Give some examples of everyday vibrating objects. Which exhibit Sz25 wkud+xy d/HM, at least approximatdy+d5uxkw2/ z ely?

Is the acceleration of a simple harmonic oscillator ever zero? Ixk kpx.t mrs jm.y;pr y55z787f so, where?

Explain why the motion of a piston in an automobile enginj/*vgexw*p h/q3bi b 4e is approximately simple hewbvg b*3ji/4x*q p/ harmonic.

Real springs have mass. Will the true period and frequency be larger orvfkdap94f,n28p5w 9r:bay xjpp4 az f.w7p ) g smaller than given dybxj9anf4pg rzfa2v .p k9)f7 apwp8p4:,w5 by the equations for a mass oscillating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a si;*pxufz9mybf c( 3on ;ur x4t*mple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scale, and v1 y3jvogls:wzxp- q :h2:vt3gz8 x a(then is released. Desclgzp qv: x xg:-z38s2wj1to h:v v3y(aribe the scale reading as a function of time.

If a pendulum clock is accurate at sea level, wic /zbj+y rgfilbg92. w*yg1:qll it gain or lose time when taken to high a2b1j ./czy*l9i:f rg byggq +wltitude? Why?

A tire swing hanging frwl y: n)7vh 7xltx yl6j3axo-5om a branch reaches nearly to the ground (Fig. 11–48). How)nlxl7txy73hojxvyw a l 65:- could you estimate the height of the branch using only a stopwatch?

Why can you make water slosh back and forth in kup)io)3z*ob6avh.e4o7j5t s 1pb gba pan only if you shake the pan at a certae t*juo.ao6igb ph3ksb z)ovbp4175 )in frequency?

Give several everyday examples idedg /bwj*4rp2)v4p of resonance.

Is a rattle in a car ever a resonance phenomenon? Eq/b s3amzquk op 9j6u8xf;+jg45dyq 6xplain.

Is the frequency of a simple periodic wave eq ( .sszlo u x8xi4mr4uvhd-h07ual to the frequency of its source? Why or whyurm7 x0 zx vs4du.oh48hs-(li not?

Explain the difference between the speed of a transverse wave tra8 eqa/( fecralfw 607n4rt3ih veling down a cord and the s0wafr h7cq(e 3ftn84r /liae6peed of a tiny piece of the cord.

Why do the strings used for the lowest-frequency notes on a piano normally havew 5hj:4)d bjqsqcir.9 wir:d j5riq4sj 9cw) q.hbe wrapped around them?

What kind of waves do you thinj89mt iz bqpxkh4zj49z jo25. k will travel down a horizontal metal rod if you strike its end (a) vertically from above and (b) horizontally parallel to its length?z8zzp4tj495q jm oki2b9x j.h

Since the density of airnwg)k -xc8jg5zsw5w 6 decreases with an increase in temperature, but the bulk modulus B is nearly independent of temperature, how would you expect the speed of soundsn6gk58x-cwz gj 5) ww waves in air to vary with temperature?

Give two reasons why circular water waves de/2 euux6.bu hmj3lg9,y-6 dno v2mhtccrease in amplitude as they travel away fromohvuu2tmn/lu3 de6 -xh 2mc, y9.jb g6 the source.

Two linear waves have thefdo* u;7e;. 5 vyuxvrr same amplitude and speed, and otherwise are identical, except one has half the wavelength of the other. Whvu; y dfv5eux ;rro.*7ich transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between two2-l86yxtq h * svezxk6 sections of cord as in Fig. 11–33, the frequency does not change (although the waveleng62xhk*s eqzyxl6 8v t-th and velocity do change). Explain why.

If a string is vibrating in three segmenbxul4/ot8 :s,vmhyj,2 jyw2 nts, are there any places you could touch it with a knife blade without disturbing the motio4jtw :, o2s2huvj,nlx8byym/n?

When a standing wave exists on a string, the vibrations of incident and relhyy t:8 ga:hd*w1/o0v v1i9o e jx2xmflected waves cancel at the nodes. Does this mean that energy was destroyed? y t91m *v2e l/wjyxxihdo0a8voh:g1: Explain.

If we knew that energy was being transmitted from one place to another, how might:d r+4cnnn 1e4.snypt we determine whether the energy was being carried by particles (material bodies) or by ndt.sn4ne 4 1:p+rc nywaves?

  If a particle undergoes SHM with amplitzl1w :oy.ia,lvf rb: )u-gj7wude 0.18 m, what is the total distance it travels f-vo:li,gj1 :wyub7)zrw a. l in one period?    m

  An elastic cord is 65 cm long f kar/a/ycw9 jt7v5 r1pv1hp 9when a weight of 75 N hangs from it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” constant k of this elastrjhkra wv 9fyap//p7 c11t5v 9ic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg driver gets int-bwzjna+o fklkcc4/lj5 9i ;+o the driver’s seat. If the car/jnc;4lco+l+k-i5a9 jwb fk z goes over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish h-nz+0,t n npd8kjg 2cdangs from it. (a) What is the spring stif+d0gn knd zn-c p8jt2,fness 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 .l6( 7rzn)n,zggjuz;*e xpnrneh6dok 3 s0 b/ when a mass of 0.60 kg is hung from it.6hulz )ns/ j0e.bo7r*nxn g , de(r3g n;zzk6p What is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicatiwh;v nhn4yea 4o5/2lk ng the position x of the mass in Fig. 11–2 at times t = o54ew42an /;h h lynvk0,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 we)4xa0ua te0n u 5r:ntdb. The web vibrates predominately with rt 0a5edu)nnu4:ax 0ta 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/;rj+nw r; gf3;hev tqr/ vmq4 with a frequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 Hz. Whv rr;jwtfq;nrmv3 eh4/ gq;+/ at is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per second withuf7o3zxpe.r8 1ank dsy,- -qf an amplitude of 0.13 m. Detq3u.fxoa1-zn 7 eysfk,pr-d8ermine
(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 maxi*e mmce/q:9v0yg3 n xqmum value?mg9:0xeym*cq/e 3 qn v$\approx$    A

A mass attached to the*u qxt w.2q1df end 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 vertical spring 0.315 m. If the spring isl o2adpiqqg*p a5 (7-p stretched an additional 0.130 m and released, how long does it take to reach the (new) equilibri(ippoq75g d -*2la aqpum position again?    s

  An object with mass 3.0 kg is attached to a spr(m88nr 9cybj-hk ku3iing with spring stiffness constant k uhn rj3b8i -kmk9y (c8= 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is moving with a speed 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 spr2mhkp4j umd;9rc86a0u k.c jding of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will the .j mu 48ajdm0h9;p6uckr2 ckd ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to *gs ;yk;xn eo cm-tq76one 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 a oqecmx;-*sg 7;yktn6cceleration 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 ; cz+yi4o*oan gusrn 04e9;s dthe equation x = 0.45cos6.4t where x is in meters and t is in secon c44gd;y;auosne+*n rsz 09i ods. 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 froc-q -guq+c *4hwvnd1i m equilibrium is the energy of a SHO half KE and half PE? u1c hd-* gcwnqi-4qv+ ±    A

  If one vibration has 7.0 times the energy of a secs t;zy089oax wond, but their frequencies and ma9 sy ta;0w8zoxsses are the same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates frhdcp bmr1 32+eom a vertically hanging light spring once every 0.2dbpc3m +r1he65 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 p bt*bf3hph hk65d3gf0arallel vertical springs, each fb53hhdp3g ht6kb0 * fwith spring stiffness constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = dz:l cd 1 sped3oe;)/g0.38sin6.5t where x is in meters ope)d 3 1;d :gczsed/land 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, label f6w:fui4itp6ed 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 =i2l c)j)3j ahpoq v53p 124 N/m) is struck by a hammer, which gives the mass an initial spe 32cpva joj i)hq35)lped 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 stif3.57/ bpdfi3zhkc to.oc nwm-fness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. Thez/wbf5.ikchtd7m.-o 33o pnc mass 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 connecte h2wqtch (usi1 .s.k)od to two springs, with spring stiffness constants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes a 0.600-kg block attached to a fixed horizontal sph+1n: k2x2df-l jm hqdring whose spring snh l1fj2xdk qm2 :dh+-tiffness 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 jumpvxw.j2ae0pl:a, yv jof0 d;7ds from a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant a a7pj jdxvd. 0l;f0: ,2wyoeavnd 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 vibrationql 2a0ds*p; xj1ax( nis 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 mak56zs) b drmbxc(9nsh6rb b,p7o.evx5 e exactly one swing per second? (That is, one complete vibration take,o6zpbc9)msx.5nbrv 76b( drs5xebh s exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its perip ac1f.6x aq rthy+3s9od on Mars, where the acceleration of gravity is about 0.37 that on Earth?c+a.f x6a 31yph qrts9    s

  What is the period of a sj8ef6qvg6b0 0,zhn xyimple 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 h.x7h,1jcigux9x z8d was a mass of 365 grams, and it is released at an a 9g1 wj.cx78iuhd,zxxngle 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 ) /bly 9jq e,po1jpp;u0.9930 m. If the clock loses half a minute per day, b; 19)/ppqylju,ejo p how should you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the max dcc5vdgqf9s e/bu*c7-(g lo9imum 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. Atq 93; yg7yqr3qi (ihyn it is released from rest starting at an angle of 73iyrqg( 39i;yqhyn q 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 boat ev 9nymdcx, 8+yeery 3.0 s. He measures the distance between two crests to b9m+ dyye8 cxn,e 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262hwd :.t9h9v: 5ug dy jdl;maeor/8:ax Hz and travels with a speed of 343 m/s How far apart are the wave crests (comprevh9oy9hxuat /;j 5 8: ae:dwrdl:md.g ssions)?    m

  (a) AM radio signals have frequencies between 550 kHz a o ;c bdw.)qsbm2tzwu8.e1 1wund 1600 kHz (kilohertz) and travel zd; su1 e mt)w.b.u18w ow2cqbwith a speed of $ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

  Calculate the speed of longitudi 2,p45c)krly jog 0 w/v,ek wr86rghmrnal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic xd2 e6.oh6+rauxkw m 9modulus, but one is twice as dense as the other. In which rod will the speed of longitudinal waves be greater, and by dk9e .+ a6xmorhux26wwhat factor?   

  A cord of mass 0.65 kg is stretched betweti7 j e7+r-vwn5k9xheen two supports 28 m apart. If the tension in the cord is 150 N, h+h9w7erk-tnj vi7x 5e ow long will 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 ley ql1 + *zoa3kxyhr-v;ngth 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the t v; a-zlxrh+y3k1y* qoerminal and sends a wave pulse along the cable. It is observed that it took 16 s for the pulse to return.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

  A sailor strikes the side of h0 7azagefk+vqb)2 qs0is ship just below the surface of the sea. He hears the echo of the wave ref f0 gqk easbzq7va02)+lected from the ocean floor directly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake trgp2)erbpl89 e-gesq1a rh4;oavel at different speeds, and this difference helps in locating the earthquake “epicenter” (where thh q8se4l pera 1e p2;rg9go-b)e 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 sini25r6o*yrf( x(-d o t5v gpibbusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequevd(r- r56tf i 2oyobx*(bip5gncies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities f2u;n ff;u5iu, and (b) the amplitudes, of an earthquake P wave passing through the Earth and detected at two points 105nfuuff 2i u;; km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is measurext,4r: etkqe,odxk2,- 4 lfwed to be :,okqx l-ftx e2, 4 ,tedwe4rk$ 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 throug+oo88 h(pg rx* oad/fbh the same portion of the Earth, but one is carrying twice the energy. What is the ratio of the amploo88g/dr*h o(bpaf+xitudes of the two waves?   

  Two waves traveling along a stretched string have tnn ;j+ .jeg8s7yjv, uwhe same frequency, but one transports three times the power of the other. What is the ratio of the amplitudes of the two waves.wn7 s njeu;8jg,j+y v?   

  A bug on the surface of a phg)g3 ppcy -a1ond is observed to move up and down a total vertical distance of 6.0 cm, from the lowest to the3ga1g- )p cyhp 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 shownurp z.ehx2s; : cfrr// in Fig. 11–52 are moving toward each other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight. What crh2:sefrxur /p.; /zhas happened to the energy at this moment?

  If a violin string v89dfsqv9xk8 ,c8 ki ajibrates at 440 Hz as its fundamental frequency, what are the frequencies of the first four haricvf 98 jakk898qs x,dmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfi-ry-o-l) zeyd ngered. At what frequency will it vibrate if it is fingered on--y d )oy-zrele-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 at a frequency ofizk99 r nnmy 2hz4d0q t5y9zcw;p1 ts9 280 Hz. Name at least three other frequencies at which it wiq 9 51n4pdwm r0;9i9zzts zhtn 2c9yykll resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the frejv3uxsbel;rx ;-z7s;zdf u6xt*72z nquency of standing waves is 475 Hz, how far apart aref7 e;lszt ;;3zv7*rs d-uz6ubxjxx 2n two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 350 Hz, what2axel+( ky4o0e av31hkqx kk7 is the frequency of the fundamx h437 k1oekx+kyevaalk02 q (ental?    Hz

  A guitar string is 90 cm long and has m ;f m6.nv8o 03tzwdtoa mass of 3.6 g. The distance from the bridge to the support post is L = 62cm and the string is under a tension of 520 N. 3oowt.m0 6 mfd8zt;nv 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 mea -1s:rpq m:tgtsured to vibrate at 205 Hz. By what percent should the tension in the string be changed to co gptsr:qt m1:-rrect the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibr82f0l8wnq h+rhb bry7 nreb-*ate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent sbb er2 qnh 7yhf8+b-w*n r8rl0hould the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attnlup2 x++4ja tached to a small-amplitude mechanical 60-Hz vibrator. Thetjl4u++p2x na string’s mass per unit length is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of the strinc 1 sd-/:bhtvjg may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave pattev-:bsj/t hcd 1rns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tubw6za s /yn3ys10hto*a at just the right frequency, the water altesy/3t0 s a1wnhaz6o *yrnately 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. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s sb 8mfr f6n2frdgva8 *7trikes a boundary within the Earth between two kinds of material. If it approaches the boundary at aa6 d *2gfr nfbm88vfr7n 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” wher az3s6(+eruauy 4co,v5fz m:be the velocity changes from 2.8 m/s to 2.1 m/s If tbe6maau o:f( cz534uyv sr,+ zhe incident wave 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 w/ vg24sxml,+i3zxjdva6*js hhen it hits a layer of cold, dense air. If the sound j jsvh+ ms2/xxi zvlg6 ,34*adwave 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 st np.p) 1l3vvdfrikes a boundary between two types of rock at a pvfndv 1)3l.p 38 $^{\circ} $ angle. As the wave crosses the boundary, the specific gravity of the rock changes from 3.6 to 2.8. Assuming that the elastic modulus is the same for both types of rock, determine the angle of refraction.    $^{\circ} $

  A satellite dish is about tyw12ibmfe 037uni7n .kvw 8n 0.5 m in diameter. According to the user’s manual, the dish has to be pointed in the direction of the satellite, but an error of aboivw7ik 8m tbew.3yunn7 n12f0ut 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 across the Pacific3hdz j nvqv/:0 Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted to the hnv/jz :dq03v shore to see stranded fishes and boats.)    min

  An energy-absorbing c) e m,axqzf/j2ar bumper has a spring stiffness constant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 15ef/jaz )qm2,x00 kg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire akj( o57+:mp c tpoqv;net 18 m below, which stretches the net 1.1 m. Assume that the net behaves like a sjc+o;p (omv5tqap 7 k:imple 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 onf:;yb8 w j k)20gdc7zyl o;ysa the 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 oscillations akl z ;;)dcjfbg0y27yoy8:w ?    Hz

  A 950-kg car strikes a huge spring a-a6nw l;sqc4.( ulp xlt a speed of 22 m/s (Fig. 11–54), compressing the spring 5.l -sqn l(u6pw4.acx;l 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 rig0 jdi2z8o( ioa ddt0a3ht pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Ed od(ad 00iz3 oji8t2astimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from dk1jdrc2n pc 5,: sb8xthe center of a 33-rpm phonograph record have a wavelength of 1.70 mmc dx5p,b :j2rs1d8nkc . What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7rz)j:ln p6tsgchag g ;0+)(zf .40t where x is in meters and t in seconds. Determine gp z)g6gs;n:0hjzr f)ta+c(l
(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 freq oifqv9e 159 us5swb/*eefv /ruency if it accelerates at 0.50g ( ib/955sv1w* sq eurvf/efeo9a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. Wglv7 5hk03 8f1ecuyzohen a 75-kg man stands on the raft, it sinks 4.0 cm deepz0 8hl uyoe5gfk3 vc17er 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 instrument are tunev,db9u+v7bvq r7y hs y,he4n;h 50zstd to play at 392 Hz (G) and 440 Hz (Avq5evy+z;u,sr hv,t s 7b7d90hyhnb4).
(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 stretc0mhqi+6kj;j q a17q pjhed 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 thatj;a1h60 q7k+mq pqjji in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and th 16tjfz2bz m8h *cb/xte tip of each prong moves 1.8 mm to either side of center./tcxjm 1zf bz*t 682bh 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 simples:)xtd4- e peq harmonic motion of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board cansxd )-ee4tq p: 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 attache*elbl1* mbm mc) s)o5dd to a ring that can slide without friction on a vl ommlm))*sb 1be *5dcertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each oncl-()f;gma ,;ehdz-m jbc:lgwso0 k 6e-way swing takes 1.000 s.; ()bas, ;oe fg:llz6cw-dhmmcgj k0-
(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 cpx2jw. :us e/81thq 64sqceousud7/ yan swing as a pendulutu: qsp8h.so 6u7c/1x dsuwe 4yej2/q m of small amplitude, but not both at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontal swings, and by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

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

  A 10.0-m-long wire of mass 1237c rz *e 80fs wqnykri7q*n-x. g is stretched under a tension of 255 N. A pulse isz s.0 -ike*y7q x n7ncwf8r*rq generated at one end, and 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 ceiling by a spri;ovu,- nhuj*c ng with spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillatiu;jhnc ,-vu* oons that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg cae4q/ js 4twfe0r at 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 the end of the cable. What is the period of the bouncing? [Hint: Refer to Table 9–1sew4jt q0ef4/.]    s

  A block of jello rests on a plate as shown in Fig. 11–56l el60dy.uo sqe9 q0x8 (which also gives 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, given that to06.l6exsye9ud 0qq lhe shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz