Give some examples of everyday vibrating objects. Which exhibit SHM, at least a;nml 7 ,hhs1sy1o9m ekpprn1skym1 lm,o sh;eh97oximately?

Is the acceleration of a simple harmonic oscillator ever zero? If sd2ha1h4v 5i67 tf aml phpo1x,o, where?

Explain why the motion of a piston in2 k.samo;hz:xk9 pe 9l an automobile engine is approximately simple harmopzmkxea; ho9:s9 . k2lnic.

Real springs have mass. Will the true period and frequenco mmr.hk; ric2 ec07r)y be larger or smaller than given by the equations for a mass oscillating on the end of an idealized massless spr) irccom0k2.e;mrh 7ring? Explain.

How could you double the maximum sp 090. . yb)ttxl3p w6eoz1cxh gsl)sbdeed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scale,e0)iha.mm,ql.+kd v n and then is released. Descr dam .qe m0hk)v,l.in+ibe the scale reading as a function of time.

If a pendulum clock is accurate at sea level, will it gain or lose time when u*zn(jkn,.p utaken ton (puzuj nk.*, high altitude? Why?

A tire swing hanging from a branch reaches nearly to the ground (Fig. 11–40oh o05llq+n3 1dqisd8). How could you estimate the height of the brn d1 q5s0l+o loi0qh3danch using only a stopwatch?

Why can you make water slosh back and forth in a pan only if you shake the pan a21 zd yclywps5 )tm+x1t a ctd1)x y z1+m2 w5pyslcertain frequency?

Give several everyday8aoi h q*y:eu18 hu,fh examples of resonance.

Is a rattle in a car ever a resonance phe 7vub*haeuy;fdrzr7g .duz5 j:))n 5znomenon? Explain.

Is the frequency of a simple perum3iyga r1bx ,977uz miodic wave equal to the frequency of its source? Why or why nur,ugymx9a7z71 b im3 ot?

Explain the difference between the speed of ajb it+:n2r b /am7z(ho transverse wave traveling down a cord and trn2a +(zi/jt 7bob:m hhe speed of a tiny piece of the cord.

Why do the strings used fyqq qz5,d- m5yor the lowest-frequency notes on a piano normally have wire w-q z y5qm,dq5yrapped around them?

What kind of waves do you think will travel down a horizontal kw3te8vfvwi ,0b (ws,metal rod if you strik,wskv8vftwb,i3e 0 w( e its end (a) vertically from above and (b) horizontally parallel to its length?

Since the density of air decreases with ah1,dj( /a:wp ed88 gum*fep jnn increase in temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound w1dpf eg ejmuh wd ,j(/*a8p:n8aves in air to vary with temperature?

Give two reasons why circular water waves decrease in amplitude as they tr ow.q hqq9)h;savel awayh)qwqos.;9 q h from the source.

Two linear waves have the same amplitude and speed, and othk-oz/kjj , hc4erwise are identical, except one hashkjc/ ,- koz4j half the wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two secw6ipj tni p9 09.-1jfxvo3 coqtions of cord as in Fig. 11–33, the frequency does not change (although the wavelength and v 9vt6p-joop 0iwx3n1q ci.j9 felocity do change). Explain why.

If a string is vibrating in three segments, are there any placesah4k671inht hhd.e a;m,9nvh you could touch it with a knife blade without h67 ;49.an1t , nkdh hheaihvmdisturbing the motion?

When a standing wave exists on a stringtng42(2 nk 5- ldbsmjh, the vibrations of incident and reflected waves cancel at the nodes. Does this mean that en 2gkl5hnm j2 sb-4td(nergy was destroyed? Explain.

If we knew that energy was being transmitted from one place to another, hkyc,jfot y (q-. ci,0low might we determine whether the energy was being carried by particles (matt.c,oc0 l-,y(fjqyk ierial bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, whath1g vxo26 iulr-(hd o 3nbb(c6fz+va / is the total distance it travels in one per/3v6(vhulrzb1x +b6fo 2-(in gaocdh iod?    m

  An elastic cord is 65 cm long whenzrsed.g .5* wo 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” constant k of this elastic corzsrw5 .*o.g edd?    N/m

  The springs of a 1500-kg ca ):sck6 6h loo21zqrrir compress 5.0 mm when its 68-kg driver gets into the driver’s seat. If the car goes over a bumpqh: k zrorci)s661 2ol, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretchzo 8g s6pg3w*df).nut- m aq1yrdk, )ves 3.6 cm when a 2.7-kg fish hangs from it. (a) What is 8.o- vgdzsrq1tfak )*,wd)pu 3yng m6the spring 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 Hz when a mass r9t/g eha2(ipof 0.60 kg is hung from it. Whthieg (29pa/rat is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x syw:bhf6uq 9h zw;(+ dof the mass in Fig. 11–2 at times t = 0,qhhdfswyu:w 96 +b( ;zt = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 vzzp51r 4k hu;o+l1ih vibrates predominatel;1lrkz o4z+h uv1p5i hy 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 vibrat6fi3 fb5h s 8db5euwr5es with a frequency of 0.88 Hz. When an additional 680ru5bi 85 6b5w3efhfd s-g mass is added to m, the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3cq3/ y9aik *g7rnhd*p .0 times per second with an amplitude of 0nrgh7i*9qa*c d y3/pk .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 from equilibrium is the speed of a SHO half tlkl61vt1fi* the maximum valuef tli1vlk6* t1?$\approx$    A

A mass attached to the end of a sprin. n 0vfc-iwk(c ;:ujpgg is stretched a distance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretches a vertical spring 0.315 m. Ifdzwyca- .fl/. the spring is stretched an additional 0.130 m and releasedfa /y.-.w dclz, 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 stiffn kbes;5s-*v9lyh2c, ntsw ur4ess constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is moving with a speed;, bhk24w 5t nsyus r*-lv9esc 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 to “lo .4wcq wwj/-pnad” a 0.180-kg ball. With what speed will q nw./jc4w-p wthe ball leave the gun?    m/s

  A mass sitting on a horizontal, frictigy+s 6 gwcqfk 1kfn536onless surface is attached to one end of a spring; the other end is fixed to a wal fkf3q6 g5n6+gywsck1l. 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 acceleration of 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates according to the equation x sf(6 u nbcs;qv**hzt gx*li)6= 0.45cos6.4t where x is in meters and t is in seconds. Determine 6t*s;nliz uf( *q)vbxgh s6*c
(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 3nms-jok, 6fsntgm-3 SHO half KE and half PE? ±gsm ntoksn,-f3- 3jm6    A

  If one vibration has 7.0 times the i3rc:s.gf-1ugu/xint ;(ec l energy of a second, but their frequencies and masses are the same, what is the ratio of their amr;3-nxfugtc sg(/.:ci1 eliu plitudes?   

  A 2.00-kg pumpkin osci vxe-o 7y*.)d w,uoikvllates from a vertically hanging light spring once every 0.65 s. eoyw*u,iv 7o ).- xkdv
(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 idev6nhvaok 8p6izws/ 7.2 ml )in;i5tnpntical parallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What will be a 8k/w7n6n6 n lo5i.ihv)i2p zm;v sptthe frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t wh m0 g,4rcjh4x*4wbfaqere x is in meters and t is in seconds. Determine ar0*4 m ,f4wxc hgjbq4
(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 examp*1o1zc h*h jziabt pv*-7 pqk6les of SHM, 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 horizontah;4:s1d2rvr r3ks cnjuh)8 ,rnxs1xzl spring (k = 124 N/m) is strrdhrrsjhrs zxx)v:,2c 4311 nk 8;nsuuck by a hammer, which gives the mass an initial speed of 2.96m/s Determine
(a) the period and frequency of the motion,    s    Hz
(b) the amplitude,    m
(c) the maximum acceleration,    $m/s^2$
(d) the position as a function of time, x = (    m)sin(4.08$\pi$t)
(e) the total energy.    J

A vertical spring with spring stiffness constant 305 N/m vib8ph e9o2f -u(gd1bzdkme62 alrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) with positive vee86 uepf(2kga1h 92d- dlbzmo locity 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 constants onxa(l40ut.c;jhq)z $k_1$ 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 spring g+x7c emdy4v lxz, s76whose spring stiffness consta ly 7mz7e+c gx4xd,6vsnt is $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with mass 65.0 kg jumps from a high bridge. After 41aqxe04dgy ju fy.0r 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 thy4q1 y0 rge j.4uxa0fde 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 e7g*i; xbyo9kmxactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly one swing per sect99(f:*j skj 26i7elshp6y n8ukgmppfq m+2uond? (That is, one co9tp7qf:l p k 6k s*9(m2 uf 8gehi6+n2mpjysujmplete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on Mars, w+cs3tiaf). a( )zga lbhere the acceleration of gravity is about 0.37 that on Earth?afai c(bz)tla.s )+3g    s

  What is the period of 4a)p zboj ubc8(u+dg8 a 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 hasv/ f8oif)l q -s60e:tz -bofih a mass of 365 grams, and it is released at an an:h 8zsi-flob -t/vq 0e)ofi6fgle of 12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’s pendulum has a le lootejnj)0 kzj7.k 24ngth of 0.9930 m. If the clock loses half a minute per day, how should you adjust the length of the pendulum? sh4k.l zn 7t)2o oej0jjkortened by    mm.

Derive a formula for wg(g6g):f o pjthe maximum 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 p :drpjqt2e/ w4zu(4izyx2l 2released from rest starting at an angle of 1:r2i lue(w4 pq4jty/ 2dz pxz25 $^{\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 aws0o*rcl-2g,tcrd .boat every 3.0 s. He measures the distantr2,0s*o lcra g-c.w dce between two crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air hmwh5kfc4 * xblw066 jhas a frequency of 262 Hz and travels with a speed of 343 m/s How far apart are the wave crests (compression* b6fwhchmlwjk 4 x065s)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 e 2s6i-tq m*xo pib.ksbow;i.ky1)t6kHz (kilohertz) and travel with a speed ski.xqw;mi- bk*pb 66 oo)1 tstie2 y.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 longitudinal waq-7ss far8 bv)ves in
(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 6ghi 7ln l-tuyv;8 :xras the other. In which ih;:-t6u8rv ll7yngx rod will the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched betweenf+zrqlshv4)j( z2e qwp v/6z5 two supports 28 m apart. If the tension in the cord is 150 N, how long will it take a pulse to travel from onj(r+w 5v6 fv )zqpsz/lez4q 2he support to the other?    s

  A ski gondola is connected to the top oc3wtz;2u j o0 c)bxu5of a hill by a steel cable of length 620 m and diameter 1.5 cm. As the gondola comes to the end owc2z0uo5bc 3x)ujo;t f its run, it bumps into the terminal and sends a wave pulse along the cable. It is observed that it took 16 s for the pulse to return.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

  A sailor strikes the side of his ship just below the st bi-1xde o6q4al 0)vzurface of the sea. He hears the ec q1 zbvlt0e4)6-xoadi ho of the wave reflected 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 different speeds, and this differ* opxl*ov9cs :ence helps in locating the earthquake “epicent l9os* xo*vcp:er” (where the disturbance took place).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced surface wave khitz6 5+y;agt4/nbp)ix .7js p 5u axcan be approximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually ix g74)tsn ii+6ta5j/xz5 h ku; .aybppnclude 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, an ilo3*ks *371 aunpsdsd (b) the amplitudes, of an earthquake P wave passing through the Earth and detected at two points 10 km and 20 km from the so*7l assnodpk1 s3ui* 3urce?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth isbv-59ht g2r2tw z8,3y yyxpcx measured to be c2t w5hyy3p9-,v2g8zxbtx ry $ 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 portio cviy)1kn 7f 6aukkt/gy*)r/ ln of the Earth, but one is carrying twice the energy. What is the ratio of the amplitut *vr glu/)k7i)/ac knk6 f1yydes of the two waves?   

  Two waves traveling along a stretched string have the : wn6km4ut;iamj7qqxj v* .r.same frequency, but one transports three times the powantj6x;irmvqw:.uq 4 m7kj*. er 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 tokomsl8l9c4ph-asbtay k f,9y 54;ti,tal 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 a 8, ytoiky;st-9blplk94 5m, s4hfcafactor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each other. (a) Sketch t eh3xh*1zv lybj9je1(paa) o0 k36hhxhe shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments latjaxlv9*)h ( hhae 113je03zxb6pohk yer. (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 g2)gn lbgm84apw j(p5 its fundamental frequency, what are the frequencies of theal)(82j gn pgmgb45 pw first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 29p8k , am/y6ujd4 Hz when unfingered. At what frequency will it vibrate if it is fingered one-third of the way down from the end? (That is, onlyupd m/jk6,ya 8 two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequency of 280 Hbo 6b6uz + lko0+:roudz. Name at least threed+k o0l uorbz6b:+ou6 other frequencies at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the frequency ofrc4(l0 jn9f-z 8d wkyr standing waves is 475 Hz, ( zn jwc9r0-4yk8rl dfhow far apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 35dztb oq 9.fk4a0)oc;khg +4vl 0 Hz, what is the frequency of the fuz oqotgdv ).9 f4h4a0;kkcbl+ndamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The disu -.q:kj/p z9i vptan295mu e3dhqmg- tance from the bridge to the support post is L = 62cm and3umtdp qa/m uv92 5-pe:i-hgkzj9 q.n 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 vibrrleoea.t t c57 vug2 m796p hh(20tsidate 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 m67c0.a rshd9o7g2h ei 5t vu(ltt p2efrequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibr3d6xocux h h+ik2 ,bb(,)g nvdate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in tu , cvdb()+xghobxn,i3 k62hdhe string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-amplitu (wv) s,89g,av.z koax5ij sbxde mechanical 60-Hz vibzjg k)x b59o, v,8aiavss.x (wrator. 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 adx)ygs )mxdg7brii( q 3wmf135justed by 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 xd ri) i5wg)s m7g33y(f 1bxmqbetween 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at just the-qbk (vk *osf 9zmxw/7 right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequ9(7qf*-wxkvb zoms /kency 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 tm6-lkw24ez,+ o,ftn v 6k/s*cjfi y tshe Earth between two kinds of t-*k,ile6ow/m, j+2stf4c y6f zsv kn 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 changes from 2.8f9 :fuj:k/qdq4.fzx n m/s to 2.1 m/s If the incident wn9u:d.q j4 fzfxf:q/kave 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 gc hm++-xx rj(0payex zaaho927 rx*3ex5/ ckcold, dense air. If the sound wave hits the corah05x( 9* yxacp7- gxk core2a+ ez3j/x+xmhld air 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 b y (5*i*xce.va( 4nr xiqzhf)a boundary between two types of rock at ahvac 4bqixz )(*.e x*nr f5i(y 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 gkp 4j+mt1bfi)yih8 ( 0.5 m in diameter. According to the user’s manual, the dish has to be pointed in the direction of the say hjtgi8p)fm1ik (+b 4tellite, 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 tre g kbh0buf38d0 6)zlkavels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safetybudk0 g 3eb zkl6f80)h? (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 stiffness constant of 55: lmqj0po 6)1osr lyt+7w la )g.,imzj0 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collidezm1i psa6ljt ,r))lwyo:j07.olg m+ qs 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 stj +ugt6iw- p4dretches the net 1.1 m. Assume that the nwgi+4j du- p6tet 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 endx(ej +luxx)e8hnn 8r 9 i.ret6 of a freely hanging spring. The mass then falls 33 cm before it stops ane 6+t9ni rjxr(neeu 8x8xl h.)d begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a hugjoe0a 5al 3l,p 7ass,we spring at a speed of 22 m/s (Fig. 11–54), compressing the spring 5ll70oas3 ,,psaae 5j w.0 m. (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 4ankb-elw06 mma,;u q(diameter 8 cm) at just the right pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the speed of waves in the coff4;euq -lb an0wkm,6 amee.    cm/s

  The ripples in a certain groove z *2zkguwl8nzhhm0ge:-cfh -b 9h6b.10.8 cm from the center of a 33-rpm phonograph record have a wavelength of 1-gn: hzmeczhuk0z8. g2b9* -6wflhhb .70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x*wi)l hp;tu(64uz z+:kav xtd =0.650cos7.40t where x is in k+:ahdi t )4(*zulp x;zvu tw6meters and t in seconds. Determine
(a) the amplitude,    m
(b) the frequency,(round to two decimal place)$\approx$    Hz
(c) the total energy,(round to one decimal place)$\approx$    J
(d) the kinetic energy and potential energy when x=0.260 m.(round to one decimal place) PE$\approx$    J KE =    J

  A simple pendulum oscillates with frequency f. What is its frequency if it a)8r2 4wkc dtwd;x0fz accelerates at 0.0)fxc4 k r a2wztd8w;d50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on the r3 .wvmo(n ja- rmvsa248c9np daft, it sinks 4.0 cm deeper in-pmvvnnca (2 4wmo8d.9rj as3 to 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 musical instrument++a5.bmr+ wsax )xop c are tuned to play at 392 Hz (G) and 440 Hz (b ropmasa+c)w++xx. 5A).
(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 trav*dj it b.12p)wiee;kw en- w(4uxcuz *eling down the 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 v( wecnj;*xi -ep) b.ewkit*dwu4 u2z1ersus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the tip of each prong moves m8o3f gqn5yu8bqxm,:*g 4mc n 1x nqcm8, mo*4m:bqfg nu3y58g.8 mm to either side of center. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillat bki(s ndx6rjz x/t-0 y(9dx,oes with simple harmonic motion of frequency 1.5 cycles per second. What is the maxixd, 6 xinobrd0 s-(z9y jkxt(/mum amplitude 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 wzg.b8 e40si3vdboq7 is attached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with one en 8b4ev gzdi7b.q0 w3sod fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each one-way swioq kid2l 52ub(h.dk 3fng takes 1.000 s ido 2ub2hqkf5(3l dk..
(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 osctwwn bu 2:99xoillate in the vertical direction or can swing as a pox w:2nw9ub t9endulum 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 amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

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

  A 10.0-m-long wire of mass 123 g is stretched under a tension of 255 2novhpp 7wo i7.e . )xycdp*:yN. A pulse is generated at one end, and 20.0 ms latci 7np*o:hep .) .vp7yox dwy2er 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 spring with spring stiffn p;v wp4onjb7.ess constant k. A penny of mass m is placed on top of the block. What is the p;4wp j 7o.nvbmaximum 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 steh cbhsx /,vgh*fr 6x7-el crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts 7hbs6/ * g,hvcrfhx-xthe 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 f :qjkggb 3g48 c:a sug3:fy+xalso gives the dimensions of thffagx+8g3g y4b::kug3s : cjqe 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