Give some examples of everyday vibrating objecye)xaego7 v 37ts. Which exhibit SHM, at least approximatg x37oa v)e7eyely?

Is the acceleration of a simplep,9q c0xfw4uh qngj8s 3p-w y( harmonic oscillator ever zero? If so, where?

Explain why the motion of a piston in an autom ztbcq wi9k,. 5xm(uf;obile engine is approximately simple harmoni9k b;m(tfw5ix, .uzcqc.

Real springs have mass. Will the true period and frequency be lz v+n9-ito)o32rypgn0x n5m narger or smaller than given by the equations for a mass oscillating on the end of an idealized massless sprinxm i2+n3 nn 5nvgytoz9po)r-0g? Explain.

How could you double the maximum rd(vd 0h6v6ej3 vbw7rp*bk ;dspeed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attac91d k zn/t)mhbdo- d21mcn-xbhed to the hook of a vertical spring scale, and then is released. Describe the sca9 dx2- oh1zn-km )dtc bd1mbn/le reading as a function of time.

If a pendulum clock is accurate at sea level- ;+eb8nlixg y, will it gain or lose time when taken to high al lynig-;+be8xtitude? Why?

A tire swing hanging from a bra)gh d(,xdh55jh iglt6 nch reaches nearly to the ground (Fig. 11–48). How could you estimate the height of the branch us,higdh 5j(g 5 )6xtdhling only a stopwatch?

Why can you make water slosh back and forth in a pan only if you shake the 64c i;hcp (oy3/ri5 p(ttizzm pan at a certc4cm3ztp6 oi; t zi(ihp(5yr/ain frequency?

Give several everyday exampl(kps:cj azrxvgpl+-/b* nn) l9)x9wles of resonance.

Is a rattle in a car ever a resonance phey8yvlu2+1n aynomenon? Explain.

Is the frequency of a simple periodic wave equal to the frequency of its+nc4g:n+1fiw lq* c rb source? Why or wbi +1c l:c4n*rfnqg w+hy not?

Explain the difference between the speed of a transverse1ymg-v/ i8*92xhm bqm 7s)idlee9enc wave traveling down a cord and teiv7y )*gsxm-d82ebm /lehcinqm 91 9 he speed of a tiny piece of the cord.

Why do the strings used for3v fr4uhra+okov a(; y*c8xr5y n/ag8 the lowest-frequency notes on a piano normally have wirx8kvf y*ru a ; (/o3nc5+rgvaryo 4ha8e wrapped around them?

What kind of waves do you think will tj)sz 1(ys ; bgdej7y.pravel down a horizontal metal rod if you strike its end (a) vertically from above and )j( 1szypjbys7e d;g .(b) horizontally parallel to its length?

Since the density of air decreases1jwz -ac w w((7y.8g qkbrwpvj (-fe1j with an increase in temperature, but the bulk modulus B is nearly independent of temperature, how would you expect th8jjj((w- cy bwpq 7 1f1a. ge-(kzwrvwe speed of sound waves in air to vary with temperature?

Give two reasons why circular water wax-mgoqe2b3j; ves decrease in amplitude as they travel away from the s oex;j2qbg 3m-ource.

Two linear waves have the same amplitude hw .+)gjbpcz2nbk 2g 45+pdhqand speed, and otherwise are identical, except one hpqh p2g gcb+.wzj )54kb2hd+nas half the wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between twoik(f1:io879gq fd(x zmno+qo sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocity do change). Explain why.91fm k foq gon8:+z(i7x(qdio

If a string is vibrating in three segments, are the/ju3z;.kv9 bbzp qg9tre any places you could touch it with a k/ b9pqgju; bz.zt k93vnife blade without disturbing the motion?

When a standing wave exists on a string, the vibrations op zq29tzf e.g.f incident and reflected waves cancel at the nodes. Does this z eq9.. 2zpftgmean that energy was destroyed? Explain.

If we knew that energy was being transmitted from one place to another, 7/p6pitl ibr:how might we determine whether the ei/ prpb7t 6i:lnergy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with6-:xfr odxf1 1elztpms +4 v*l amplitude 0.18 m, what is the total distance it travels in one 6 +t4vx1sm: pzlfrl x-o ef1*dperiod?    m

  An elastic cord is 65 cm long when a weight of 75xlsjl;h 3+.;xlw yk l: N hangs from it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” constanyl ks;llw3hl ;xj.:x+ t k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kgm 1cb (ekbd8:g0vy (yeacaff1/ug b16 driver gets into the driver’s seat. If the car goes over a bump, what will b1 cdu efb gb1cyy8 f v(/g60mae:b1ka(e the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cl dva3):a5h, p;zlzf zm when a 2.7-kg fish hangs from it. (a) What idzp 3hfa)a z:;l5l zv,s the 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 o- 8tqo4 ojfkbdmher)f w+.)(h f 0.60 kg is hung from it. Whdkh-orhe8fm .b4)t)ow qfj (+at is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x .pbtpkc) *4z/i06yb 1n 3r n zaxlrv2pof the mass in Fig. 11–2 at times t = 0,zi)nx b0l3/rpctny26z.1 pkr 4 vab* pt = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 sh ,h-z +k:ttizpider’s web. The web vibrates predominately with a frequency ofz:itthk+h,-z 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 dq7+mzr gq)8k vibrates with a frequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency isrz qm)kq+8d 7g 0.60 Hz. 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 anbdfsy2wu* -eo4hvafg) igk -5s- hs56 ampls5h-6 g ws2-ivfa hs)db oyug ekf5*4-itude 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 from equilibrium is the speed of a SHO hal0cs.u 45sx b9j3j2sxm1xi jzxf the maximum valjc5xj04z3ss u ji2m1 9sx bx.xue?$\approx$    A

A mass attached to the end .;h45+;epyfe u kcc ;gspv af0(o1ohl of a spring 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 verutei2tp17 c3mvy ,-nmbi 49d btical spring 0.315 m. If the spring is stretched an additional 0.130 m and released, how long does it take7cebytm1 ,- bni i39t2ud vp4m to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with spring stiffness cyhi7lzs 3 djt:j+8t/sonstant k = 280 jhztd8 7 si+yl/ sjt3: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 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 compr9 n 0akhmwq(bcncx0sf1, i p)4ess the spring of a toy popgun 0.200 m to “load q0ks9c,n(w4ix nbmp)1c f0h a” a 0.180-kg ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal5er.fnai2t(h w5 cmk 4, frictionless surface is attached to one end of a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the e (2cim54h wra 5fnt.kspring 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 = -u p px8sw5n6gep4s d*0.45cos6.4t where x is in meters and t is in seconds. Densu6s epp-d*g45p8wxtermine
(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 zqq,,3 ng*q.kqsh 7veis the energy of a SHO half KE and half PEqg7*,vn. , qkqzes h3q? ±    A

  If one vibration has 7.0 times the energy of a second, but their frequenn1*1zw0 rv9 si n:ruoicies and masses are the same, what is 01nu *zr1 n:vwiis9rothe ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light spring onc /o 7pvsc8nd i8vr*9n (ydg9uae every 0.65 s. v vod* 9ydunicp (ng/a8s879 r
(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 ouz ug3z/icy 0h/aw 0xbp;t5-, each with spring stiffness constant k (Fig. 11–49). What wi-h0; /wyb0p otazz5 x u/ugc3ill be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t wh b ktpjgr1973mtog n.c9 2mcs*ere x is in meters and t is in seconds cm tn r sbg*23moc9.ktg197pj. 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 of0a av.2ajuf q+ rqan;* 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 horizontal spring (k = 124 N/m) is9y*kom mxriz-;au 9 x) struck by a hammer, which gives the mass an initial speed of 29x- *rkmx9y zoium)a ;.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 sojbhuc37g*e 7pring stiffness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The massgu3e j7bc7 *oh passes through the equilibrium point (x=0) with positive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two springs, with spring stiffnes:otb f2u /*9c zceets)5p7uyk;bur:l s 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 attachedo z04an* gen3c 2e qw9sa.,jnb to a fixed horizontal spring whose spring stiffness c2.9nn3*qo jbesz 40n,gawa econstant 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 reaching his - .:okx .wmawplowest 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 bew am:ox.k-pw.low 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 vibratio 5;l3c bnsb;da1cxk9ons in 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 exactly one swing per.iobcwec)t ln,h7: ;h4uhb f 6 second? (That i7, bfh 6l e4c u;c.nitw:ohb)hs, one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on Mars, f+q+(;he tf7;w nooopjnzz8 4where the acceleration of gravity is about 0.37 thatz8 o+f;ofoth4pe+j7qnz ; (wn on Earth?    s

  What is the period of a sim.1tb8rq k-qi7mqy s 8fple 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,95lvql1fo u5/io5wkws);*agw tc dp- the pendulum bob has a mass of 365 grams, and it is released at an angle of wod 9k-f q */cgw1its5w5l)l; uavo5p12.0 $^{\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. l:c 7gppy3.ai9930 m. If the clock loses half a minute per day, how should you adjustppya :g.i7lc3 the length of the pendulum? shortened by    mm.

Derive a formula for the *4l/pzp rd5nmd vyg+ /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 released from2x 0e*el 1 mcqbuzc/o2 rest st*20qc m/b1eue2xzo l carting 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 -ougk,-r q 6gaboat every 3.0 s. He measures the distance between two crests to be 6.5 m. How fast are the waves traveling? u-gqk6o r,ag-   m/s

  A sound wave in air has a frequency of 262 Hz and travels with a speed of 34s/qj llycomz8) ;ph.83 m/s How far apart are the wave crests (compressions)?. /ypzj; 8 ohqmlc)8sl    m

  (a) AM radio signals have frequencies between 550 kz:r91r4zz tz ,r+eqbxn v(c 2iHz and 1600 kHz (kilohertz) and travel with a speed ocr2iz zxvtqzz+,r4nr(91 b e: f $ 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 lon:j7;ew:,.n-v(nna detzxwhx gitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elast0b/sggn0/-ilc8x llw7b wv/z(u(xgm ic modulus, but one is twice as dense as the other. In which rod wil 0ggzx(m0sb(wwu 7nl //xvilb/lg8- cl the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 s9jtip ai6h :;kg is stretched between two supports 28 m apart. If the tension in the cord is 150 N, how long will 6it:9ja;s phi it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to the top of a hill by a steel cable of length 620 mbk63wfm p61chl u ew7. 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 it took 16 s for the pulse to rhwmbp.k7 ul3 e6c61w feturn.
(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 i 3 ew3y4ob+ar (t(tfmbelow the surface of the sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s latoa+(3et4ymrbw3if (ter. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel ativxt2( t//f ue different speeds, and this difference helps in luite vt/f2/x (ocating the earthquake “epicenter” (where the disturbance took place).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced surface wave can be approximatdbcv xc4t2 /5sed by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture ob5/ctcd42sv x f 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 intensi/b 8myzmt++m)*mhiwi ties, and (b) the amplitudes, of an earthquake P wave passing through the Earth anh)/z++b timmiw y*mm8d detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth ie/ 1gbegv 2)rbs measured to be e /gbvgb)e1r2$ 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 frequq .+) e*wgd+ixsj3iamency travel through the same portion of the Earth, but one is carrying twice the energy. What is the ratio of the amplitudes of the two wave)igdea++ sq3i*jw .xm s?   

  Two waves traveling along a stretched string have the same frequency, but onq imypz.: rdm3+v7rn,e transports three times the power of the other. What is the ratio of the amplitudes of the two waves+ n:m.vrqry7 d3m,zpi ?   

  A bug on the surface of a pond is obsngu b*ung(u5m jnz h i.z5/89 aan8f.nerved to move up and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change? zza ( naufm.j/ *u8gnbig9nnu5nh8 5 .  

The two pulses shown in Fig.hb1ygy hb3 88u 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 strub g8813hby hying is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundamelsu t 31;okrsh 9phm+:ntal frequency, what are the frequencies of th9upk1 ;:h mh+ossl3 tre first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibras 4xxi*ty.7b m) yy t -qt6y5mc0f6jautes at 294 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 of the strint5y jxyyb .iamsf7u*x6-)mq0 4t6y t cg vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequency of qhj lga(r+-*k280 Hz. Name at least three other frequenc*q al j+(h-rkgies at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string istlm q2-0ik- wb 92m/s If the frequency of standing waves iskm0wit- -lb2q 475 Hz, how far apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string y 2coh:)il3l fe0,xl5cqqp.r are 280 Hz and 350 Hz, what is the fr25eflylr0 c olciqp ,:.h)q3xequency of the fundamental?    Hz

  A guitar string is 90 cm long andbqe y9i45 c;p 0bv/qmh;alsw3 has a mass of 3.6 g. The distance from the bridge to the support post is L = 62cm and the strin wq 4h;il3av c mb0y;qb5eps9/g 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 H6hu .r2k8;agjk 0 ;u:nor(9i zykzacqz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct tha29 ynz r8gi r.(0; oukk;6j:zuhqcka e frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibj9vhkw8cr ,so fkzf;(4pt7in z+4tv7rate 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 freque+47j4iw9z t(t vrnh7,k8;vc fsfzpk oncy? decreased by    %

  One end of a horizontal string is attached to a small-amplitude mechanic:x*z2r9+ln r2j ,trwsbf- cfkal 60-Hz vibrator. The st*-rk nw2r2frf bx9s+l cj: ,ztring’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 gtx* lyscl/ 4 .dtl;ew8/6vt eof the string may be adjusted 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 bld;e lte8c. s glwyvt4t/x6/ *etween 10 cm and 1.5 m?   

  When you slosh the w4v.d po)5jclwater back and forth in a tub at just the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. v.5o)cjp4dl wWhat is the speed of the water wave?    m/s

  An earthquake P wave traveh ,p qw-ck+92qfq f+-uybig 6yling at k.0 km/s strikes a boundary within the Earth between two kin f qqh6,cy2yk-i bq-f+p9+ug wds of material. If it approaches the boundary at an incident angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “shelf” where the vex)xw;pl+cgv 0locity changes from 2.8 m/s to 2.1 m/s If the incident wave cre cwl0;)xxp+ vgsts 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 h3(ftcxgh+o l,i - svi7its a layer of cold, dense air. If the sound wave hits the cg7(i csti 3vhlo fx-,+old 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 types of rock at ax qnn42ntdo lbh92w51 3n 91x h l2b2qtow4dnn58 $^{\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 di3y,d-gwm: s rdameter. According to the user’s manual, the dish has to be pointed in the direction of the satellm:rd -w3 gsy,dite, 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 velom fx5psoqsw)v 5t0;+s city 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approxim s0 tp;s+5qomfw)v5sx ately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness constant of 550 ax bfv0/ j0tqqf*2 /pskN/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 (approximately 5 mi/h). [Hint: Use co02q*pq0//x ab jvffstnservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m bjgt8* l e3wny0elow, which stretches the net 1.1 m. Assume that the net b ny3wl*ge 80tjehaves 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 th(8vn4c75lf(id 4f3k rt ssk obh-v:jb e end of a freely hanging spring. The mass then falls 33 cm before it stops and begins to rise. What is the frequency of the b s5l s hdbrf:4ck4nv(7t ki8-3fvoj(oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/1kgej 5rj7f b0s (Fig. 11–54), compressing the spring 5.0 m. (a) What is thegfb51rej k0 7j spring stiffness constant of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of coffee (diameter 8 cm) at just the right pace : d*n1 qciwk9uof about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over nd1w kuq:*c9ithe top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm frox3,fqal,d+(3f dkx aj6efs8 rm the center of a 33-rpm phonograph record have a wavelength of a3sk, e8 dl (+63rfqjxf ,axfd1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the e dj1* b)bf ,;d+ry03pub f:stz (igldjquation x=0.650cos7.40t where x is in meters and t in seconds. (dp j;srzifu b y*d,t:)+ljf gbd1b30 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 -y yg6p exee+w *wi3r(musg- x /r2l5sfrequency f. What is its frequency if it accelerates at 0.50g (a) upwary-w +rge632wmys(p5u-ige*xsxe /rld,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg wbks2vv 2 0;jtj8c)siman stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the raft vibrates for a whi8vv ;bki22t sjwcs0j)le.
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a musical instrument are tuned to play at 392 Hz (G) and 440 Hb b )f*eo(sclh,;j uw*z (A).f,(hbsj *l;*ueoc )w b
(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 downw1q;yok9wne lft9+ bzv7lz/ 5wvt0ye:+ je8 t 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 versus that in the lighter section, and (b) for the rvvnb f e 0:; w/ w +ot5t+y9zt9ylzklewqe8j71atio 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 ofo(bm e(q15uv m each prong moves 1.8 mm to either side of center. mbq v1(5em u(oCalculate
(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 m d,, jbnpml(e.gv (n-harmonic motion of frequency 1.5 cycles per second. What is the maximum amplitude wi jg,.p(( ln dv,m-enmbth 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 asabfui5q: zu* iaz 489ttached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such *zbf sau4: 59uaqi8 zia string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each oqf8w;x ,3+-mrz 5ik-wkrxka b ne-way swing takes 1.000 sm5 kki-3karf, w-rx+ qzbx w;8.
(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 direction or can swima+ut)q sw:g5vhim (j0,v :r1r bol1ang as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontal swings, and by what amv qwu amslviao0rrhg(,+mjt) 1:1 b:5ount? [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 tm) ;t,k c1cw;ua q5v4b0vrw6ek 7nctmass 123 g is stretched under a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at the o1t rcu7,b;t0cwae)t q c wk4kn;vv5m 6pposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spring with spring stiffness id py6q)i0jlz3e+/e ;hru. qhconstant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillationd;+zr eqi/6l hhi)y3p0q.eu js 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 thtw*mjjao -:vbga2uja 4+z7f 7 e junkyard. The steel crane cable is 22 m long and has a diameter of 6.4 m7zj -tg uav:+of4m2aaj7w jb *m. 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 j ;7 xc8c9bivmr49 dfrgives the dimensions 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, gi79j; v4c8mbfcd x9r riven that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz