Give some examples of everyday viic div0e : ghl:ze3 +/bwe-e;nbrating objects. Which exhibit SHM, at least approximatee+:/cwe h d0ibeeg;i :v 3lnz-ly?

Is the acceleration of a simple harmonic oscillator q bea8 bz u;08i3gunr:ever zero? If so, where?

Explain why the motion ot*v9ov+u+qhy xzjddsin 57; :d(lb3x *m o-vcf a piston in an automobile engine is approximately simple harmoz- vmxn*x ou*9bt ds3jiq7ydld+ cv(: h5;+ov nic.

Real springs have mass. Will the true period and0af28te kf )dk frequency be larger or smaller than0ekfk2tda)8f given 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 simple harmonic oe *x)5.ps ce)saek 5p jqw*7kzscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scale eds+/m g0fac l 8q9yg)vp()od, and then is releasedv d 8qme0 agy(+/)l cs)gfpo9d. Describe the scale reading as a function of time.

If a pendulum clock is accurate at sea level, will it gain or lose time when ta k2s 2js5)ceycken to hig csk5) 2esy2jch altitude? Why?

A tire swing hanging from a branch reaches nearly toz.q22xd3 uv6bfy rb -s the ground (Fig. 11–48). How could you estimate the height ox-.sbzy 6r2v 3q2ufdbf the branch using only a stopwatch?

Why can you make water slosh back and fo xxi,+nnohi m/1xso ,2rth in a pan only if you shake the pan at a c 2/no,oi hns1,i+xxmxertain frequency?

Give several everyday exampledn8b8*va lc+idi uu86 s of resonance.

Is a rattle in a car dd6qzp pa -v;6y:sms8ever a resonance phenomenon? Explain.

Is the frequency of a simple peri,dy:o ekr+vuk92 fg1lodic wave equal to the frequency of its source? Why y1 ,dkkvlf2u:9o + greor why not?

Explain the difference between the speed of t/z9kjx xi7 o7a transverse wave traveling down a cord ank9ti7xx/jo z7 d the speed of a tiny piece of the cord.

Why do the strings used for the lowest-frequency notes on a piano normally have*f .fvl0mp3t g7ghw1n wire wralnwh.g7 fpf3g*0m v t1pped around them?

What kind of waves do you think will travel down a horizontal metal rod i :7dl ao39- dyra/zduy2oz.d rf you strike its end (a) vedyld3d9a /7 -oyd: .zrorzau2 rtically from above and (b) horizontally parallel to its length?

Since the density of air decreases with an increase in temperature, gqy* l:khr.3 bw. 5omgbut the bulk modulus B is nearly independent of temp5g .lr *:o gyhmk.qb3werature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circm1 wl3a,2ixoyular water waves decrease in amplitude as they travel away2aowy lmx,1i3 from the source.

Two linear waves have the same amplitude and speed, and other- g 0iy(;h*ymzsnhr 5gwise are identical, except one has halhg *m5yr0nzys (;g-ihf the wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the bo/)es e b.taop7+vpq-m undary between two sections of cord as in Fig. 11–33, the frequency does not change (although the eevs) t. a/7qpbm o+p-wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there any places you could3v3v+yl jxcnq i: ja,7wm +b3c touch it with a knife blade w,nv 37ic3:jlwbxv 3 qa+cy +jmithout disturbing the motion?

When a standing wave exists on a string, the )r2lxebc0xp ke:qj q:5;st8-coth .ivibrations of incident and reflected waves cancel at the nodes. Does this mean that energy was destroye:c2b:x 08tjsr.kxqe q; eoltp5 -i)ch d? Explain.

If we knew that energy was being transmitted from one plac* qeya1w jj8 oq5ilryy;+z:-rvg) e dax*:0eoe to another, how might we determine whether tre*wjyjz0 ae*v:;- ey )5o+iqlqr8 d:ayx g1 ohe energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amqbthe4*v ,y9z vt)9) dscuyb.plitude 0.18 m, what is the total distance it travels in one pete,c. *9zt d)s4yqvhbbvy u)9riod?    m

  An elastic cord is 65 cm long when a weight ofz+q .da2ybf z/md / czkges:48 (ve(wf 75 N hangs from it but is 85 cm lk+/f :4(8 /2z( y mgzdd azsfbe.qwecvong when a weight of 180 N hangs from it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car cow3gy 4e ur-):+ajq1d3oxer sx mpress 5.0 mm when its 68-kg driver gets into the driver’s seat. If the car goes je w3x e:qo 3rru4-s )ga1dy+xover 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 hangs from it. 99t0j p)-g 5g tku-(vnasurs e(a) What is tgus 5gtrts-ja9)kp ( ve9-u0nhe 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 Hd(4+*ccof19 m( kio0ncfr*gfuiw ex7z when a mass of 0.60 kg is hung from it. What is its fregeriw 4n0 (mk(co 1c*7fucdx*9ifof+quency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating thsowouv pn;/sps048 /ke position x of the mass in Fig. 11–2 at times t = 0,wn/4k;so v o s/0sppu8t = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

  A small fly of mass 0.25 g is caught in a spider’s web. The web vibrates ky isk r1 ytf5+y*a ifj5:z(h/predominately with a(5i/ *tfkj z:yi1s hyy krf+5a 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 s7.nto vxu24+ qxzenq) pring vibrates with a frequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 Hz. What is tvqnxxu.o4nz+ t) 7e q2he value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per seconuq48a+wk94r*h k haxc-tn yq4 d with an amplit9tna8*+4cq h q-uaxyr4k hk4wude 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 fr2 phnwfk5cpf o,1m m9:om equilibrium is the speed of a SHO half the maximum value?2:f pw 1ck9,mom5nhpf$\approx$    A

A mass attached to the end of alieep9 m-,x 7k 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 strefk/h:/ c e3qswabx i86tches a vertical spring 0.315 m. If the spring is stretched an additional 0.18cw/k63:ex bf/i sqah30 m and released, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a sprw*0m,tq wgpk*jo +nwj. 9 zrf9ing 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, itfgmtw9jkwnj p*w.rq +*z0,o9 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 spring of a toy popguncq9c98un hz8 h 0.200 m to “load” a 0.180-kg ball. With what speed will the ball leave the gu8u hhqnczc99 8n?    m/s

  A mass sitting on a horizontal, frictionless surface is at3 bnzass++,ii 79k pv4c+nxv xtached to one end of a spring; the other end is fixed to a wall. 3.0 J of work is requirx ,7bkv ai+in+3s4x9+nzspv ced to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, the mass experiences a maximum acceleration of 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates according to the equation x = 0.45cos6.4t where x iy5w2 1twn;qd rs in meters ann 5rqdy 21wtw;d t 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 4tye (w;*,fg urxnbn)from equilibrium is the energy of a SHO half KE and half PE? ± uw(nxn tr ,*bg )eyf4;   A

  If one vibration has 7.0 times the energy of a second, but thezg rwcrq6 )ig8r5s x6ov4:s, f*;tcts ir frequencies and masses are the same, what isz)s8s;cg:st*rxw5 r 66qi, ovctr4 fg the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscilla773tv k*e r+nfla 1+mr-njkvrtes from a vertically hanging light spring once every 0.67nr7l+ nt fa3jmv*+rkr v 1k-e5 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 paral stf4zq(ht tvn b)k48e g:i;a0lel vertical springs, each with spring stiffness constz4ebi8tk:qg)a f t ;h 4stv(n0ant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation xtdlo0 p,-kf,x5x f:mx = 0.38sin6.5t where x is in metef x:,5ol-0fp xdxm,ktrs and 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 f003kjwarq l p:do8-e 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 horizon86eyogu qv,+ xtal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.96m/s Det,o +vye6q g8uxermine
(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 stiffnesloabd6v7.j 4n s constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass pa.lod67vnj 4a bsses 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 stiffness constants 9wg y*6aizz(n $k_1$ 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 atta6 -k0 yq(6dbsa3yxxo ached to a fixed horizontal spring whose spring stiffness constant is k s0 xy3(dqx6-aby6ao$ 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.j5om 2r l5nk+k0 kg jumps from a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight k2 5+lnr5ojkm 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 60 s. Wha(mly cpf+rrdk1rn ; 40ccpe7+:py k3 nt is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is tsl(0jwp( ;k 7n7qyerto make exactly one swing per second? (That is, one complete vibration takes exactly 2.0 s.yqk 7s(rwlt j70e( p;n)    m

  A pendulum has a period of 0.80 9gcyxy8,e0crv no 8x)s on Earth. What is its period on Mars, where the acceleration of gravity i 8c v0gx,ry8c)xe 9noys about 0.37 that on Earth?    s

  What is the period of a simple pendulum 80 cmy: hmxo/) m)dt long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 mbg0rq+bme+h 6lw2w f-, the pendulum bob has a mass of 365 gram 0fmw -+g+2wrlhq6ebb s, and it is released at an angle of 12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’s pendulum has a length of 0.9930k r kk5)k)2 ga-mes 7ott:whp7 m. If the clock loses half a minute per day, how wp k5g))77 e-thkk str: 2aokmshould you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximum spe+7v d(g8 *wa).cih tp wbtc;kqed $v_{max}$ 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 frequejqon9e xk4d2jy18;q lncy of 2.5 Hz. At it is released from rest starting at an q;okn1xdejl2j9qy8 4 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 umfh9 m+tmb6u )899m o2wkmymbow of his anchored boat every 3.0 s. He measures the distance between two crests to be 6.5 m. How fast are the waves travel926mwmu bm hfm mtk9+9 8o)yuming?    m/s

  A sound wave in air has a frequency of 2mh*nrv:j 6 vk-fkzh/562 Hz and travels with a speed of 343 m/s How far apart are the wave crests (compressions)?vj* h:rvhzf/ 5- 6kmkn    m

  (a) AM radio signals have frequencies9f bik*l9j3wa between 550 kHz and 1600 kHz (kilohertz) and travelj k3*wbl9ia 9f with 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 oq50q(pl+ 2y 7hwmvmjof longitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one *l(bot6i qx9o mb zo59is twice as dense as the other. In which rod will the speed of longitudinal waves be gr*x o lo6o5im b9qbt(9zeater, and by what factor?   

  A cord of mass 0.65 kg is stretched between2l3:gb6 xt2tbn7lh o* /xsedo two supports 28 m apart. If the tension in the cord is 150 N, how long will it takts 2h ogbox3d2le6*l:7 bxt/ne 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 64268qkcwyw liqc+ .fe 20 m and diameter 1.5 cm. As the gon8clw6c4iy ef .w 2k+qqdola 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 return.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

  A sailor strikes the side of his s +i2fr2cnlj4i hip just below the surface of the sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is th24c nr f+l2jiie ocean at this point?    m

  P and S waves from an earthquake travel at different speeds, and this differenan6abs ak7 +rm8xe*v 5ce helps in locating the earthquake “epicenterr7nkbs ea 6ma5 x8+v*a” (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 eag(+2vaw1nsy :2v5f+z sl xa a sinusoidal transverse wave. gxfnyl( :vza5es2 s w1a+a+2vAssuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, anvef29i8 vpi dd-9 rnz:d (b) the amplitudes, of an earthquake P wave passing through the Earth and detected at two points 10 km andnp99riiev:d -vdz f82 20 km from the source?(a)    (b)   

  The intensity of an -h+rn/ :f0msvtq8 pa 7 ck4wcaearthquake wave passing through the Earth is measured to be rc w0:8h tcnfsvqa-/mp+k 74a$ 2\times10^{6 }J/m^2$ at a distance of 48 km from the source.
(a) What was its intensity when it passed a point only 1.0 km from the source?(round to one decimal place)$\approx$    $ \times10^{9 }W/m^2$
(b) At what rate did energy pass through an area of $5m^2$ at 1.0 km?    $ \times10^{10 }W$

  Two earthquake waves of the same frequency travel through the same 5d*j t6+3+e 0 rvgxlntjbono4gl9sx,portion of the Earth, but one is carrying twice the energy,e5glxo vsno4n t+ 6 jgrtj b*9+dx03l. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling alongf-.mp( m/ tin,sw pl:l a stretched string have the same frequency, but one transports m m/ls tf,-p pnwi.:l(three times the power of the other. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move up azo 2+s h-;wlband 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 maximuba;-lo wh+sz 2m KE change?   

The two pulses shown in Fi34m1 0lw 6a e*tuv9aqmeqcqh) g. 11–52 are moving toward each other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the strin1ct)le 9m qa3qeuwm60q 4v*ahg 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 fundamental frequency, what a5 f6q;y2a fkoza2r8 ip9x,czrzv) nm 8re the frequencies of the first four harmonicav,) zcxi9pf2 2r6z ro nm8k5z qa8;fys?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what frequ25m doh81tpqs+jg 9 nwency will it vibrate if it is fisjdw 5gqm9h1op+8 t2nngered one-third of the way down from the end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops atx*sq+)hpgm t3s*u;ts 8 6wh hn a frequency of 280 Hz. Name at least three 8ttu)hsxw m*h* shqg;+nps63other frequencies at which it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If thu-rzq 8/gn2qfaf e l,80fi2cems3c g. y 6lwo7e frequency of standing waves is 475 Hz, how far apart are two adjacent8y6qnq e- a 70fou, gcr8zwe2fif.lg3m2cs l/ nodes?   m

  If two successive overtones of au)/2ms5cp a lr vibrating string are 280 Hz and 350 Hz, what is the frequa pusm52rc )/lency of the fundamental?    Hz

  A guitar string is 90 cm long and pstl8.xfgir: l-0dqq, l hx+,has a mass of 3.6 g. The distance from the bridge to the suppoh+ilx0 g dtl q, 8rq,.xsf-p:lrt post is L = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string izdl-59c n)8mzqw, j fiwe,q*5zgq iz1s supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent shw 8 j d5*lzc,5eig,q-qinzq fw1m )9zzould the tension in the string be changed to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is 6h7+ryh6)*j,a f q-bozemby nsupposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hj hbyzbf6m6yq ,rh+ a*7ne)-oz. By what percent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a sma embu5w af**i/ll-amplitude mechanical 60-Hz vibrator. The strin wm*u abf5*ei/g’s mass per unit length is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of the string may be adjustedxd18e /pqcn/d by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave p/ecx1nd8p qd /atterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in auov.a2w sxf d2 dtj,* cc6n*/k dejk6- 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 6*nk-c u td xodds2kj,.* fjwv6/e26ca5-cm-wide tub is 0.85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a bou, kjhk p h)m3a;,mzuw7pkx. ):ccg1ay ndary within the Earth between two kinds of material. If it approaches the bo)hm) ckzpa jpx,1u,mg7a k: 3 ykch;w.undary 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 velo5b 6kino8rc.v 4h nwa6n-m-q ycity changes from 2.8 m/s to 2.1 o-rb-mak n45yhqnnv 8ic 6 6w.m/s If the incident wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air when it hits a layer4h;y6ih o rp;qy16j ak0n,)p1rdcm xn of cold, dense air. If the soup40c np,xqojhnr6 myh 1yk;)a6rdi; 1nd wave hits the cold air interface at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave strikes a boundary between two types offc l dm/u1a*cn.h.z1h/vcooxmc; (- n rock at a 38c1an1 -m/ dn/;.c lzc. *fohu(c xmvho $^{\circ} $ angle. As the wave crosses the boundary, the specific gravity of the rock changes from 3.6 to 2.8. Assuming that the elastic modulus is the same for both types of rock, determine the angle of refraction.    $^{\circ} $

  A satellite dish is about 0.5 m in diameter. According to thenfrh.55-m uvif ob p38 user’s manual, the dish has to be pointed in the dih5-ivn.r f3m f8ubop5 rection 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 )iku.s;mj e 5k s)zqcw466vuyvelocity 750 km/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 absence ys 6iuu.e )csk6kwqj5zv;4 m)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 5.t8n2jz;zedg r itjqj 2 l:2o550 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 (approximately 5 mi/h). [Hint: Use conservation of energy.dge8ltjt;2:rzj2 5.zjq2 i on]    m

  A 65-kg person jumps from a window to a fire net 18 m below, which stretspvob:1 k2f4rm;i jw( ches the net 1.1 m. Assume that the net behaves like a simple springo(:4 vrpm2bfsji wk; 1, 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 hb9nu*0 w,bq )jn+jz gmanging spring. The mass then falls 33 cm before it stn)n,mqb+z gbj 9w*j0uops and begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge x l+ u0fllo-4/v7n lwzspring at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring sx llln7lof/0 vu4+ -wztiffness 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 cdg72 +;qwk,iey z5 ybw+ ius-loffee (diameter 8 cm) at just the right pace of about 1 step per second,,gy5qweii2 wzs7+kd+; uby -l the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the center of a 33-rpm phonog6jh2lb t g*-5pcc.bwmraph record ha bj. -b6cw2* lgmh5tpcve a wavelength of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650co8f2hfir1i+ee; l8s n is7.40t where x is in meters and t in seconds. Determif8enlsie2hi+fr i 81 ;ne
(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 );di khcmtt56if it accelerates at 0.50g (a;dcm) 5itkht6) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. Wg -m4 jk1iopg:hen a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, 4 1gj-ogmipk :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 musicamzf 4sm0+ zws:l instrument are tuned to play at 392 Hz (G) and 440 Hz (A). sm:m+z0s w4z f
(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 two-partev* r3hxi:dxhli,40 y cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is thexxd h*y 4,ir:h3 l0vie wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the tip of each prong moveta3mp:qb o, 7bs 1.8 mm to either side of center3:7bbqm,pot a . 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 a2d d3kh c80nhof frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board cnk2 8da 3chd0han 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 tlh (w )7+qfhqif that end is attached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine thhqfhw(qt+ 7) le wavelengths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has b+u5+5 i)hv q.tob,wm6tb mosa period of exactly 2.000 s — each one-way swing takes 1.000 oiwbt.sm o + qb5+ut),h65mvbs.
(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 sprinira) nhd7c2 +cg can oscillate in the vertical direction or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period ofia+rdc )hn2 c7 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 ten;t 9 :i5d+rad5 h*nxiuxj8 hvlsion of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at the opposite end. Where will td9rld5 iut hai h j8v5xn;:x*+he two pulses first meet?    m

A block of mass M is suspended from a7i-u yj*3xedb)nqlr* ceiling by a spring with spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillations that will allow the penny to just stay on top of the block? (unrd3*q l7bx)e *- ijyAssume $m \ll M$)

  A crane has hoisted a 1200-kg car at the w09kl)xab*n x 9xnbqa 6ff7x2gd(ny 5 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 periodafbn( 67xxlb y995x)n 0d2axwq kg*fn of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as fdhwh( sbihktk( /y +.df(,:tshown in Fig. 11–58 (which also gives the dimensions of the block). You push it sideways as shown, and then you let(bs (wkfi+tfht d(h:d,.h/ yk go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this vibration, given that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz