Give some examples of everyday vibrating obvm;05kr gh+b(l8.uf1bvw af sjects. Which exhibit SHM, at least approximate+rmkhbf0 ;s(5 vvab8flu1gw .ly?

Is the acceleration of a simple harmonic osc+v nr52) wv5 odaehwm5illator ever zero? If so, where?

Explain why the motion of a piston in an automobile engine 9g(-+9uwlqxn61hnklii ,dvc is approximately simple harmonic c+ lx91(uhiwqn-96,gdilvkn.

Real springs have mass. Will the tiyk*3qzaebgf6zu)*d -5is- true period and frequency be larger or smaller than given by the equations for a m -iutg z*bk-6 )eaz5qy*i3s dfass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximlu*-8;6yc hzl q.ikz aslc8tea 50 m.mum speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook xow6z7ir)j mml*,43ohfz hp5of a vertical spring scale, and then is released. Describe the scale reading as a funcif)orm hz*j zo6p,3lh7m5 x 4wtion of time.

If a pendulum clock is accurate at sea level, will it gain or lose time -iq6arj21 d gtwhen taken to h-6jir 1 ag2dqtigh altitude? Why?

A tire swing hanging from a branch reaches nearly to the ground+xfxwk3l ))p:ob hx-zh *e.tn (Fig. 11–48). How could you estimath-xew*. +xpt bl ok)z nxh:3f)e the height of the branch using only a stopwatch?

Why can you make water slosh back and forth in a y,cy08tny at) j8tg f-qpng7+ pan only if you shake the pan at a ce,qnpt -g07fy8 y+)y8a jnt ctgrtain frequency?

Give several everyday examples of resonance.qqkg o7p;atrw7h *g3-

Is a rattle in a car evezwgc m((* mg :4fl5nrpr a resonance phenomenon? Explain.

Is the frequency of a simple periodic ae -zmxd /yp7+*f b1pv ye 7gfcul+6d6wave equal to the frequency of its source? Why or why nov17 p y b z6m c/+dp6e-*da7+fyulxgfet?

Explain the differenb:1zm-sfse zx . kr-j/ir:xl,jhn.b6 ce between the speed of a transverse wave traveling down a cord and the speed of a tiny piece off s6s:n,e b-x/il zrjh1.jx rm-kz.:b the cord.

Why do the strings used for the lowest-frequency notes on a pianoeoy jg6u+ed qm ).y)-k normally have wire woq -6 ).+eyyg mjdkue)rapped around them?

What kind of waves do you think will travel down a horizonta2ao t6i1sv*0dqcqr* u l metal rod if you strike its end (a) verticala0v qoqi26sdu* 1c*rtly from above and (b) horizontally parallel to its length?

Since the density of air decreases with andy jc; ds9g:w1 increase in temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound waves in air to vary with tg;sy1:djc9 wdemperature?

Give two reasons why circular water waves decrease in a:+t,2f ekf1wd kpdk.w mplitude as they travel a1pk.kdf edw t+w:,k2 fway from the source.

Two linear waves have the same amplitude and speed, and otherwise arel i 5v:.ks+/fu 9.dxpgie 5j-tlhf x*u identical, except one has half the wavelength of the other. Which 5 x vjpk/l+:9.t5gi eud-ifxl fs.h* utransmits more energy? By what factor?

When a sinusoidal wave crosses th (iy 05/zxmw) fcd.wase boundary between two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelengthwfzm/ 0 5ai.dyws(x)c and velocity do change). Explain why.

If a string is vibratay eo6y-k/g;8wjsv )qing in three segments, are there any places you could touch it with a kni- w8ey6gjy)sao;q/vk fe blade without disturbing the motion?

When a standing wave exists on a string, the vibrat 43 u2vcxqp7-ceda:lw ions of incident and reflected waves cancel at the nodes. Does this mean that energy was destr l xp 7ud4-vecw23:caqoyed? Explain.

If we knew that energy was beimqqp2-tq) +2y r)p/cjzw muj3ng transmitted from one place to another, how might we determine whether the energy was being carried by particles (mz/jmc3 qq w) yj-p+2r)pq 2tmuaterial bodies) or by waves?

  If a particle undergoes SHM with amplitu +vpeeas kq;;;d* n:fhde 0.18 m, what is the total distance it travels in oeked+a;:;s ; p f*hnqvne period?    m

  An elastic cord is 65 cm long whe ako1rn03 p8; ufrab*o,1 8mldf *avien a weight of 75 N hangs from it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring fk0*anlpm 3*ua; r,ra18e8 bf1dio ov” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compres)mhy a r8ng8-xs 5.0 mm when its 68-kg driver gets into them8 h arny)xg-8 driver’s seat. If the car goes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 31 8fxucqb9 yn7.6 cm when a 2.7-kg fish hangs from it. (a) What is the spring stiffbqfyn98xc1 7 uness 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 fu8ftu y8 6m9azrequency of 3.0 Hz when a mass of 0.60 kg is hung from it. What is it6yufz u8a8m 9ts frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the positirk e;hc10-p xgh ndq( 4(ont*bon x of the mass in Fig. 11–2 at times t = 0,t p;(h-1h4ernc dqo g* t k(xbn0= $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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(m2 qdvku uh.:oz;7c6 q:eeoe web vibrates predomid eve26 ;qo:q7 z:k(e.muhoucnately with a frequency of 4.0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a spring vibrates with 7sz.s lig3hl5 a frequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 glsz li.5hs73 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a sj g :qi1bm2hh4pring vibrates 3.0 times per second with an amplitude of 0.13 m. D:ij1 hm2bqhg4etermine
(a) the velocity when it passes the equilibrium point,$\approx$    m/s(round to one decimal place)
(b) the velocity when it is 0.10 m from equilibrium, $\approx$ ±    m/s(round to one decimal place)
(c) the total energy of the system,$\approx$    J(round to one decimal place)
(d) the equation describing the motion of the mass, assuming that x was a maximum at x = (0.13π)cos(  πt)

  At what displacement from equilibrium is the speed of a SHO half the maxim3n*p 1ezhb c;qprb,2i um valu i e,qz3*cp bbph;1rn2e?$\approx$    A

A mass attached to the end of a spring is stretvh 3uuvh6f 6i5ched 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 sprium7,2i/adh )1tz xlring 0.315 m. If the spring is stretched an additional 0.130 m and )/idt h2lau7mz,x ir1released, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with spring stuy *w 7sgno)y4iffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium 7*)nogu 4wsyyposition, it is moving with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compress the spring of a toy popgun 0.200 m nx fyuaw zq0j(8u5h 7.to “load” a 0.180-kg ball. With what speed will the ball leave ay8n0f q 7.w5hj(uuxzthe gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attae xda(9 9fu1xxched 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. Iu1e dx99ax(fxf 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 according to the equatioc-f*k p0mw hx*n x = 0.45cos6.4t where x is in meters and t is in seconds. Deterwph*fm 0c kx*-mine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equilibrium is the energy of a SHO half KEvmsb8 9:9cn;mbu wy l0 and half PE?uc:0 8bm;9lmwn vy9bs ±    A

  If one vibration has 7.0 times the energy of a second,tj-i 5vcsjc n lq+n.8) but their frequencies and masses are the )qj8-+ts5n.l cvjnic same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging lighozq6 gjvp3 j)40; hkkct spring once every 0.65 sk 0 zhjvp3;okcg qj46).
(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 su:, kcb./kw5l e :rnhdgpported by two identical parallel vertical springs, each with spring stiffness constant k (Fi5:kldk:gnr / h,bcwe .g. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the eqv- 8ne(0n-j8 rsj0u d wbqx3bduation x = 0.38sin6.5t where x is in meters and t is in seconds. Determine bqve8(n j jw-xnddbs8u r0- 03
(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, labyco*2m5 03h+n q ndafieled 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 a hor 1h0wrg v8(lu *k2abz:bmv oa g1i:ng7izontal spring (k = 124 N/m) is struck by a hammer, which g :bg71*amol k2u(g gzvv8 wnih 1ab:r0ives 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 spri,df4dfy/vy3w *o ir3m ng stiffness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 k3didy vf,fmo3* /ryw4 g 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, with spring stiffness cofcud,m a/,:funstants $k_1$ 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 atteat-e5( d gsq;iyot/;42 l atdached to a fixed horizontal spring whos/so(ya- td et5 ;2idgqat;4lee spring stiffness 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 3w62b jsg q b/7k)jm:o rdo9ttfrom a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness 6 /trk9w d7m23toqgb:j) jbsoconstant 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 90 -zjhjm9o- jf gh*zyis its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make er1rfa 2wuu. o+y,ssmlwg9 1* lxactly one swing per second? (That is, one complete vibration takes exacwo1am129swy. fl+ glr us*,ur tly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its per-cw6 j5dz2ybdc /puxav78 2wriod on Mars, where the acceleration of gravity is about 0.37 that on Earth? 52zad6ww2curj/vb7d-8xc py    s

  What is the period of donb ,bb3(bn m /kqt0ya 49wf2a simple 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 0.760 m, the pendulum bob has a mass of 365 g:szyvw hitylu, -28* ;7hqez trams, and it is released at an *i,-z2yyet8h7 u: ; ltvq zhswangle 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 (w 0xjvdf )kcj5ksb.g8yx.u3’s pendulum has a length of 0.9930 m. If the clock loses half a minute per da5(j0)gk d8.yu svxb jf3xwc.k y, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximum spe8al- g(xi0d lqed $v_{max}$ 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 released f6vnf(szej0h) 3 s fd8grom rest sh8) 6n3fsdv 0eg(zj fstarting at an angle of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests pass the bow of his anchored boat every 3.0wct7z/a b )f(1iyxftp(sz1e7 s. He measures the distance between two crests to be 6.5 m. How fast b1ftzf7 xti1w7c(ae )/pzs(yare the waves traveling?    m/s

  A sound wave in air has a frepv9r3deh51sk m .j)ppquency of 262 Hz and travels with a speed of 343 m/s How far apart are the wave cresmv 9kj1.3dpersp5)p h ts (compressions)?    m

  (a) AM radio signals have freque v 7h6x-/jrxqincies between 550 kHz and 1600 kHz (kilohertz) and travel with a speed ofqx76j- i/ vhxr $ 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 idxeqe9y +r /6pn
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one is twicn0kl71 wk*)u)mxgh xz2 1dpahe as dense as the other. In which rod will the speed of longitu kgnkp0271a)x*xzw )d h1mu lhdinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports na+rcum/7e e +28 m apart. If the tension in the cord i++enr mce/7a 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 top ox bok/i*bq3+v uhup(,f a hill by a steel cable of length 620 m and diameter h(v+o xkbp*u/ib3 uq, 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 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 sie,nbwbw 1 vt7q.wrca 3 86iv/nde of his ship just below the surface of the sea. He hears the echo of the wave reflrw/83ewn7. qwcv1nv,t6a b b iected from 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 u d2qmh5zch7 7different speeds, and this difference helps in locating the earthquake “epicenter”hcd27 hmzqu5 7 (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 surfaccje xymd8)cva,6b( 0 le wave can be approximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of v,xj(a0ybel) c mdc86 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 acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplitiop si ny:b y;1 :4:nvo2vre0yudes, of an earthquake P wave passing through the Earth and detected at two poinye:n :b0i1n;v osryy2pv: oi4ts 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is measured to ag k,xnr( y,3d8xjj) p3z cox*be )( nj d8,3,xkcxoyrpx g *zj3a$ 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 -6 --n5shdcjcg rqv7v the same frequency travel through the same portion of the Earth, but one is carrying twice the enc7 - rv5vq6-cghd-s jnergy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stre9fz-l mo yezg*q2xl2) tched string have the same frequency, but one transports three times the powelom9 e-qz2)xl*y2fzg r 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 dowpxllt ; :fh xb:b79vu;n a total vertical distance of7x9 h ;l;b:bx l:ufvpt 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 bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving9cqjk d 5t,hos7l:1oq toward each other. (a) Sketch the shape of the string at the moment they directly otj1s9k qod75ql ch:,o verlap. (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 fy4 0llov2y m+da;c, .hj6ba6ui 3usssrequency, what are the frequencies of the first b+0v yh 6lml6di3u j.sasa2;yu,4ocsfour harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingepv - mxh-u2w/hred. At what frequency will it vibrate if it is fingered one-third of the way dow-/ mwx h2vp-hun from the end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonhwl/wgtykp75yr g9hf: :,b5wates in four loops at a frequency of 280 Hz. Name at least three other frequencies at which it will r /hrkh 5wgg :tlp9wy7yfw, 5:besonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If t maysk -3,4gnj3/mwbbhe frequency of standing waves is 475 Hzb4/w jayn3mbs-3k , mg, how far apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and t7ixz7 afxilfkn5 5j4fa-2a ;350 Hz, what is the frequency of the- i75flia52t;ff7zx njak4 ax fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distance from the brie.cfjcm-4/gaq vagr:y s 5+5q(yi ct7dge to the support post is L = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundame5ea(gayy5-crcf i+gq 4 j.c7/v:q smtntal and first two overtones?    Hz

  A particular guitar string 4q 8mw8aw;f(9 a lz;s,dpvrsljhd92b90phe l is supposed to vibrate 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 frequency?So the three frequencies arq pwhll aslzsb8dvdm49a2,9fr(8j 9 pe ;;hw0 e,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hz, but i2hjcvrp63x+lf yn19 mt is measured to vibrate at 2pc1hx63ymj2f rn v+9 l05 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 au 3 kpnc- 1n1-5osi +yeawl2pjttached to a small-amplitude mechanical 60-Hz vibrator. Thyl 31 an21+w-up -nkpcios5eje 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 stri/tuz6ug.wg tj,4/e b lng may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, bw,tu gg/.6j t/4zue lhow 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 injn)yc+ wvs 2mnhgvdxj69t* b 1 h:2ik) a tub at just the right frequency, the water alternately ribnjgsc2h :mnx6)9v dh vt*)wk iy+21 jses 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 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundary wi2*hvtowg(u a 9is/h*tthin the Earth between tw*wh*2/9gthovt (as iuo kinds 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 underwater “shelf” where the velocity changes2md+y1lx y4f p from 2.8 m/s to 2.1 m/s If the incident wave crests make axyd4ym1lf +2p 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air whe(p wu-how: g/cn it hits a layer of cold, dense air. If the sound wave hits the cold air interface at an a: o-ucph g(w/wngle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave strikes : 2kbmze9 t+vgsoe7a 9a boundary between two types of rock at a 389ez2m:7tk+ s a9veob g $^{\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 b+ gvmxqk4o e(cla:,t ,o0 o2oin diameter. According to the user’s manual, the vl+,bq,too2: 4o k exgma (0codish has to be pointed in the 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 v 3s)l5k+i mne8vo;x racross the Pacific Ocean. As it a8 mkv5vnx e r3s)lo+;ipproaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring sthoj:3 g4jied-0 h7l igqvr(l 3iffness constant of 550 kN/m Find the maximum cojgdqi37 ehhol(l4v:g jr 03 i-mpression 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/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m below, which stretches thi2;mtul,jnc-op qj9/ e net 1.12-iqm j,;9nult/p joc 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 the end of i860 l1wa yjyta freely hanging spring. The mass then falls 33 cm before it stops and begins to rise. What is 16jwy8iy0al t the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 11–54), comprn zzr6u9+ h(4ir s4zllessing the spring 5.0 n z6hlrs +4izrl4(9zum. (a) What 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 (diapsp e2-c. c8sxmeter 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 o.-82 ccps expsver the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the centerf3a y b8j0qa6yd/exo 5 of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the e8 ay/qobd6 35jax fy0frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t where x is ztawk(d- +3hd8peuh * in meters and t in de*dtwhh( uk8 +zpa3-seconds. Determine
(a) the amplitude,    m
(b) the frequency,(round to two decimal place)$\approx$    Hz
(c) the total energy,(round to one decimal place)$\approx$    J
(d) the kinetic energy and potential energy when x=0.260 m.(round to one decimal place) PE$\approx$    J KE =    J

  A simple pendulum oscillates with frequency f. What is its frequency/v y9,e- pfqfqtw,vu4 if it accelerate uypt veff,9q4wqv/,-s at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a x9; a9jcqeicm:7 ab;elake. When a 75-kg man stands on the raft, it sinks 4a9 c97c;ebe;a:jx miq .0 cm deeper into the water. 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 music u ou:ub7.ugxg :9z1hval instrument are tuned to play at 392 Hz (G) and 440 Hz (A) ouu1vbh u:z9:7. gugx.
(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 qqlhf,c)36 h gnohkykt4(-gk:vl4n,stretched two-part cord of Fig. 11–33. Determine 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 frequencf6nl -kvntl,3 qch:4kgqkhgo y4),h(y 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 )e83idsys3 bm+ ;o tr u*nl8icmoves 1.8 mm to to3crns) i8luys 8 b;3m id+e*either side of center. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simple harmonic motion of frequency 1.ophlljbw, 85 90x;i ir5 cycles per second. What is the maximum amplitudl8lwp ,ri jo;9 05xibhe with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board during the oscillation?

A string can have a “free” end if that end is attacyxgo l1)*9 epj sh vqs/32pw/nhed to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of /v/oy3pxspn9g j2* )l esqw1 hthe resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly; rbmgv -qqeo-8o;(j r 2.000 s — each one-way swing takes 1.000jo--qom8 rb v qg;r(e; 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 dixa9 qg ffu7)g4gngq73 rection or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, t)9n77gfggugq 3f ax 4qhe 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 undeu*bai; vyy 7kk45l fr+r a tension of 255 N. A pulse is generated at one end, an ku5+ir vlbyky;*74f ad 20.0 ms later a second pulse is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a sp;a)idy 0u(b z2y0 yn- dzithg9ring with spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillations that will allow thei)yai 0dhntzy ;b0-g u(d 9yz2 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 2frw nh6dq2t1 -yw8rra7 40fan2 m long and has r8d4rnfq a-h7f10r twwny2a6a 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 (which also gives the pdj+m lszgc 40r6jq2 dt282ildimensions of the block). Yd26 lq i0sdtjp42+2jm8r l cgzou 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 (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz