d8stretched 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 oppositdd8a a8mg7q v+e end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spring with spri4z/owt +tue0zn+/o ning stiffness co/nwoz ztn+4+t0/ue ionstant 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? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel cra4 ws h4)mimzh4ne cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. What is the period of the bouncing? [Hint: Refer to Tablezms4i4hm) h4w 9–1.]    s

  A block of jello rests on a plate as shown in r5ok (cpx0d9sFig. 11–58 (which also gives the dimensions of the block). You push it sikx( 0o5rdcsp 9deways 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 (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz