Give some examples of everyday vibmo 7-1x9l fthasrv1-w2:qor brating objects. Which exhibit SHM, at least app 1:2rrtlb7ws xhfa oq-o9 m-v1roximately?

Is the acceleration of a simple harju wv . 1-vhljo3tryups-*zopa6z3(5monic oscillator ever zero? If so, where?

Explain why the motion of mz6z(9q0ry1 nilqon5 a piston in an automobile engine is approximately simpl51mqyl(6zqn rnz o9i0e harmonic.

Real springs have mass. Will the t 1s7 wt;rud;xmrue period and frequency be larger or smaller thanx 7;r1mswu;t d given by the equations for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximff-gp vkdf fy)cs96ph)5 )(rxum speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a v-i+8ys lzci0:z,6e hdxw.uj vertical spring scale, and then is released. Describe the scale reading as a functeuz-i,jyx d8. ls:cw+06vih zion of time.

If a pendulum clock is accurate at sea le q3-b(ot4lg v+vfa;lovel, will it gain or lose time when taken to high altitude? Why?+bt3(og a vflq;ov-4l

A tire swing hanging from a branch reaches nearly to the gro; p1rl+ivv5* e qdeoyp/sr0c5und (Fig. 11–48). How could you estimate the height of the branch using only a stopwa l;ipcd515*sepve +rq 0ryo/v tch?

Why can you make waterz/ 0j77l-f+jww lrhus slosh back and forth in a pan only if you shake the pan at a cr 0jl+z/whu7-wslfj7 ertain frequency?

Give several everyday exampl6,;rnzejk s 1ves of resonance.

Is a rattle in a car ever a resonance phb0moj))*h xe a:t;vkm. d z3s11 vnazpenomenon? Explain.

Is the frequency of a simple periodic wave equal to the frequency as*spxgo : :u8of its source? Why or why nots xo:apg*u8 s:?

Explain the differenc 9n ruxl. 1apiyw-ay-li s;t9(e between the speed of a transverse wave traveling down a cord and the speed of a tiny piece of the col99 (-n-yasl.trp;iiyw1 u axrd.

Why do the strings used for thu/4hhw09 wvj(jhb*y e e lowest-frequency notes on a piano normally have wire wrapped j(hh/4 w9vu*wbyh0 jearound them?

What kind of waves do you think will travel down a horizontal metal rod if ye jz0 g5m0th1you strike its end (a) vertically from above and (b015 eytzh0mg j) horizontally parallel to its length?

Since the density of air decreases with an increase in :11ntdw h;rs(x wapp6 temperature, but the bulk modulus B is nearly independent of temperature, how would you expe1 wp;(1 aptr6nhdxw :sct the speed of sound waves in air to vary with temperature?

Give two reasons why circular p e.)j/ytkv nln rtys z2-(.i)water waves decrease in amplitude as they travel away from the sotsnyn ejl (v)2 iyz.- /pkrt).urce.

Two linear waves have the same amplitude and speed, and ot; *f,0mqk: npora)dxap, c-bgherwise are identical, except one has d;g,ran):bx a0fk- ,pmo*p qc half the wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two sectiouh7.ru jlxj* )ns of cord as in Fig. 17) *xruhul.j j1–33, the frequency does not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segme w ix,t /5utp98wp+u q61ueglhnts, are there any places you could touch it w8xp6u, h+gwte5li1t/puqw9uith a knife blade without disturbing the motion?

When a standing wave exists on a st u *ju-lgn*5uihfcp);wqr5i 5ring, the vibrations of incident and reflected wavesnil5uu*h q jfgw )*c-5uip5r; cancel at the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one place to another, how mi r9cr.sx1dc v,ght we determine whether the energy was being carried by particles (mv1xs9cd ,crr. aterial bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the.l8pcai lw 1 w8xj zio0f7wj/* total distance it travels in *fwpz0ixa88 jwjl/ clw7o.i1one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hafy9qf0o ozou*f/ v f h);iv7:lngs from it but is 85 cm long when a weight of 180 N hangs from it. What is *l0 u /f;f i)9:hvyqo fzvofo7the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg driver gets nn 0m6 m/uzgj3ip9(npinto the driver’s seat. If the car goes over a bump, what will be the z6/g0j 3nimnmp9 u(pn frequency of vibrations?$\approx$    Hz

  A fisherman’s scale strettx)a;hml, )pkg-e 3 ioches 3.6 cm when a 2.7-kg fish hangs from it. (a) What is the spring stiffness constlh))o e;t-ax ,mik3gpant $\approx$    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 Hz when a masi g9g+hqzrj,6s of 0.60 kg is hung from it. What is z9,j+g 6ihrgq its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of to)rr jg8 498thrl f(e 3g f(ocmy8p:gohe mass in Fig. 11–2 at times t = 8 h4f9r gcrmo(lto:pre8jf 3yg)o8(g0,t = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

  A small fly of mass 0.25 g is caught in a spider’s web. The web vibrates pred5yfc+6i+ y.tlr 3dkvslgdq93 ominately with a frequency of 4.0 H+y6tcg s5 3ivlf+ldyrdk9q3. z.
(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 spri*o c1kx nae); dwn:jh(ng vibrates with a frequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 H(; jo 1enhxn:kawc* d)z. What is the value of m?    kg

  A 0.60-kg mass at the end of a spry4h f/6ukp/:utc 9kvpp59 wo ning vibrates 3.0 times per second with an amplitu4f p /u/9n5 pokw9v6:ku chptyde of 0.13 m. Determine
(a) the velocity when it passes the equilibrium point,$\approx$    m/s(round to one decimal place)
(b) the velocity when it is 0.10 m from equilibrium, $\approx$ ±    m/s(round to one decimal place)
(c) the total energy of the system,$\approx$    J(round to one decimal place)
(d) the equation describing the motion of the mass, assuming that x was a maximum at x = (0.13π)cos(  πt)

  At what displacement fromij ) hxn(t:v/jh:cw/g equilibrium is the speed of a SHO half the maximum value)xghvtn:w ci(h :j/ j/?$\approx$    A

A mass attached to the end of a spring is stretched a dis8p 1jn z6+w+jgu.g-or nr-6xy)jaxswtance $x_0$ 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 vert u;sea/ul5t3(jn mw91 hnv,bhical spring 0.315 m. If the spring is stretched anu , v5/tm anej;wb3l9hh(ns1 u additional 0.130 m and released, 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 withvsm9gg1e , dd1 spring stiffness constant k = 280 N/m and is executing simple harmo 1,d9egdvgm1s nic motion. When the object is 0.020 m from its equilibrium position, it is moving with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to com 5b5lc jl0u8jh3)v lcy*pdtq6press the spring of a toy popgun 0.200 m to “load” a 0.180-d)p6t uv*b5qhy35cl0 jlc jl8kg ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to one end of .-za eq3v,f8ifdt y8b a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, the mass experiences a maximum accel8y df tbiev.,8zq-3af eration 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 acco+3:kbb. ekidarding to the equation x = 0.45cos6.4t where x is in meters and t is i bid3.:+kke abn seconds. Determine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equilibrium is the energy ofw;7u mrgcp-j; a SHO half KE and half PE?g r -mj;p;cuw7 ±    A

  If one vibration has 7.0 times the energy of a second, but their frequencies /hh6biu:mc ;xfmic+ 3and masses mix; mic3c+ :bhf 6h/uare the same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillatewcrxf2 ehjz:9 .kym b-:i9-kks from a vertically hanging light spring once every 0.65 s.k-hxfz 9ki-: e m:kwc b9.j2ry
(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 twgwb,iym cf,*1 o identical parallel vertical springs, each with spring stiffness constant k (Fig. 11,mcf yi,1 *gwb–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t where xso4eb 5 xckv5o)4alb2 is in meters ana5 bo)ecs4 o4x kb25vld 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 S (j:1wh:kd nns :.ae;ww jwgp3HM, labeled A and B. For each, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on the end of a horizontal sog :.j4i /mepypring (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.96m/s Dete y:gpi/moj4 .ermine
(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 stifps *r)g3 rnu 7y*whmun.9, kuofness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes tu9,*h*omuk .r ursyp)wn3g7nhrough 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 a+ p9,m8rq esy 8jvn3nto two springs, with spring stiffness constants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes a 0.600-kg block attached to a fixed horizontal spnbl0pi8au6: q-0fva g7t 8bcv g*sd5 iring whose s7 lai: ud 8a-05qgf*ntbcp s b80giv6vpring 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 from a high bridge. Af4 sr/ s/du +/:sn pffjqg+rakn ()blx/ter reaching his lowest point, he oscillates up and down, hitting a low point eight morpfldsgx+ /b4 n+rss /q rku()j//a:nfe 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 irna6h/z* c/iytqz6 ck8)ne 5in exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactl:0ieh4.1w h1i zoy fify one swing per second? (That is, one complete vibration twf1:fh4.i yii zoe1h0 akes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is it+ xilma 49m/ ccg;6jkp)c+v l 77oai5byd qow+s period on Mars, where the accepgi a +cqjk4+/ iy)7cxlv 95;+wac m7bd6m oolleration of gravity is about 0.37 that on Earth?    s

  What is the period of a srl8 d07w7ai imimple 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 0.760cy8hn1 z:sw- twnh/2c m, the pendulum bob has a mass of 365 grams, and it is released at an angle of 1st1wcz n/ch2hnwy - :82.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’s pendulum has a length of 0.9930 m. If the clock lose,+ag8v..r ;eq m8ajv krpb gf5s half a;gaq5v,. b+e.ka frr8 vjmpg8 minute per day, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximum spqcb)0*4f7s.s-y(rcgl/ jd d s+oo if aeed $v_{max}$ 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 fe;s.+vtte v z3requency of 2.5 Hz. At it is released from rest startingtv3s v.+zee;t 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 anch 8 rhbx/-c8kx: jewxw5j y6hz8ored boat every 3.0 s. He measures the distance between two crests to be 6.5 m. How fast are the waves travejb8ewk/5x wz hcj:xr8- h8y6xling?    m/s

  A sound wave in air has a frequency of 26+qa7vhqh-h+ *y2wsru 2 Hz and travels with a speed of 343 m/s How far apart are the 2q+ uhh7-hr +wy*avsqwave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 160)9/ufs+ ), d d80a lghcs71pedputzht0 kHz (kilohertz) and travel with a spfh ez l987,t) gdc0td uapspu d+s1h/)eed 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 loi 8c5muf l*my/ngitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have th 6q8fvx(ltlo7 e same elastic modulus, but one is twice as dense as the other. In which rod will the speed of longit6 (fql 8x7ltovudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between j 0i.jy(ui 5althei 9/two supports 28 m apart. If the tension in the cord is 150 N, how long wil5i el(jjahti0 i9/.yu l it take a pulse to travel from one support to the other?    s

  A ski gondola is coned+p+mfzva, /b8zj s0nected to 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 observed that s++jm pzfz 8eabd/ 0v,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 sisb-ho i; e4k;+iz/ wzhde of his ship just below the surface of the sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s /+h zz4okbiwsi;;- ehlater. How deep is the ocean at this point?    m

  P and S waves from an earthquake(tjspvf *o n38gg-9)wr g8ahn travel at different speeds, and this difference helps in locating the earthquake “epicenter” (wsntg)*fpgj3ao v9r(h8w- n8 ghere 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 q5mlrcco/ (t1 p3czxx a7/of+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: c/r(ctcp +omx 5af7qlo 31z/xSet the acceleration a>g]    m

  What is the ratio of (a) the intens6.ui,(y nin-odv )lvhi.w u+iities, and (b) the amplitudes, of an earthquake P wave passing through the Earth and detected at two points 10 km and 20 km from ohd-wv. )n.n u,il+uv yi6i(i the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is me.. odiwlnf 26dasured to be on6. d2.l wifd$ 2\times10^{6 }J/m^2$ at a distance of 48 km from the source.
(a) What was its intensity when it passed a point only 1.0 km from the source?(round to one decimal place)$\approx$    $ \times10^{9 }W/m^2$
(b) At what rate did energy pass through an area of $5m^2$ at 1.0 km?    $ \times10^{10 }W$

  Two earthquake waves of the same frequency travel through the same por. klit g2n0wqc*:w qge- vpn8( lim)(rtion of the Earth, but one is car:mkn)wgvqe 8gci n(q *2ltr0w-(li .prying twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string qpn.d6x5e- po have the same frequency, but one transports xqod p-.5p en6three 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 down a total sf37 t;t45ep;f ryx)ha(bk wo 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 factorhef kby7so;t ptf3(w5ra 4x); does the bug’s maximum KE change?   

The two pulses shown in1m.x27 e9hz;dly msn n Fig. 11–52 are moving toward each other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each om;9hd7e m. 2nzsy1x lnther, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its d 0y4p uqkhp2.fundamental frequency, what are the frequencies of the first fou .yqhp2dpu04k r harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 2942t *66tibdka g Hz when unfingered. At what frequency will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds otgi *6b6ad t2kf the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frev.za +bn6l 1k-iprng) 4 vttp9quency of 280 Hz. Name at least three other frequenznnp+v pvi9)k r6 tal4t.1bg-cies 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)*q r c5t. )wo-m(f hjzhtxac2 frequency of standing waves is 475 H t .h)xrzmq)johaw2-f(tc *5cz, how far apart are two adjacent nodes?   m

  If two successive overton 48es / vgz-yo5r57epus. qsvxes of a vibrating string are 280 Hz and 350 Hz, what is the fr zpereqgs8 57os v4-uxy5s. /vequency of the fundamental?    Hz

  A guitar string is 90 cm long anuy ylvzx nm1t3ck9s6z n6* jzxf11l6 :d has 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 are the frequencies o 6*z:fnj kvxymylt1x6sncz1391 z ul6f the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, but it is measured :( 0;)wpnita y*wjo7 spm8t isto vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?So the three frequenc(s sp)iim y* p8:aj no7twtw0;ies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200 Hz, but it is measured z xpyts *;g9 v(*im efa 5)wgai9)y7ihto vibrate at 205 Hz. By what percent should the tension in the sz sy)*9;yxgi9i(mvi*5) af epgwtha7 tring be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-amplits(.fo dh-r-rn(w0 wjl ude mechanical 60-Hz vior0(lh-jsf -(rdnw w .brator. 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 string may be adjusted by7xco*h1wdp*u: c :mpl moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying L betwee*7uch px:*ml1d: cw opn 10 cm and 1.5 m?   

  When you slosh the water back 1npx85 sn rafuux+,g3 and forth in a tub at just the right frequency, the water alternately rises and falls at each endxr3 nuxf8 u5 1+sg,pan, 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 to k/(mbtekc: lti /7/fraveling at k.0 km/s strikes a boundary within the Earth between two kinds of material. If it approaches the boundary at an incim:ekblk/t /f(7 otci/dent 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 changes from 2.)c1ut,ok5 ayl8 m/s to 2.1 m/s If the incident a t5),ylucko1 wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in wa)iv bwj 5)ed*fw*jk:s+ uc+ cqrm air when it hits a layer of cold, dense air. If the sound wave hits the cold a wjcv i d+*q)jce5 s+fubw:k)*ir interface at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave strikes a boundary between two types of rock at5sc+rq k . f1uuu80ewuen))di au c1)dfs.kieq)r5+ nuueu0w 8 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 dioqkjb+epuy k p))7v1hzr-u *sy .1)bqameter. According to the user’s manual, the dish has to be pointed in the direction ob uqkh rep)j )+b.oy1*u z7pqs ykv)1-f 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 acrossg4d i0b m0 9rg1zr*rmx the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted to t10 imb0*zg9g rxd4 rrmhe shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness constant of 55xn-i b2*0k-uhmb m 7ss0 kN/m Find the maximum compression of the bumper if the car, wih0k*buxm-2 7 -binmss th 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 5;zgitnc v;4h a fire net 18 m below, which stretches the net 1.1 m. Assume that the net behaves like a simple spr5zgtn c; i4hv;ing, and
(a) calculate how much it would stretch if the same person were lying in it.    m
(b) How much would it stretch if the person jumped from 35 m?    m

  A mass m is gently placed on the end of a freely hanging spring. The mass them5:cn9uut6fy5 k *popn falls 33 cm before it stops and begins to cfpm 9 uy*n5tupo5k :6rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a hu3nm-iyk s8c 5q2be ft/l*pfl2ge spring at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffness constan* f/85mbq-nsleflkc ip232yt t 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 6+nam4 9md; wdcaxsr;the right pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the speed of wavesmwmr9 c+;n xd s6d;a4a in the coffee.    cm/s

  The ripples in a certain groo oup0 1)9y,*cjlgynsc ve 10.8 cm from the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be *0onysypg)c91 jl,u c the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.0ayi5. mq)d yf+vev9g40t where x is in meters and t in smg 09a .edvyi5vy )q+feconds. 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 - ;dnswh.k;eyx 2:ac tits frequency if it accelerc;dhxt se2n ayk; -:.wates at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on the raft, it3jii7 gcqf0m+ sinks 4.0 cq 7ficj3g0 +imm 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 music6 +o3ee hqny;ciybi;yp5 , yr. ty6ki6al instrument are tuned to play at 392 Hz (G) and 440 Hz (A). py6 e+, hy36ni.;roy tk ;ieicb5q y6y
(a) What are the frequencies of the first two overtones for each string? G : $f_2$=    Hz $f_3$=    Hz A : $f_2$=    Hz $f_3$=    Hz
(b) If the two strings have the same length and are under the same tension, what is the ratio of their masses ($m_{\mathrm{G}}/m_{\mathrm{A}}$)   
(c) If the strings instead have the same mass per unit length and are under the same tension, what is the ratio of their lengths($L_{\mathrm{G}}/L_{\mathrm{A}}$)   
(d) If their masses and lengths are the same, what must be the ratio of the tensions in the two strings?   

Consider a sine wave traveling down the stretched two-part cob*(r 5 ml2at)5zkq,e ueag w0ar1t8ucrd of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of th8rgku cetba5r01e()m, 2qz5 u waa *tle 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 atyu)se8aqsw- ;r g ;(zt a frequency of 264 Hz, and the tip of each prong moves 1.8 mm to eitheu; q zasgyet-s);(r 8wr 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 1.5 cycles cbdrvt )x/ve/ot9w94 per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placed there /dvxo9 br4 9/tctvwe) (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 rr tljwy a p/k1-m2t9 dq8ta*9ting that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a strinr wtq28 dyj 9t*-kam1tt/9 alpg with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — a 5tbyt* i*ij gk93y1x;n3n syeach one-way swing takes 1.000* xiak n;i yt3byg31t*jny s95 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-(utzuz; /wwxyjjn0 ) the vertical 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 oscillatiow/xw z 0jut);yn ujz(-ns or the period of the horizontal swings, and by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

  A block with mass $M=5.0\mathrm{kg}$ rests on a frictionless table and is attached by a horizontal spring $\begin{pmatrix}k=130\mathrm{N/m}\end{pmatrix}$ to a wall. A second block, of mass $m=1.25\mathrm{kg}$ rests on top of M. The coefficient of static friction between the two blocks is 0.30. What is the maximum possible amplitude of oscillation such that m will not slip off M?    m

  A 10.0-m-long wire of mass 123 g is stretched under a zkhl.b0;vt 2,p.ta wftension of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated ,zwatbl.0vp k. t 2fh;at the opposite end. Where will the two pulses first meet?    m

A block of mass M is su ,1ntznz2uc;mu,dg g 1spended from a ceiling by a spring with spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillations that will allow the penny to just stay z, 1t dggm1z2 uc;n,nuon top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel cx t 3:el :2h)fbhyd1hsrane 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. Whaty :)h3d1ehtx 2b:l hfs 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 ds+q4yj 9n gr:q9nqq+4srg jy :imensions 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 (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz