Give some examples of everyday vibrating objects. Which exhibit SHM, ac:ad; rh6at/,q/vg hdt least apqt:hg/cd 6rhd/a a; v,proximately?

Is the acceleration of a simple harmonic oscillatobd;ibs+-w)zp 2 fpk 6z*dptw8r ever zero? If so, where?

Explain why the motion of a piston in an automobile engine is approxnhoj8 1 mqs5n,imately simple harmon1n5,h m8osq jnic.

Real springs have mass. Will thwa4 z:.a* 3:lvpvq/ddzt/;tkoy osh.e true period and frequency be larger or smaller than given by the equations for ..akv;3o/:atpszqdhw: *t yv l4zo /da mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of af;jkga.vvrrhd( +szy-2 ,e+q simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical sprin53neg /,n ))xgusc8grgor4 lp,vd(cd g scale, and then is released. Describe the scale readingu)ng8g5sve,ncd(,pogc r3drx /)4lg as a function of time.

If a pendulum clock is accurate at sea level, will it gain or lose time 3o5qkqb2f4a +b( +b4egkq bp ewhen taken to high altitude? Wepb kq(q okb5g3b+q e4b+4 fa2hy?

A tire swing hanging from a branch reac/tb 9y;c7eqnaam(es; hes nearly to the ground (Fig. 11–48). How could you estimate the height of the branch using only a stoaacebs7;(;my n /te9qpwatch?

Why can you make water slosh back and forth in a pa2 rz;x*:vdn tpn only if you shake the pan at a*;rn2v p dxzt: certain frequency?

Give several everyday k ij mm-cx s7t,)o;ki,lybdf6v )b*2xexamples of resonance.

Is a rattle in a car ever a resonp8zb2 z+m y0,hvwrs 6gance phenomenon? Explain.

Is the frequency of a simpzp16y4yg18bb fd )v*v(i s wxcle periodic wave equal to the frequency of its source? Why or why no)sy*i1 8pgcvw bbdy4f1x z 6v(t?

Explain the differennr uk b6h6i sbr6y90 743jir gojxulx584djq)ce between the speed of a transverse wave traveling down a cord and thjn8lruxi x9jqjh6bir b 4yr603d u 7o6 kgs45)e speed of a tiny piece of the cord.

Why do the strings used for the lowest-frequency notes on iwr agi0jn/; 7a piano normally have wire wrapp /0a7r igniwj;ed around them?

What kind of waves do you think wilc4 -fwy7wca,n0 sz+9gp qrz92 xndl. el travel down a horizontal metal rod if you strike its end (a) vertically from above and (b) horizontally parw.92x a -epgq7 fdnyw4sz9+r,cn0z lcallel to its length?

Since the density of air decreases with a u+f gqsrb8(ae:u1 vi/n increase in temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of sound wa gbrs/1f+ u(uqavie8: ves in air to vary with temperature?

Give two reasons why circular water waves decrease in ampli 7hicz7ad-(diyb49wb tude as they travel away fromb4-bhca7 w dzyi7i9d ( the source.

Two linear waves have the same amplitude and speed, and otherwise are identicqwgj fqg*/1y*sql+;val, except one has half the wavelength of the other. Which transmits more energy? By what factor?; +*sgqlwqv/1*gjf yq

When a sinusoidal wave crosses the boundary between two sect nj dl/z c6:beaqe( j(i uqbvttx;5-;-ions of cord as in Fig. 11–33, the frequency does not change (althoqj ecx5ql6n-;td(/;u b-b ez ai:tjv(ugh the wavelength and velocity do change). Explain why.

If a string is vibrating in three se 6nd (jjl)jlg(gments, are there any places you could touch it with a knife blan j(j()jl6l dgde without disturbing the motion?

When a standing wave exists on a string, the vibrations of incik ih*6kq7*wsedc n*i+j(mv.a+c8l /z)aihcj dent and reflected waves cancel ac*h 7ia/ ) a6msl.vhc+ keq8n(z +*jwkic*jid t the nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being transmitted fro8odqp3 hvm,, )bfazp, m one place to another, how might we determine whether the energy was being carried by particles (material bod)qop,z,avh 3fmdp,b8 ies) or by waves?

  If a particle undergby:nfne0eygk./1 w5ko* f6mluy83dw oes SHM with amplitude 0.18 m, what is the total distance it t f*lgm o6 :3fuynby/ekw5wke0y 1d 8n.ravels in one period?    m

  An elastic cord is 65 cx/7abog1c:3 fglgbo-m long when a weight of 75 N hangs from it but is 85 cm long when a weight of 180 N hangs from 3xl7o-oacb1 fgb/g g:it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg driver gets into thga;4nv5o89ce9fk a je e dfa cgo4a95k e98en jv;river’s seat. If the car goes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale kzv( :+ fn ;:qub x:h+dnkfmj2stretches 3.6 cm when a 2.7-kg fish hangs from it. (a) What is the spring stiffness czf+n::;+v : hxnkj(k2ufdqmbonstant $\approx$    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 cc 8us4mrk, m5k1a.mpa mass of 0.60 kg is hung from it. What is its frequency im5ms4c 1 apcrm.8 k,kuf only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of theal v,-eygc1 .rlt/,wf mass in Fig. 11–2 at times t = 0f g -1wry,/cv l,el.at,t = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

  A small fly of mass 0.25 g is caught in a spider’s we2dh y j/yd2t yinn501jb. The web vibrates predominatelyn/d2ht ny20 jiyydj15 with a frequency of 4.0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a spring vibrates with a(i1v6kn** nylm+ ilhs frequency of 0.88 Hz. When an additional 680-g mass isyn6 *i*lhv1 sml(i+ kn 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 3.0 times per sech7oj*r4astc2b8y1qz dubfp8q 1 t76oond with an amplitude ofporq1s4c 78z 7 b8t62d1jhu * fqatoby 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 half the maximuk+i d8gyev;9 pm valu9v8+dekgy; ipe?$\approx$    A

A mass attached to the end of a spring isf*4j6lm.(e lye 6tb ul 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 0.31oj8 pf5 ucoc7/kq k6;x5 m. If the spring is stretched an adq5kjc6xoop f7c/8k;uditional 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 attache5 z14vne c bfv5kh/ ytfj.,h p,6ype5ud to a spring with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is 6cb/kf .55yjt,uhf45,e1 ypzhvpev nmoving with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compress the spring of a toy popgunvczj7nqvz*k mp3vo501 t q18r 0.200 m to “load” a 0.180-kg ball. With what speed will the bavn5 7q 8z3*0v omjrzc1qvkp1tll leave the gun?    m/s

  A mass sitting on a horizontal, fr ptvs d2l3+t:aictionless 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 spring by 0.12 m. If the mass is released from rest with the spring compressed, the mass experiences a maximum acceleration of 1d2 t+ as3:vplt5 $m/s^2$ 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 = 0.45cos6.4t where st:l+p4sl a,xx is in meters and txll ,psa4: ts+ is in seconds. Determine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equi j os0m12a*nqzlibrium is the energy of a SHO half KE and half PE? ± * zo1n0s m2jqa   A

  If one vibration has 7.0 times the energy (:wr(qad gla+of a second, but their frequencies and masses are the same, what g: q(war(dl+a is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light spring oncf j49hddax24l brwtxmj;(/:f 2r aka/e every 0m4xa;haj(4ft 2 jr lfrd9/ 2b x:/wkda.65 s.
(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;zo /t;ecmqffp h8s15 vertical springs, each with spring stiffness constanteso18zh ;;f ctm/fp5 q k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to thb(x:+b1cfz5p )fq ibqe equation x = 0.38sin6.5t where x is in meters andqxqic+z) 1b5:bbffp( t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows two examples of SHM, labeled A and B. For each, whx4vssms+/w ,z at 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 = 124mqnegw,w4a;)er8 1x-m x )qce N/m) is struck by a hammer, which gives the mass an initial spee4n aw8qeqerx ,gxe)m ;m-1c)wd 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 stiffneirt 0 z-wi8d6waw7p y8ss 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 velocw68 y7pr- awzt08iidwity 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 coah0 9ct9q -5ysnmau )unstants $k_1$ 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 s2 wmhayp.e;0nwb-cx6pring whose am ncxh.wwe;p60 2-yb spring stiffness constant is $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with mass 65.0 kg g -.lf+vp9qou jumps from a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eighulfq- + vog9.pt more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrations in exactly 6 5tl64 +kiezeb0 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to hmhkhb2 299v ws 8id7nmake exactly one swing per second? (That is, one complete vb8 m7hw9nh hds229 vikibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its p7sis rj0tva dk1a lma1z, 2h(8eriod on Mars, where the acceleration of gravity is about 0.37 that on Eart1( 27s ,d saakz 8vthaij0rm1lh?    s

  What is the period of a simple penduluxahrp wcnc)) *pw*:0om 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simpl 9.cvd: 7i/d.mi7undu(mbv 1ex m7irje pendulum is 0.760 m, the pendulum bob has a mass of 365 grams, and it is released at an angle7e:/dc7mdmrx j.nvv 9dm7bi(iu u .1i 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 0.9930 m. If the clock losdw;jgpmb)y2bx ,hy+ ,es half a minute per day, how should you adjust the length of )m hpd,w;yx b+y j2g,bthe pendulum? shortened by    mm.

Derive a formula for the *+y.pe rf0/7j q/t uttzn,bwkmaximum 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 fralowzol(g ,t 7:k3w+ aom rest startingw(wgo3atz:a, +7l l ok 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 thz :ykgq (9jn2uat wave crests pass the bow of his anchored boat every 3.0 s. He measures the distance between two crests to be 6.5 m.jy9u :2(kn zgq How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with a speed of)u - x1;hdn7,jrrb teo 343 m/s How far apart are t)n ,;xhd7 1e jorb-urthe wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and st,;j 0qq je6j1600 kHz (kilohertz) and travel with a speed of qjt js e6;j0,q$ 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 loy vwc5rtjzj r: 2ri;y/2(-c dnngitudinal 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 de :bn7ecdf()dn k .h;danse as the other. In which rod will fn(h)c;e dkb d7n da.:the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two ogr;eali:31 i w 1zah6+o9stbsupports 28 m apart. If the tension in the cord is 150 N, how long will it take a pulse to trav w+ 3taaz19;:r e ob6l1hiisogel from one support to the other?    s

  A ski gondola is connected to the top of a hill by a steel cable of ledjfm0vufla oo +o44d ;1k)5xdngth 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and sends a wave pulse along the cable. It is observed that it took 16da0 of)xomvk j1ol445+u ;ddf 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 sidee3/l omkh vmlb cp3,5) of his ship just below the surface of the sea. He hears the echo of the wave reflected from the ocean floor c5 3loep mm3)hlk/,bvdirectly 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 differencwd8yi om 0b)gt( (wx-5stj6lwe helps in locating the earthquake “epicentely- w 0ji8t m(to(x dws)b56gwr” (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 approximated by a sinusoidalch x t4m,rkkocut1119 transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin tox tt1u1cm4ckkhr o,19 leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplit brl8*h xktw./p5dxz(i k23ypudes, of an earthquake P wave passing through the Earth and detected at two points 10 km and 20 km from the s*hipl ( d35kt.xrzkw y2xb/p8ource?(a)    (b)   

  The intensity of an earthquake wave pas d;gvr +/c/mpu1.csne0htb)0edb9 iwsing through the Earth is measured to be bv+9hcd;d1/ pg rci/mnut0e 0 webs. )$ 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 t)qya 6sb (pg1wx .jkf)u (avh-cldpq0 : w+ip)ravel through the same portion of the Earth, but one is cb)w.as6qdc0g-xalf :()jvw(+pyh q ikup)p1 arrying twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched strin*: wfzx 81adwbg have the same frequency, but one transports three times the power of the other. What is the b*wf awx:z 18dratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is ob vf4hzo(..czc served to move up and down a total vertical distance of 6.0 cm, from tf(czc vzoh ..4he lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown ,q27bdc +jf ;2 goow-cr*msxrin Fig. 11–52 are moving toward each other. (a) Sketch the shape of the string ,oro2*dsb j w c+qf-gc2r7xm;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 string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fundf6 cj3/ta wn zgb)( alic+t6i5 po7bl/amental frequency, what are the frequencies of the first f l/ ai6jlwb 36iof/ntg+b7pz)(5acct our harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what frequency will it v 4r.o . z8w iyp0jr:3bpo+ryhiibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of the string vibrates as ybrrryio+j0: i o3z4w.. p 8pha standing wave.)    Hz

  A particular string resonates in four g okx0 ixiu;ouj :3j v)(:dgd5loops at a frequency of 280 Hz. Name at least three other frequencieujo(u:d :503vjd) g iki;xog xs 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 2 cw2/br iz4,ybm0r wfthe frequency of standing waves is 475 Hz, how2i,zcrwb 2rmb 0w4/yf far apart are two adjacent nodes?   m

  If two successive overtones of a vibrcz owdu l6+x fnh t1/oc72(4ojating string are 280 Hz and 350 Hz, what is the frequency of thhxd4lw (z /f couct67j2 o+1noe fundamental?    Hz

  A guitar string is 90 cm long and has a mascxi3gpj w:rw b0b9 37qs of 3.6 g. The distance from the bridge to the support post is L = 62cm and the string is under a t:337 rqixb bw0c gpj9wension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is suppose vvl89e2 qs4or* eh+pgd to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to corr4p 9v8greh eq+svlo2 *ect the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 2005pcy*ftz2.cckdt s( ;),n xz a Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correfx cc tzyas ;5c .t)kn*z2d,p(ct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-amplitude mechaniczmd0 0wm-tf*/dwxn8 f al 60-Hz vibrator. The string’s man /w8w0m0tzfd d*m-xfss per unit length is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of the string may be adjusted by moving 2 rl( t*rv s3cm..tkh t/yunv1the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may bm23(.thruknvt 1vlr *.t/s cye achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at just the right frequeg k qu,jr.:c7gncy, 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. Wh7.qk :jrgc g,uat is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundary within the Earth scb56ia-, cu gbetween two kinds of material. If it approaches cu,g c6a -5sibthe 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 the4 qed kgz;i20h velocity changes from 2.8 m/s to 2.1 m/s If the incident wavigzqh204 k ed;e 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 col0km0m/ 8 liq5 ik9pkt:uu -r(e ueemw2d, dense air. If the sound wave hits the cold air inm5k m:ewp0ukkurtii/e 0-2um 8 l(qe9terface 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 ron1ac:k+p )zi vck at a 38 1paz nv: +kic)$^{\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 . c3tkq4(+vvmlwjm;w for,, hm in diameter. According to the user’s manual, the dish has to be pointed j rhvo,klvc,+;w .f(t4qmw3m 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 uyc ;quyes etc ,jw0.y0 9bu0ci6kn*./h travels 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 safety? (In the ayu0;enk0ybw .6 0 , *.cuctj c9usyqeibsence 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 7y ,trhf46a rhof 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 (ap ht6a,rrf h4y7proximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire r) g,/l/kunliowlu2 gyxr.6 e;c/rv;net 18 m below, which stretches the net 1.1 m. A/ ;n;rulr wicu.2)g/ ye,x6r o/lgkvlssume 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 hanging spring. rj,8rtycrmh /tj 5rb.kd8u 66The mass then falls 33 cm befor68tj,.mcy 5hr jrub/d8r6t rke 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 heuo** 1/vonosz( 8jwm/s (Fig. 11–54), compressing the spwjohesn*1( o* v8u oz/ring 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 coffee (diameter 8 cm) at just the righjn6cqdj:g 8r3 t pace of about 1 step per second, the coffee sloshes more and more until eventually it sta6qdjn:crj g 38rts to spill over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain grovt9kxi i .v vz-2r -:9gz e63rj;8rvz2n ihvyoove 10.8 cm from the center of a 33-rpm phonograph record have a wavelength of 1.70zogv ihivzx :v96rv.jny 8v i;tez3-rr -k292 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 where x is *j0 td+ )l5 not5jdxuz(x/ zpwin mew)5xdunlt*(z5j pdotj / 0 +xzters 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 ikc4 3( bdx c;a4qj,iwnf it accelerates at 0.50g (a) upward,4 (ciw,;3ck4qbj ndxa    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on the raft7*5d jn) k0h iw i88l3tcxq m4cqjw+ra, it sinks 4.0 cm deeper into theahcj)tkdx 7 jw*l iwqr8 5cqn8304im + 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 are tun)c jty0p7):* o z ys:v.copokved to play at 392 Hz (G) and 440 Hz (Ay *opkzjoc0) ps7 vvo:c):y.t ).
(a) What are the frequencies of the first two overtones for each string? G : $f_2$=    Hz $f_3$=    Hz A : $f_2$=    Hz $f_3$=    Hz
(b) If the two strings have the same length and are under the same tension, what is the ratio of their masses ($m_{\mathrm{G}}/m_{\mathrm{A}}$)   
(c) If the strings instead have the same mass per unit length and are under the same tension, what is the ratio of their lengths($L_{\mathrm{G}}/L_{\mathrm{A}}$)   
(d) If their masses and lengths are the same, what must be the ratio of the tensions in the two strings?   

Consider a sine wave traveling down the stretched tw ; tfpg :vy8rz8r+d;njo-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) fornrg fdyvt88 :z+;p;j r 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 pron a)qm0 bee1fgya)iszy(d( m9,g moves 1.8 mm to e1y dbfa(sg,aey m)9m i(zq0e)ither side of center. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simple harmonic motion of f0tm:u3h39z ii* fxvriekn2d e))me. grequency 1.5 cycles per second. What is the maxim.: f iz9nmdkxh r)0v* it)uee g2iem33um 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 attached to h0ed.(zac-ivrw; g mrrb s78sj3(b( ha 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 fixed and the other free. 0hw7z3hj( (erib8 (a rvsr.;g- bcd ms

  A “seconds” pendulum has a period of exactly 2.000 s — each one-way swinn4i6n zht0pj 4 qg4iy zv9z1yboe x23)g takes 1.000 s. e2391i6z)y np40v4zb xjtq4gzh y in o
(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 the1 8c ws l/uuzjt3(prwq8woe+. vertical direction or can swing as a pendulum of small amp8 (3 ocrwj.pu wz1 qw8ls/tue+litude, 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 N. A pulsebxvc-- a32x1pfkc*v h is generated at one end, andc3f1px cv 2x- vak*b-h 20.0 ms later a second pulse is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceil1d xav.pbex:,,u1 z rqing by a spring with spring stiffness constant k. A penny of mass m is placed on td.urqe z1pba,: v1x, xop 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 atvof03l 7b5va*m f)5+rgg laxflx cl o+-t/ tu0 the junkyard. The steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at 0)+3fbm7-t+5 rllx*ao0 v offult v lc/ xa5ggthe end of the cable. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (which also gives the t3emo iff4l( 7 p2urya 0)sn,tdimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrate. In3tfpe ar,()o47 i0fum2 sl nyt 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