Give some examples of everyday vibrating objects. Whtib9u(r ju9y 6s z);xjdp(d;w ich exhibit SHM, at least approxijx w;(jst y )i(9;rupdz96dbumately?

Is the acceleration of a simple harmonicilrp06-k 4h4cdepdu 1 oscillator ever zero? If so, where?

Explain why the motion of a piston ingw*fm0nz)s i h:hq- 12bb2i sl an automobile engine is approximately simpihim1sz2 0hg2*lnbwf q-: b)sle harmonic.

Real springs have mass. Will the true period and frequency be larger ows8:kdd b j* 6jxkj/e-r smaller than given by the equations for a mass oscillating on the end of an idealized massless spring? Edbx s/j:kjw- 6d*ke j8xplain.

How could you double the maximum speed of a sidjf3o38d ubz7ah x63 l) wdj)rmple harmonic oscillator (SHO)?

A 5.0-kg trout is attached j:8 ei 5h;pal9 eb r/e1jam,nvto the hook of a vertical spring scale, and then is released. Describe the scale reading ;e an 8 bhvj5erj/laie:mp9,1 as a function of time.

If a pendulum clock is accurate at sea level, will it g + e70wx+ehmms sf7v hi.q0gh7ain or lose time when taken to h7fx7emh g0e7v h0s.h+q iwm+sigh altitude? Why?

A tire swing hanging from a branch reaches nearly to the ground (Fig. 11–48). Ho40m emimdlyl4(me 7odq* e69ow could you estimate the heigoy9l e7id e 4oemdq604mm *lm(ht of the branch using only a stopwatch?

Why can you make water slosh back and forth in a pan only if you shake the panwyv3lp 0q3o 7,s+343i *hi mf0y wojyp+toc cb at a certain frequencys 7vioy q 3mtp30+wowyc+i*jbhc0 4y,3po3lf?

Give several everyday examples of resonance.+aqarajankk ,6): .hpemmt g3w3-q2 c

Is a rattle in a car ever a resonance phenomei b m4*d -*gczo2talz7non? Explain.

Is the frequency of a simple periodic wave equal to thq ff :6q- rc5mk,x6qjde frequency of its source? Why or why not? rjc-5dqx6mq,f6 k:qf

Explain the difference between the speed of a tr+4sr+lz-hpn:ggxem v.4y8g bansverse wave traveling down a cord and the speed of a tiny piece of the p4gxmh-gn bs8 legv4+.yz+r :cord.

Why do the strings used for the lowest-frequency notes on a piano normally haty ssiss txn1-sn4-21ve wire wrapped aroun2s 11nss-ts4xni ts-yd them?

What kind of waves do you think will travehb we/ttb;2t3u pm* r:l down a horizontal metal rod if you strike its end (a) vertically from above a tburp;wbt:2eth*3 / mnd (b) horizontally parallel to its length?

Since the density of air decreases with an increase in temperature, but the r-rys* wi-762fx seltbulk modulus B is n xfl6ys -serrw7* ti2-early independent of temperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease ins802msrj qc 2n amplitude as they travel awa22qn0sr mj8 csy from the source.

Two linear waves have uw/w9n+14zmark edk 6 the same amplitude and speed, and otherwise are identical, except one has half the wavelength of z19dk +m6e uwkr4/wnathe other. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundarh 7*guqgd2my2r um4:g1 cb3 0j9vbhesy between two sections of cord as in Fig. 11–33, the frequency does not change (although tbg*7123e 02dq jvu4: mu c sb9yghgmhrhe wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there any places you bj2+yf7 vvm;:3 1ywihsk)pn wcould touch it with a knife blade without disturb m j71v2)3y wkh;p+nfivsb:ywing the motion?

When a standing wave exists on a string, the vibrations of incidentfx9 zg(8- rxeg and reflected waves cancel at ther(8 x g-x9fgez nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being ti,rl u q57iig0 pfeo63ransmitted from one place to another, how might we determine whether the energy was being carried by particles (material bod3 rlqe6iiugip07,f 5oies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the totpn0+bv)-:jpp7 ij gku q6j y7mal distance it travels in one perypm p6 7 7j0+ q-vjjkigpu):nbiod?    m

  An elastic cord is 65 cm long whayd 4y*ita1h r9st0.p en 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 thih .0 a*9s4drtyt i1apys elastic cord?    N/m

  The springs of a 1500-kg car -(pbtyg*zw; ftb(ju) compress 5.0 mm when its 68-kg driver gets into the driver’s seat. If the ca*ty)- upwz;g tj(bf(br 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 hangs from it. (*) l(b x9f .wt*lnxjtz) jbw4ba) What is the spring stiffness constant .jf94 *tl)(*btbxb jlxw nz)w$\approx$    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 vibratziqo6-r qb:j ya+25jqes with a frequency of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency if only 0.38 kg hangs f- qiyq5ao:b2 jz6q jr+rom it?    Hz

Construct a Table indicating the position x of the mass in Fig. 11–2zdzkiqc/+nf 9 *rxn2 2 at times t = 0,t dqiz92+ k nczn/f*xr2 = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 0.257t p/4d3,kk y fsupfl7 g is caught in a spider’s web. The web vibrates predominately with / ydt77kpsl f3,fu4kpa 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 with39k5 z31 tenr wdh3savkt- -hfn):udy a frequency of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 Hz. What is the value of nts35ah3- h 9drvwuft1dye:3- zk )nkm?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times p7/dv cgahp q1sl4z afw0)u30fer second with an amplitude ohcg)sqf a1v zwu0p0l fa/3d74f 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 maxi7bpgmy*,7q+ubnfvmh 9pqa8 o( 21y o rmum value?v29y1mg (*yrh+an7 buq7o pb p8oqf,m$\approx$    A

A mass attached to the end of a sp(6vwsx1 u6wk3)ftorrp3 p- znring 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 sprincn 3(uhp (;udlhfu/e9v k*3jfg 0.315 m. If the spring is stretched an additional 0.130 m and released, how long does it take to reach the (new) equilibrium position again? fd/3; k((ln cuh*fjv3 hp9euu    s

  An object with mass 3.0 kg is attach39qpmzl ugj 0*ed 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 m*0u39zjgqp lits 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 spring of a ,fxmrk4u 8xai5+lxy6toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will 8x4rx,im 5fay ux6+lkthe ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to one end of (lc. 3( tuyacbqk*r/ea 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 /k( uyc.al *3 cer(tbqspring 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 l1 t o(ytr:n8:famj2b x is in me:r ( am28:1 tbljotnfyters and 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 fredgci5)dp k 2*om equilibrium is the energy of a SHO half KE and half PE? 5 cdkgdp *2)ei±    A

  If one vibration has 7.0 times the energy *rvaee6 on70w of a second, but their frequencies and masses are the same, what is theovr *n 7aw6e0e ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light spring oncpww*j q 632oime every 0.62m6iqow pw*j 35 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 supn: h* zqvcnn-5xedt *. v/ele6ported by two identical parallel vertical springs, each with spring stiffnevenenq -dec:* vx /*z thl56n.ss constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the h) we+bsd5ixo:4-l2 wtg e w.xequation x = 0.38sin6.5t where x is in meters and t is in seconds2 oeb.hxt:ws wdg4 +w- 5xe)il. 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, labee9-3du rs6t;hl 5 e 18 ry-m1c/ aknpiiuyap9bled A and B. For each, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on the end of a horizontal spring (k = 124 N/m) is syth3se9 5gm)ltruck by a hammer, which gives the mass an initial speed of 2.96m/s Determhtl9yg5esm 3) ine
(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 stiffness constan 9zln segf 9cxgqegi:1/8yfg .mx-,a6t 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium p.zsxgf19/e ia:6eg9nfgqc8 mxl,g - yoint (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 c(y5 ozm*6+b pz-) dausiu zgo,onstants $k_1$ 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 attac;j p/*lq-1mgy6kct yahed to a fixed horizontal spring whose spring stiffness cl*mgac6yt j-pqyk/1; onstant 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 6o ;zqyevx53qhp1qb2- :s; srj5.0 kg jumps 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 and 5bhxo1 rqqsqv;-;:syezpj3 2 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 qi4i:,waa e-uwhi; tf1 wl4+v60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to map :*da3:rgp)d+evvkc ie3 d(n ke exactly one swing per second? (T) kc( *i3+ga dv:edp:pne3r dvhat is, one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its periou9 9s2j.c:v tyvi2 3ij,voqwx d on Mars, where the acceleration of gravity is ab,v:2c9w2iouvsq yv 9 ijt 3.xjout 0.37 that on Earth?    s

  What is the period of a simple pendulum 8b: 4jn8 vcb9rk:c syc ,ue61z,lrg.jb0 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, th* gv)o :c0zgwqe pendulum bob has a mass of 365 grams, and it is released at an angle *zo0cg)qg: w vof 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 00x, +q 7qibbmdne/b(z.9930 m. If the clock loses half a minute per day, how should you adjust the lengt+bb/0q iq zd,x7emb(nh of the pendulum? shortened by    mm.

Derive a formula for the maxlx gklyh214y 9kt9 v*himum 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 oscihw+w(d6 )dzhcw sg. akyu12:ullates at a frequency of 2.5 Hz. At it is released from rest starting at an ang :dasc. y )u+hk6uhd1wgwzw2 (le of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests pass the bow of his anchored boat every 37jsv1 yhl2nwf1- o4f o.0 s. He measures the disto1 vjf7 sw2fn4y h-o1lance between two crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air hg ;ollp6s0 c0f4ekrj6 as a frequency of 262 Hz and travels with a speed of 343 m/s How far apart00 lf;6rp kecg6 s4jol are the wave crests (compressions)?    m

  (a) AM radio signals have frequenciesztk rg/,(4g mt between 550 kHz and 1600 kHz (kilohertz) and travel with a speedgr(t, /mgkz 4t 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 longitudina f- 8cnacp8kpzso 52k-l waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one ispdps7xsfo 0 ku: ()7i e6h8mjx twice as dense as the other. In which rofph 7ou:)sx6 (x0jped7k8mis d will the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two s idolk6k:b oyw67dkq6o;u7in i* z2y( upports 28 m apart. If the tension in the cord is 150 N, how long will it take a pulse to travel from one suk nd;6 6y7lw k odokzi:bqio*6y iu7(2pport to the other?    s

  A ski gondola is connected to the top of a hill by a steel cable of ly1j br fo9gcx7wtf (h+l;0/s t/fa) ft(q0m wwength 620 m and diameter 1.5 cm. As the go/wqt9(1+ rhs/ ayxcjmtfwb( 0wgl)7f; t0f fondola 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 ship just below the susw4xhyn. 4c 9jrface of the sea. He hears the echo of the wjsn.ch4w94 xy ave reflected from the ocean floor directly below 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at different speeds, aq8 o)l64vjh+ua; je bqnd this difference helps in locating the earthquake “epicenteejqj6vba8;l4)h uq + or” (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-produced2tg1k0dhbw9 f surface wave can be approximated by a sinusoidal 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 to lgt219h dbwf 0keave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplitusn u9*eo zhzu9lus;e, z(i;g *des, of an earthquake P wave passing ; u9gs(h ez*;iz,9u*zn sleouthrough the Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is*vvy.wi3wt 6 .y gxom) measured to be v) *.6 w yygt.vmxw3io$ 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 thehu 37 9ptpvn6-kfqv9 z same portion of the Earth, but one is carrying twice the energy. What is the ratio of the amplitudes oz f9vh3 - 7n9up6tqpvkf the two waves?   

  Two waves traveling along a stretched string have tmd 85*ibm 8berxw.2xd he same frequency, but one transports three times the power of the other. What is the ratio of the amplitrxixmwb8 2m5*d. d8beudes of the two waves?   

  A bug on the surface of a pond is observed to move up and downkicqti g+vc/6 o)* fv/ a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wavf i/* qc 6g/+kit)vocve passes. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving tuj;, cp/g0rsjoward 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 pps0; uc g,/rjjass each other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440v/1l *hma 0zw-o8 la9 rkpvahvm:3lf: Hz as its fundamental frequency, what are the frequencies o81fvlp 3 l0 kmhol a::-whaav*/rm9zvf the first four 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 vm,42sb aa.(5wh 5o*uhxxof dcibrate if i .shx2o*,mx5 cbd(ufw5h ao 4at is fingered one-third of the way down from the end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequency of 280 Hz. Nam+(u(rxnasas 8yj2 :ii 44h duhe at least three other frequ+ srua (iyi: 4nxdshu4 hj8a(2encies 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 the frequency of standing waves icejz:kwg+ c88x a8f.rs 475 wkre: zjg +a8c8.f8 cxHz, how far apart are two adjacent nodes?   m

  If two successive overtones of a v r8qq+zd+ qu:nvs/;a vibrating string are 280 Hz and 350 Hz, what is the frequenuq qv+;qzd+:a r 8sv/ncy of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. Tuxogt+ uiwl u7:cj 7 w/3nv9q8he distance from the bridge to the support post is L = 62cm and the string is under a tension of 520 N. What are xjt7niuw7 qvu9g8/o+lu:3 cwthe frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is suppose3t6p qy.mhj rr*jmz12 ko:3idd 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 correct the frequen op6d:irt zm.213 *krj hmy3jqcy?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate atg7r7 )gjzfxa6w cq8 2wb+iaf- 200 Hz, but it is measured to vibrate at 205 Hz. By wf)xc gga82z6w+ iwr-77b jq fahat percent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small- r(47;.oqt.w zcpdvfvamplitude mechanical 60-Hz vibrator. The string’s mass per uni. po4v;( twfz.r7q dcvt 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 m etc 3k,cjmmd2x..hy 2oving the pulley. If the hanging mass m is fi. cejt kc2x3h.ym,d 2mxed at 0.080 kg, how many different standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at juju:j4 c8/ :s,j(fgfuz+hw rzu st the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. f8j/u +j,w z:hs4 fcu(r:jugzWhat is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundary withinyd9x jcqv2i /* the Earth between two kinds of mater v2xjyq* d9i/cial. If it approaches the boundary at an incident angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underc3r0-v mw ;2n v):z; rlqbie,vyh /odrwater “shelf” where the velocity changes from 2.8 mv v,) hqr;crew-mbd;o:vln 2z/i3 yr0/s to 2.1 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 2+.rqrm) ; zhhwk;f p0(nasgx air when it hits a layer of cold, dense air. If the sound wave hits the cold .gfp+2;xhk rnwsq zh0mar ) (;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 boundary5 )nj ucubq nfs2ana f6l91wu4. :de lkn+)f.l between two types of rock at a l.k.)qw ba 2n15 ejusu6:udlfn)fn4+l9n fac38 $^{\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. Accorg)vy *.c okh.h6auty gl 0,5npding to the user’s manual, the dish has to be pointl6g,0tc )hvg5kphy *.yon u.aed 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 velocitxe. i0t60 dsdz2i,rh.mg4 m ghy 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea lgrehxth d d .z2msm06igi.,04evel 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 shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness constant of 550 kN/m ,yq5curtk:vbz f 0,; rFind the maximum compression of the bumper if the car, with mass 1500 kg, col5 kcr:bztvfq;0y, ,ur lides 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 jumpsfho(z0zi*ah 9 cf47sw from a window to a fire net 18 m below, which stretches the net 1.1 m. Assumfo9h *ih(az f4z7c ws0e 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. The u rl,szoqp,nja(z3, i2c*fi.mass then falls 33 cm before it stops and begins to rise. What is the frequenz*2io3f(,usz c rqapl.nj,i,cy of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s ( ,telzalvq( 0 gbb0,-hFig. 11–54), compressing the sprz0tqv,e (b ablhl-0 g,ing 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) ; vk ana929)bmeqbyyegf1k/ b+vk*j+ at just the right 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). Estimate the speed of waves in thevae+n+) kygv*2/k eab ;9k9 1qjmbfby coffee.    cm/s

  The ripples in a certain groove 10.8 cm frucl*lcg /(k34mp2j sjom the center of a 33-rpm phonograph record have a wavelengl(lm 4/ pck j*u23jcgsth of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t 0d7jjfbvg xl y 4v5upw1-3k(hq m*rcwg84t7 p where x is in meters and t in seconds. Determx*5vcf7w1gg8 4pm -yv( jdbt ur j4whlq7p0 3kine
(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 fde/ov 061ew6ytuy :y h(1 wbzfrequency f. What is its frequency if it accelerates at 0.50g (a) uph1 6ydf u10we6wy: zoet( yv/bward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. W y: +grwws7/nhhen a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the raft vibratesw g:7yrh+/swn 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 tuned to play at 392 H v *gjhof7i6ou9t.-83pmk euuz (G) and 440 Hz (A)io3 p ktu.u8m7 9j h*fu-go6ve.
(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 downgjwdhht b*r-s*; ze19 o2nu5r the stretched two-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus th-* ro5bw h zd9*srn ;2guhtej1at 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 frequencyhhzaq6 bh 9*j4 of 264 Hz, and the tip of each prong moves 1.8 mm to either side of cehq6bjhh4a*z 9 nter. 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 ha3y3p3eb-ks zo,f(injrmonic motion of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board during the osc(e3fk- s pi3 o3,zbnjyillation?

A string can have a “free” end if that end is attached to a ring that can slidkujx ;+ ;vvwjzvww*3d81 s6a qe without fricti u3s8xdjz w;6*wv; +akqwvj v1on 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.

  A “seconds” pendulum hasu l;5-k -;jgzt nqgrcogv3r. 8 a period of exactly 2.000 s — each one-way swing takes o.gjgqcl;r ;-- t3v n5gr8z ku1.000 s.
(a) What is the length of a seconds pendulum in Austin, Texas, where $g=9.793\mathrm{m/s}^{2}$    m
(b) If the pendulum is moved to Paris, where $g=9.809\mathrm{m/s}^{2}$ by how many millimeters must we lengthen the pendulum?    mm
(c) What would be the length of a seconds pendulum on the Moon, where $g=1.62\mathrm{m/s}^{2}$    m

A mass hanging from a spring can oscillate in the vertical directionlof9f :qn *)ex )sx5h8gr -wsn or can swing as a pendulum of small amplitude, butxr5nx*f9 -l: sn8ho gfew)qs) 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 in;svz,ew:p0hn ha/p,s stretched under a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at the opposite end. W z,:/;pnhhnpv,w0ea s here will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by ad,a ix3f7a1g y2xtd1n 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 allx agd t,37 12nxyfdi1aow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted ap,l/ ipds9 l2fw1 .;,ewnujwn 1200-kg car 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–lnj,uiw9, np1 we;f.wsld/p2 1.]    s

  A block of jello rests on a plate as shown izkbi0 (e57pz jz* /fxtn Fig. 11–58 (which also gives the dimensions of the block). You push it sideways as shown, and then ybz7fjx0(5t/p zi*kezou let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this vibration, given that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz