Give some examples of everyday vibrating objects. Which exhibit SHM, at leasia: 7t/;nmfi ct approximatelifm i7a;:t/cny?

Is the acceleration of a simple harmonic oscillator ever zero? If so, wher*x:auf*hp 0 1f8k+6lrbfi vd fe?

Explain why the motion of a pnh-yb,d fmh -8( .bwyciston in an automobile engine is approximately simple h- -w .,md cbhhynb8yf(armonic.

Real springs have mass. Will the true period and frequency be larger l1mj1*os -1r i ngepso7,jz2k or smaller than given by the equations for a mass oscillating on the end oi7m1 1z2 seo *1r, pjj-gnsklof an idealized massless spring? Explain.

How could you double the maxim) bi.y+/ n9j10 pk jlwarm2awwodc76eum speed of a simple harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a ij6i(-a. 0ag aggzq2wvertical spring scale, and then is released. Describe the scale reading as a function of timeq gz0.g2a- (aaiig 6jw.

If a pendulum clock is accurate at sea level, will it gain l7oot b/u :01rm/ibkeor lose time when taken mbl0kubto/7re/1o i : to high altitude? Why?

A tire swing hanging f90vbxc, 3-nesai;o lb 0p :knerom a branch reaches nearly to the ground (Fig. 11–48). How could you estimate the height ,e ;n:-klc0bxevanp s3i9bo 0of the branch using only a stopwatch?

Why can you make water slosh back and; ay-1op/rl tc forth in a pan only if you shake the pan at a ce cra1/ltop ;y-rtain frequency?

Give several everyday examples e,q2im:v em f6cj tq/ w2s7ov4of resonance.

Is a rattle in a car ever a resonance phenomenon? Expla-h9x ze;bl ee/in.

Is the frequency of a simple periodic wave equal to the frequency of its sourly /fg rw,0)1*nldwtpx 1nn/a ce? Why w/*lagr t 1)dnfl ,x0y1wpn/nor why not?

Explain the difference bh. iu:0:bf1db ao (lgpetween the speed of a transverse wave traveling down a c:(:g uodbfa.pibh01 lord and the speed of a tiny piece of the cord.

Why do the strings used for the lowest-frequencnsw1m8gk/5gse+ sr h :ai/7qzy notes on a piano normally have wire wrapped around t na+gk/gw:zq /se578h 1srsim hem?

What kind of waves do you think will travel down afs+ ;1wwkz v81ggery ; horizontal metal rod if you strike its end (a) vertically from above and (bgg1+;;r vfke wsw1zy8) horizontally parallel to its length?

Since the density of air decreases with an increase in temperature, but the bum(:pzmc, rgb/fl d 8fike 1wq 55r,ag+lk modulus B is nearly independent of temperaq r/g c(i 55ml 1d8gmefw,r ,ap+fzbk:ture, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water wave4tzj); nmwis.1 td)b js decrease in amplitude as they travel away from the sjt1) zt);nwdbsj i4. mource.

Two linear waves have the same ampl7 xul2-mcd8b i)oq6w, fpsqmi1 4hb6 bitude and speed, and otherwise are identical, except one has half the wavelength of the other. Which transmid-m bp )47xmcbhqiws12i,6 floq6u8bts more energy? By what factor?

When a sinusoidal wave crosse (khi/9y6s(jpvj- cbbs the boundary between two sections of cord as in Fig. 11–33, the frequpkscib9j vh -6/j(b(y ency does not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three segments, are there any places you cou +t/no )dz7usdol+1xh ld touch it wit7+ +u)zdsd1n/o h otlxh a knife blade without disturbing the motion?

When a standing wave (;h ;qgo*necwoxlgg8:a.) ecexists on a string, the vibrations of incident and reflected waves cancel at thxc n:ge;gg*8w.;)aqo eohc (le nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was be*sv;;sy8i m wqing transmitted from one place to another, how might we determineyvs w;m8 is*;q whether the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the tt +4ulf*)rbb kotal distance it travels in ontk )fu+ rb*bl4e period?    m

  An elastic cord is 65 cm lo3rgsy0 mc hjx2tciv76 pe i75)ng when a weight of 75 N hangs from it but is 85 cm long when a weight of 180 N hangs from it. W) y 60i 737vcpj gxheritm5c2shat is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car comp 2 p.0xmz 0msp:sea*cnress 5.0 mm when its 68-kg driver gets into the driver’* n2memss :ca0px 0zp.s seat. If the car 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. (a) What cxv 0 yvpq)c4)/jchb* is the spring stiffness constantyp /4hqc*cjb) xvv)0c $\approx$    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 /sv;e61ck sulk,,u.x-ndkk tf(c/eb frequency of 3.0 Hz when a mass of 0.60 kg is hung from it. Wev (/,b.6ufstx , u;ls k ckdk/e1k-cnhat is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicatin+c q y89-d otnx4ols*v2 a(mizg the position x of the mass in Fig. 11–2 at times t =taoivc 4dm9x 2s+8(zy*-nol q 0,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 weo wazlbarb g34+nd.8 *b. The web vibrates predominat8bnza ol gabr*d4 3+.wely with a frequency of 4.0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a spri3t1ageg;lgi/xc1 7v j .(glxwng 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 the value of m? ai3 ;wc.v/eg7llg1 gj gxtx (1   kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per s .n/vvmm)(aphc 1oi n/econd with an amplitude of 0.13 m.)./h vnp1oc /(manmvi 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 fz..njjeq 3 ns9rom equilibrium is the speed of a SHO half the maximum valj93en s. qnj.zue?$\approx$    A

A mass attached to the en2pts;qpuu:,q :5oe3 tm+vaap d 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.-6 kf c*uoi;fo If the spring is stretched an additional 0.130 m and released, how long dcuo-* fko i6;foes it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with spring st8 jxzw8byl,f3te/;bjj dz/r 8 iffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrwlyj3dx/z/8 b,j ;zr8e 8jfbt ium 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 x-bz)mm, 0k*dysfo. mcompress the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With d-my0 mks*z,.b mxo)fwhat speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to one end of 12 )vdo saac3sa 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 mo)d1s s32caav ass 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 vibra.uhpw gy b 6)h5)jxals(t6ah;tes according to the equation x = 0.45cos6.4t where x is in meters and t is in seconds. Determine)asj.p5h6xb;hl w(yu)h6atg
(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 fro6nbcjv62b e im x lw9o1,jf);zm equilibrium is the energy of a SHO half KE and half PEizm9vbjxoe6n jfl,1 b62)w ; c? ±    A

  If one vibration has 7.0 times the energy of ax4i*;8slm khqbwj/5wz ,tp 9x second, but their frequencies and masses are the same, what is the ratio of tklb; 5x t whp4*8 qi9xjmws,z/heir amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging lw9qo-f/ xka rw5nffp :4:zic2ight spring once every 0.65 sknxp:zqi 9w o-2 /af5f 4w:frc.
(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 paralle7w+j,ipd wsb rs;rb e/wqj i() l joq-cj7;u*/l vertical springs, each with spring stiffness constant k (Fig. 11–49). What will be the frequ rjd ;oj bj7+)w qi/,e jr(c/7-i;wpq*swbsluency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38s s+(tjw;+wek rin6.5t where x is in meters and t is in seconds. Detrj+ (t+kw esw;ermine
(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 o+zu9wiz4 uv)u+z *,rd/pwjuw w- hp8af SHM, labeled A and B. For each, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest okp-5 cc29hlz;lq lg9 qn the end of a horizontal spring (k = 124 N/m) is struck by a hammer, which gives k29zl9hc5gl-; p ql qcthe mass an initial speed 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 stiffness constant 305 N/m vibrates with an ampl6ju05ldzykm,n-no 0yxq)g wpu9 2f)aitude of 28.0 cm when 0.260 kg hangs from it. The mass passes throughxmu0d0-y zg2,9y5nu pkaq6fw)j)n o l 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 constanty xvg zz,-z::es $k_1$ 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 strik 6g9j.fk-0rbi(ewm1xsvy g g8e52ql ses a 0.600-kg block attached to a fixed horizontal spring whose spring stiffness lqry(v6js2.wge k- 0 59sxb1 g8fmg ieconstant is $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with mass 65.0 kg jumps from a h 9w-3)ydfxi+9tu g8qyup5d*n9ag bf migh bridge. After reaching his lowest pointqaw 3d-u5d ymfx +b )8y9n*9f9ugptgi, 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 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 6060jmb 7m 9gquvhw1*eax / mer0 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to e5q0p c dwm,s6wq 22mkmake exactly one swing per second? (That2,dmeks5cpm20 qwq 6w is, one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on0ez7 rws3k* vqv+q7a r Mars, where the acceleratiorsvev7+az*0w3q q7 rkn of gravity is about 0.37 that on Earth?    s

  What is the period of a simple pendulum +j. er:sy85+vibbn0y os mi9qfj;g p980 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple penduswbj+g :6x z8esvhu4, lum is 0.760 m, the pendulum bob has a mass of 365 grams, and it is relehj8+xbg4se:,wz6s u vased 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 0.9930 m. If the clock , hv;b 1c5f;u yyxe1/j)j.dp u )axylkloses half a minute per day, how s . );byj,x )v ap1/y ec;dk1lhujx5yufhould you adjust the length of the pendulum? shortened by    mm.

Derive a formula for the maximum speed z, imy5st.,tq2xgk sy :x6(yh$v_{max}$ 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 2.543y;uom,o-s 8vumxv c2 asu(c o8bn0q Hz. At it is released from rest starting at an angle of 1,b8o8 nm0smuvcu cx3ay;v soq 4uo( -25 $^{\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 j msadh g+-qp:s03x4tboat every 3.0 s. He measures the distance between twodj3ts-p qxh+ma g:0 s4 crests to be 6.5 m. How fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 27vgf 78b6kyye hs.x-t62 Hz and travels with a speed of 343 m/s How far apart are the wave hg8v7k fxtesyyb6 7-. crests (compressions)?    m

  (a) AM radio signals have frequeol;rt .xp ,+ nigsw.d.ncies between 550 kHz and 1600 kHz (kilohertz) and travel with a speed of.g wp .rsdn,;l+ xio.t $ 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 longitudinal waves i9(:;yqb v uk n:cdwzz1n
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one ittl:x - xrkr84d4 bz o7lv,/xls twice as dense as the other. In which rod will4l-:tvdz blxxlx /8rt,4o7 r k the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretchn 7q3a )u:s jkkklsbfw))n+ :qed between two supports 28 m apart. If the tensik) :sfqusnl wj)73)+n q :kbkaon in the cord is 150 N, how 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, 7w5v:a nrp k42a /kb -7wjb(sdntmna steel cable of length 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and sends a wave pulse along the cable. It is observ /snta(w,7w va k j2:kpd-bm54rna bn7ed 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 ju il;s545urg2v l,fzq jsb:p2sst below the surface of the sea. He hears the echo of the wave refbr2524uvg; li,5pq:ssjsf zl 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 travel asf*m21qb e2fn t different speeds, and this difference helps in locating the earths fqnf1ebm2 2*quake “epicenter” (where the disturbance took place).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced s+j0qoox8,((v z gdg djurface wave can be approximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actuallq d(jovjz(o+x,gd0g8 y 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, and (b) the amplitudes, of an tgcbth67opb ,v 4 . 1gu,rlt)gh6gg1jearthquake P wave passing through the Earth and detected at two points 10 km ab g1gl4g,h. 1tg76j)gro6vt p btcuh,nd 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is 9 h 0tqhm)u2,p1fbggg+b6ps8+ ms lkf measured to be + hpp)8fg0+gsgm bq9k tl,2bum 16sfh$ 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 the3jh k j(sfh;kt(fqg +, same portion of the Earth,t fsq,gk;j3h(j+k h( f but one is carrying twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same frequency, b q./4alj0: y kfwydcg)ut one transports three times the power of the other. What is the ratio of fdc/a4yjl0g.k y w):qthe amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move up and down a total verti) up(un /dh65mk f.1,-shfgvh bjtf*pcal 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 bd,n) 5 .hphf u( fh*6f/jsmb1-kg pvtuug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving2nkxqy. 8g* jb;jjr0 r 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 latjb;2.g qxykjr *njr 80er. (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 70cp+8g8:yd eg jybmz are the frequencies of tmc0 zybpj7eggy+:8 8dhe first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates a3fb)f kwt65pj t 294 Hz when unfingered. At what frequency will it vibrate if it is fingered one-thirb5jk )6ftw fp3d of the way down from the end? (That is, only two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string ces72 vvr 9ck.resonates in four loops at a frequency of 280 Hz. Name at least7 k 9cvsve2rc. three other 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 the(xvshzva1 y71h y nyy2(z9sa ) frequency of standing waves is 475 Hz, how far apart are two adjacent nodesysxz vyays a1 ()h1y(n9z2v h7?   m

  If two successive overtones of a vibrat+;cy9uzft 7q fing string are 280 Hz and 350 Hz, what is the frequency of tzu +y9cf q;7tfhe fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g. The dist4az yg1wrx+lvg/79*nb: jr +qh4ojv jance from the bridge to the support post is L = 62cm and the string is under a tension of 520 N. What are the frequeja:zj4lrrh y9*+ j1qg /nwgo7vx+4 vbncies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200ili h; sk(7-9yjli .+ileqza9 Hz, but it is measured to vibi9 zy( ihll a j9el;ik-.iq+7srate at 205 Hz. By what percent should 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 supposed to vibrate at 200 Hz, but it is meab6 hbrn2) za(x+;yrzvsured to vibrate at 205 Hz. By what percent should the tension in the string be chr2xz+vbz;hy)6 ra(n b anged to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a small-amplitude mechanical -9z 6lqqe gl5gvv4m8k60-Hz vibrator. The string’s mass per unit length v69q 8mv-lle4z5kgq gis $3.9 \times10^{ -4}$ 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 lev;s03fuhmp c- ngth of the string may be adjusted by moving the pulley. If the hanging mass m fp0-mcu3 shv; is fixed 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 just the right frequenmqet1) 6 hrqg0cy, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frrhm6g q1q)t 0eequency 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 strikes a boundary within the Engmdaff41bvlu(u (*1arth betw*1u1mvu4fbdglaf (n( een two kinds of material. If it approaches the boundary at an incident angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “shelf” where the vel+9x7juvnu-rxz96lxw:fci: jvc b * 8yocity changes from 2.8 m/s to 2.1 m/s If the inciden89 iwx+ jxbv*6 u7 9 cfyzrxu-jv:n:clt wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling ibm l3 4vlv12s:+ton g35thezmn warm air when it hits a layer of cold, dense air. If the sound wave hits the cold air interface at t5vm 32lmh1+ z ls:3b4 evgtonan 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 om591 ho i3 i,kxxy7zgbf rock at a g ,k7zomiby53 1h9xix 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 0.5 m in diameter. According to the user’s manual, td:cza:onj x+wia91p -he dish has to be pointed in the direction of the satellite, but an error o a19xz pc+no:wj d:i-af about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 250 km and velocity 750 km/h travels across :4,alnkdnf5 7//ug xc mw j 7ly);msaqthe Pacific Ocean. As it approaches Hawaii, people observe an unusual decreas /yn5l nksja)ldu ,7fg wm;xa7c/m:q4 e 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 shore to see stranded fishes and boats.)    min

  An energy-absorbing car b7 bfpix3.3l nhh6,wveumper has a spring stiffness constant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approip3 ,7.h blf3h 6xwnveximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18wd-rev628 kup m below, which stretches the net 1.1 m. Assume that the net behaves like a simple sr6 -k v2duew8ppring, 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 malq9-bi hxawg. xdeq+5). px 4ass then falls 33 cm before it stops and begins to rise. What is the frequency of the oscillation? dgxbl.a a.w+-5x )exhqi4 qp9   Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Figk.p1zsz8,p,36md q me8 y pzgv. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffness const ,v36g8p kzyzsdemp18 pzmq,.ant 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 ,8 spy,k( h,*imybiazcoffee (diameter 8 cm) at just the right pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill overk 8 ,a,(*m,sypy zhbii the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certaile,c(xzhyc 7 .n groove 10.8 cm from the center of a 33-rpm phonograph record have a wavelength of 1.7c (lz7c,ehx .y0 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates accordod:oe *2t 1jxcing to the equation x=0.650cos7.40t where x is in m :tj2ooxd1*eceters and t in seconds. Determine
(a) the amplitude,    m
(b) the frequency,(round to two decimal place)$\approx$    Hz
(c) the total energy,(round to one decimal place)$\approx$    J
(d) the kinetic energy and potential energy when x=0.260 m.(round to one decimal place) PE$\approx$    J KE =    J

  A simple pendulum oscillates with frequency f. Wg-61byj nhno 3,m 6ohqhat is its frequency if it accelerates at 0.50g 6 61-yjn,ob qo3hgmhn(a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man stands on thet;w(u jx2 il2s raft, it sinks 4.0 cm deeper into the water. Whel2; u2jxs(i wtn 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 musi*iq0qyrc ao(q mu f)d+(+fja:cal instrument are tuned to play at 392 Hz (G) and 440 Hz (A). mqo d:( fy0aqq)+a+j*fu(ci r
(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 dowk x 3d4dylmza)0nrfbs 7zn,1+n the stretched two-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the 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? yrn,fax 1)k+szmz 7lndbd 043

  A tuning fork vibrates at a frequency of 264 Hz, and theq ui+3+nt; tuif /rey6 tip of each prong moves 1.8 mm to eit+fi t6nu+;3ruetq / iyher side of center. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates .vfb r4r9bys0with simple harmonic 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) willr 49.svy bbr0f not lose contact with the board during the oscillation?

A string can have a “free” end if that end is attached to a r;;h-t ,qpl4pao4 (48(m nykaopjl n gging that can slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the r4p ka;lnmpoot- jn4 ygh84pg ;( q(l,aesonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum hasxb9 his m5audbkn 5-.4n.j ya7 a period of exactly 2.000 s — each one-way swing takes 1.000 bn5sjaxh.-.7aduymkbi 94 5ns.
(a) What is the length of a seconds pendulum in Austin, Texas, where $g=9.793\mathrm{m/s}^{2}$    m
(b) If the pendulum is moved to Paris, where $g=9.809\mathrm{m/s}^{2}$ by how many millimeters must we lengthen the pendulum?    mm
(c) What would be the length of a seconds pendulum on the Moon, where $g=1.62\mathrm{m/s}^{2}$    m

A mass hanging from a spring can oscillate in the vertical direction or can swdr; vlsr40p7 wing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period of the vertical oscillations or the period of the horizontal swings, and vr4r0p 7ls; wdby 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 st /f+pvzi*ub0i an3 lo(retched 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. Where will the two pulses first meet an( 30ol+z/ibipfu*v?    m

A block of mass M is suspended from a ceiling by a spring with spring 1kklul* 9lf unr-4ho3 stiffness counl3f4h 1l9krlk u-*onstant 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? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the jupej /5n hi3abe(d 4 zl,s j;:w7-lpygjnkyard. The steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bounci(sin/a7w ll bd-j5ep ;yghjzp:4je3,ng at the end of the cable. What is the period of the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (w tol vo/w;a24qyx12jehich also gives the dimensions of the block). You push it l2/x;q4oov1 awy 2etjsideways 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 the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz