Give some examples of everyday vi3aa :a ft wklhmh9,e:*brating objects. Which exhibit SHM, at least approximat le th:k9wm:aa*a3,fhely?

Is the acceleration of a simpl2..qeyr l7rep e harmonic oscillator ever zero? If so, where?

Explain why the motion of a piston in an automobile engine is approximaet; )jpd7c g+) u)3*husgcwl td82tvwtely simple harmo2w ;lde)*)upt c8v wguhs+ 3dt)cjgt7nic.

Real springs have mass. Will the true period and frequency be lah 9hh2b 5lp9hnc k;nn(rger or smaller than given by the equations for a masbkh nhpnl92hn5(; ch9s oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple harmonic osg9z4rlwt (go 10rite033s hqr njw );zcillator (SHO)?

A 5.0-kg trout is attachedmc+oz 7cpd) a u n9+fg(k(s1gy to the hook of a vertical spring scale, and then is released. Describe the scale reading a u(+nfk7c9ym gs1a+gcp( z) ods a function of time.

If a pendulum clock is c pv-:-tf,ktc accurate at sea level, will it gain or lose time when take- :-cvtft pkc,n to high altitude? Why?

A tire swing hanging from a branch reaches nearly to the grou8qb3 3akb((0irrlv/:rtest 1jv ea k 2nd (Fig. 11–48). How kar:a/ti3b1rbv0 2ver3qk ((e tls j8could you estimate the height of the branch using only a stopwatch?

Why can you make water slosh back and forth in a pan only if you shake the 225otsij v;/pb c.ubvpan a vpiojsvb5b u/.tc;22 t a certain frequency?

Give several everyday examples of resona,yv5(+iwlkhxf;w ar.y2r rm 6nce.

Is a rattle in a car ever a resonkhb9lcupf( r.gbe- u14n0li 7ance phenomenon? Explain.

Is the frequency of a simple periodic wave equal to the fre.jd)k 7h1l purquency of its source? Why p h.jur kl)17dor why not?

Explain the difference betweenmix ,f y1xd.56a* inrz the speed of a transverse wave traveling down a cord and thi*i 6xdmayfr nz5,x.1e speed of a tiny piece of the cord.

Why do the strings used for the lowest-frequency notes on a p26)gy( /tur y 3rf2lr;vrdjvbiano normally have wire wrapped around thembrfvr6(/lvj2 u;3 trdyy r )2g?

What kind of waves do you think will travel 1fv )o h rv+zl87qar3hdown a horizontal metal rod if you strike its end (a) ve)z h a3r1ofr v7+vqhl8rtically from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase in temperature, jswb-tlnhs eie ,)c *bazg;p)m/zl2p4 4p r3, but the bulk modulus B is nearly independent of t) 2*ah3trb l sip b;4gpm, c,ej spl/z-)n4ewzemperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in amplitude *kv/3t lggg3 xas they travel away from the v/gg3tl* k3gx source.

Two linear waves have the same amplitude and speed, and otherwise are i5-brw ;+o;v l nn9kfqkdentical, except one has half the wavelength of the n k nf r;9lo;bv+q-w5kother. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundaf9l0n6 .,ih /um evykury between two sections of cord as in Fig. 11–33, the frequency does not chang/yun 9 lihvke6 0u,f.me (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segm3tv,.rtmh1dueqym p4 ;fz-q3ents, are there any places you could touch it with a 3uq ,fd.-qmr;1vh3t em4ypztknife blade without disturbing the motion?

When a standing wave exists on a k/r2fj6dswvq w *ul/fnlvj91 k::2jz string, the vibrations of incident and reflected waves cancel at the nodes. 6krnd swvll f/j*:j/k w2vju9f :q21z Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one plxx w2h qpo6np; 28*kqaace to another, how might we determine whether the energy was being carried by particles (material bodies) or 8x2xqw6po *ka2hqn; pby waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the total di 65bz40*4s,lxmxym5 a kwqrohstance it travels in one period y5xqkslbwzx 4m6 a45*h0mr ,o?    m

  An elastic cord is 65 cm dv1v. ./ztd,m: ppzghlong when a weight of 75 N hangs from it but is 85 cm long when p. vd./tzpmd1zh ,gv: a weight of 180 N hangs from it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when2- v ge*gviha*l 0bj.1rx ,uyt its 68-kg driver gets into the driver’s sexb2rt*. eli* ah0-,gvuj1gyv at. If the car goes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 3nqo*z:,/zz/nq. yj9 k(i,ty p,tuym wnzn/t2.7-kg fish hangs from it. (a) What is the spring sn/,3y,izpz*tn ,wn q/o (ymyn:q ktju/z9 tz .tiffness 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 of 0.60 kg is huzot0(*it mxhp -+k( hgng from it. What is its p+k(hx-h*i tmot(g z 0frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. 11–2 at time;-z2 i+hwdd lwbw1adj.)m1 r js t = jblw1d+wmzjdw.h)r1 adi -2; 0,t = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

  A small fly of mass 08ptm4j vjg j9h1 y1mb4.25 g is caught in a spider’s web. The web vibrates predominately with a frequency of 4.0 Hz4m 4mj1y8jb t hp1vgj9.
(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 9k c;t+m))-ios rck nmumrb,.a spring vibrates with a frequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 , sn citr+kk 9-umm)).;mcrobHz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per second with an yez9xw7e (kw)6o:nhbief0b21 *jygiy9q(vu amplitude of hxyeg( bbywyu7o v)*n ie9901 q2ejkz wi(6:f0.13 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 fr;g neg usoxeus, p1l *;o3(y fvoh0t:6om equilibrium is the speed of a SHO half the maximum valp*6s o ho(;:e soglfeynguvu0; x1 t,3ue?$\approx$    A

A mass attached to the end of a spri c oe0tep55qeth9oihsg5;+ r 0ng 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. Ifytauuse*v ;k.a9fb8 c 9b 3fh+ the spring is stretched e c9h +3ufayufbak *ts 8v9b;.an additional 0.130 m and released, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with spring stiffneut-0 p r6 c6eohje19jwss constant k = 280 N/m and is executing simple harmonic h6to1pe0 9jw j6rcu -emotion. 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 vwl+4pa j8-gm N to compress the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. Wglm -p j4wa8+vith what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached w eos7kc(wn31to one end of a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, the mass experiences kcw ns7e(o13w 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 = 0.45cos,s iog y8c;klk 3dq-3itucy2;6.4t where x is in meters and t is in seconds. Determikilsg;ui2;q3 c k ydt8 yo-3c,ne
(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 KE 26tl2gp:lvezzlc r8*/ls ge 6 and half PE?t* /zrplce8vz6l gl2 :sle26 g ±    A

  If one vibration has 7.0 times the energy of a second, but their f3 )*mma26g rrm0spvkag,a6a;i su7czrequencies and masses are the same, what is the rati2crv 7k)aa66r um 3sam,asi*0zp g ;gmo of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertica,iy;3f/ psl /)up9q v3 mcnpfzlly hanging light spring once every 0.65 s.p)s3zu9ncp 3fmyi,;/ lp/fqv
(a) Write down the equation giving the pumpkin’s position y (+ upward) as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. y = (   m)cos($\frac{2\pi t}{0.65s}$)
(b) How long will it take to get to the equilibrium position for the first time?    s
(c) What will be the pumpkin’s maximum speed?    m/s
(d) What will be its maximum acceleration, and where will that first be attained?   $m/s^2 $

A block of mass m is supported by two identical parallel vertical springs, each ovu-x0/ q-:njla1 apn 2mp umk4qj:v 8with spring stiffness constant k (Fig. 11–49). What will be the jv:p1o-a8q/xu ml2qupkn4a-nj: m0v frequency of vibration?

  A 300-g mass vibrates according to the equation, x3kp-nm3 hk2vhn-p d x = 0.38sin6.5t where x is in meters and t is in sex,pphnn 33 mdhvk2k--conds. Determine
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows two examples of SHM, labeled A a f6 g i;+tosqnze i;l+:w.ch)tnd 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 spring (k = 124 N/m) is xd at/5 xqee 1vte- 0/u-:dfzsstruck by a hammer, which geevase :tfqtxxd05- 1 d//zu- ives 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 0fd 5cxfh3 *,w+kcwyh spring stiffness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) with positive vec wfy ,x+ kfhdhcw305*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 conq8k a.n(,7sj dmvlbuiag69 0zstants $k_1$ 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/bs mii-a2twf p4twx:3qac); 0.600-kg block attached to a fixed horizontal spring whose spring stiffn /aiw;tfac4) mqb ip2-tw:3sxess 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 brbr (b:k dse9i+idge. After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally cbb(9 :ed sik+romes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrations in exactly /rdyphh)jb7aw8 )narxx )g 64 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 fq/8wi , urd .azw/*;7tl8eszx)ipt kper second? (That is, one,8kiq i;xztpu)*as7/elw .8r fzdtw/ complete vibration takes exactly 2.0 s.)    m

  A pendulum has a perimuy 3+nn)jr2cod of 0.80 s on Earth. What is its period on Mars, where the acceleration of gravity is about 0.37 that r cm jnu)23n+yon Earth?    s

  What is the period of a simpl3j+0: tjuubho8tp pp k4qs j, e:eis*z)8y)gle 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 nwjy 7s.d*1xggrams, and it is releasesx1.7dy gj*wn d at an angle of 12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’s pendulum has a length of 0. mhx :ooyzznc 9x.qi 7/4r4fz09930 m. If the clock loses half a minute pe z4xnrmz x/0 iqohz 7:co.yf49r day, how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximum +(n.xnl 7c lpvspeed $v_{max}$ 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 q(3 u- rm2mum ektxn.yco0 f:4 -if*wu it is released from re3fwuyc(m.tmer40nu*k2:-muo x- fiq st starting 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 bobtowi:9gb8i4 at every 3.0 s. He measures the distanc9i bw8igo: tb4e between two crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frd9m dx8od,b,iequency of 262 Hz and travels with a speed of 343 m/s How far o ,bd 89dixd,mapart are the wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz andgx5sm( a7b-i1 2uas (vjs1xdm 1600 kHz (kilohertz) and travel with a speed ofmsxaxbd g1s- 57u i2j(m1avs( $ 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 lm 2*5a*yc1qpi bw3dqdongitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one is twice as dennxcl94p j,)t 7h chsv9se as the other. In wh ,p 7lhc 9jvhxst94nc)ich rod will the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apar 9yx zil*vfmks0 jm+y03t4d a7:06tw jqrq b+zt. If the tension in the cord is 15 +idwxkzs :azrt9t f0*6m003qj+jylyvq b 7m40 N, how long will it take a pulse to travel from one support to the other?    s

  A ski gondola is connected0zsk e0tbn2nn1q qy ;fi32- (ufb9v rv 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 thatvue1bt9r y b2qniq- s0n ;2f(zk0vn3f 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 7bq 7g7s;y; yg(fagbzof his ship just below the surface of the sea. He hears the echo of 7g( by7 ag yqb;7fgs;zthe 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 eartok-tla8 ywfz k5l32:h hquake travel at different speeds, and this difference helps in locating the earthquake “epicenter” (where the disturbaz2th -f8llk35 yaw:oknce took place).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced surface wave can be approximated by a sinusoidal transver*-uprn1z3dh+* m zijcfj m8m8/s. bqxse 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 mf1r z+b zu/xn- q8*jdpi m.hmsjc83*with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) tqqxz *nk(- jk2he amplitudes, of an earthquake P wave passing through the Earth and detected at two points 10 km and 20 km from the source?*j 2kx(nqz-k q(a)    (b)   

  The intensity of an eqap y859a e-ptwo11z xarthquake wave passing through the Earth is measured to be p51zx8ptq 9we-yaa1o$ 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 portion of ,fz pt+ 9sd)rvthe Earth, but one is carrying twice the energy. What is the ratio of the amplr pst+ )9vzfd,itudes of the two waves?   

  Two waves traveling along a stretched string have the same frequency + nj.tc2,swyc, but one transp+ w2s ,nycjc.torts three 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 m iu3(zlob w zc;p(,nc4ove up and down a total vertical distance of 6.0 cm, from the lowest t n (ioz,ubl4pw;czc(3o 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 Fi,7ligdkxr 7d *g. 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 other, the strinxd*l,7i dg7kr g is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 nikx4usdjp+b kg l:3+shh-5g):dt,r Hz as its fundamental frequency, what are the frequencies of the first four hahlsu gh-k :dbx3j)ip ts k+:4g,rd+5 nrmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfiais7sp6 vvl //ngered. At what frequency will it vibra7vialp/6/ svste if it is fingered one-third of the way down from the end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops atk5x:: -3 n/nyxtchced a frequency of 280 Hz. Name at le5: nt3dc/kx: yhxnc- east three other frequencies at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If th+nqy9nx+q6 x ze frequency of standing waves is 475 Hz, how far apa+9nxznq +6 qxyrt are two adjacent nodes?   m

  If two successive overtones of a vibratinbc+ *n:sxq(2o q:kdn jg string are 280 Hz and 350 Hz, what is the frequency of the b(s *k nox+:qj:dqnc2fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The distance frdti,4fv x: t)odk;etj f .j30rom the bridge to the support pt.4ttrokj3 ex d,vffj:i0;d) ost is L = 62cm and 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 vibrate at 200 Hz, but it is meascwgv)whck 7u*5 1wpa2ured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?So the threp51kcww)uchv w 72 g*ae frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string buq a;n 5:chl(is supposed to vibrate at 200 Hz, but it is measured to vib h;aqcn(l5u: brate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-am5 lpc3)tz2sybz6 bld9plitude mechanical 60-Hz vibrator. Thy l 5lt29bdbzczps6)3 e 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 q)kvx*r* ,n-axpd l;gthe string may be adjusted by moving the pulley. If the hanging mass m is fixed qd)-gv rn pkxa* xl*;,at 0.080 kg, how many different standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and for3:lk7-0+ww6em jpd; s vuh kmmth in a tub at just the right frequency, the water alternately rises and falls at eamd; p0-h6+wwmv37e u:lj sm kkch 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 traveli1 hugi1e. su-h.v irc7/gf pg7ng at k.0 km/s strikes a boundary within the Earth between two kinds of material. If it approaches the bound1s p7g/i vu.-hci ref7hggu.1ary 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 yqu/y 1rkw/gjy q6rz1r8 -ta4from 2.8 m/s to 2.1 m/s /6gw1tj8ryur y 4qr1qz -y/ak If the incident wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is travelii(c3tn7;p3hc2 yfm njng in warm air when it hits a layer of cold, dense air. If the sou (hnc7f 23pctmi ynj;3nd wave hits the cold 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 a boundary between two typess,f4,o. wqved of rock at a 38,4. dsqwefov, $^{\circ} $ angle. As the wave crosses the boundary, the specific gravity of the rock changes from 3.6 to 2.8. Assuming that the elastic modulus is the same for both types of rock, determine the angle of refraction.    $^{\circ} $

  A satellite dish is about 0.5 m in diameter. Accordw9w54fi 3g eu ;o jth70gg+xn:*fnzl ting to the user’s manual, the dish has to b ng7j e9x u+:ifwlgt 5o 30nhfg*4wtz;e 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 ay6vzw )(c/(p7 kaoxs3f mh6macross the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately hoa7o(w( v )ykmspm6h a/xz6cf3w 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 stiff wln )iijtnl:a*p;g n)cwj4 34hjkm24ness constant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approximkmn4njlwj)gat3cj*;w:4n2)4i pi h lately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m below, whic/mbb q 8cn)1vdp8.bq lh stretches the net 1.1 mv n.b/bbc qp8q81 d)ml. 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 a freely han b0rv. )x5gjnnging spring. The mass then falls 33 cm0.xn)b 5n rjgv before it stops and begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 ,d n:vl7vy ;ro-gcz(lsz*ht2 m/s (Fig. 11–54), compressing thrvt o,l (7lcz ;z*v-sgd2ny:he spring 5.0 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 cofeykiye* +)xjy x1y)psf7c*25g76n vw:qaao ffee (diameter 8 cm) at just the right pace of about 1 step per second, the coffee sloshes more and moxa7q7iy e*1c)oy :+yw)exgf5*j6fp asykv2 n re until eventually it starts to spill over 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 center eonfm:7 ,m;a s mkdrtc/s6d9/4 h :bqkof a 33-rpm phonograph record have a wavele;hq m9 sd7ka6ctkf4:sm b:,m//orn edngth of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t 6l8yvd./,vzqz u ssn4k6w jf1where x is in meters and t in seconds. Determine szvz k/w6y8.q4vl1j,6sunf d
(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+6 )-ske . 2kwr+vlvow vj+du jmbn92i it accelerates at 0.50g (a) +il9.uje+svwb)kk2m + n-vw6rjd2vo upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on ruk yzv8r5;8za lake. When a 75-kg man stands on the raft, it sy5zu8r r;kv8z inks 4.0 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 musical i/ xy h)2giudg2 uq6x.ajm+ wf*ur1pp;nstrument are tuned to play at 392 Hz (G) and 440 Hz (A)16+) pywur g u. xp*idu22jqm/gaxf;h.
(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 the4-.of uj,vs;; pnq68qmih t l3nhtlq2 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 frequency is the same in both se2v j um;qll3t8isnq6o4tnf;-.ph hq ,ctions. 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 3bmdu; w k.pne qrz)j/5z*6z. i vin2 tjo68lkof each prong moves 1.8 mm to either sirlu..nwj5ii6)ezvt o;/38kkzm*q d pj bzn62de 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 p )z)ix1xw uds +xi+o(harmonic motion of frequency 1.5 cycles per second. What ii+xou(i +zx x1)s) wdps the maximum 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 is attachehf0 v x dzgoler f 0:,g6och1f3k.f5-ed 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 end fix lhcz dh-fofvf:g50 0.6xe3egk,1 froed and the other free.

  A “seconds” pendulum has a period (ry 6/uon)7phxrcht-/+glhs)2.u3dx eys jn of exactly 2.000 s — each one-way swing takes 1.oc. )3x +yuu)s/jrrs6xyen7dlhh 2 ngh(/-tp000 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 directf)z 2w *at)fbv0 dt:qpion or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period of 2f0t z*ft)pdavw:bq) 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 w25 8dj5fdrnounder a tension of 255 N. A pulse is generated at one end, and 20.0 mn8f oj2d 5dw5rs 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 ceili / .rpoq(ebdcj8 y79bcng by a spring with spring stiffness constant k. A pennyb8j (.ccob7 qpe9y d/r of mass m is placed on top of the block. What is the maximum amplitude of oscillations that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The steel crane cable5adw513knmfv-c 6 5 p,ubpebe is 22 m long and has a diameter of 6.4 mm6m5upc pvne5b,kwfd1-a 53b e. 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 gic*w(u ksc:r7yves the dimensions of the block). You push it sideways as sh c(7uskc rw:*yown, 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