Give some examples of eca8h : zeobw62veryday vibrating objects. Which exhibit SHM, at least approxim abo8zwc:26eh ately?

Is the acceleration of a simple harmonic oscillator ever zero? If kgahd849 oajp-ue f* :so, where?

Explain why the motion of a piston in an automobile engine is approximately simye1. tkmh bz35ple harmoniy3eh1bz .5 ktmc.

Real springs have mass. Will the true period d88 vbtscpskjz,8z1(j7c i4xand frequency be larger or smaller than given by the equations for a mass oscillating on the endjz,b81sztvs 8i 8j4cdcx p(k7 of an idealized massless spring? Explain.

How could you double the maximum speed of a simpl2a(klyd ey -x4e harmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scale, and ; aarm26 a1 bvzy2xwox4c,-tv then is released. Describe taarcv2z1-xa2ov wtb4,mx;y6he scale reading as a function of time.

If a pendulum clock is accurate at sea level, will it gain or lose time when tko:701s /kgx /o onjdmcyvl-,aken to high altitude? Why?yjg sk-on0k17lxcovd :,m/ o/

A tire swing hanging from a branch reaches nearly to the grou gmbndbc+9 t)/mz0kqkke 0+-o nd (Fig. 11–48). How could you estimate the height of the branch using only mb kcedmg 0k +/-b0)nqz+9 okta stopwatch?

Why can you make water slosh back and forth in a pan only if you shake the panxpcu/mp3fn lh86ko8 8 wx9clkn73f6n at a certain frequencmnxlx87nukh p pw 69c6/f38 f8olkc3ny?

Give several everyday ex)t, 3tqw ez4yxamples of resonance.

Is a rattle in a car evegjxg6;(ln f18ana ,ror a resonance phenomenon? Explain.

Is the frequency of a simple pey5p.8 ea+t2ci 4 lldvyriodic wave equal to the frequency of its source? Why ole+.c8 2 t di5pvlya4yr why not?

Explain the difference between the speed of a transverse wyys o83hm4aw5 0,u+ przt0t gj+7qft rave traveling down a cord and gsu83 jzt+5,rmt7ap +y0f0 wh4y otr qthe speed of a tiny piece of the cord.

Why do the strings used for the lowest-frequency notes kb+7xziw6h i0on a piano normally have wirezbwi 7i+k60xh wrapped around them?

What kind of waves do you think will travel down a horizontal metal ro rpd;,v2* j4vcjiy0x ad if you strike cj j*xr0p4iva2, vy;d its end (a) vertically from above and (b) horizontally parallel to its length?

Since the density of air decrwrx,8- iuk(yc eases with an increase in temperature, but the bulk modulus B is nearly independent of temperature, how would you expi-,rx yuw(kc8 ect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decreas hgre+ 6h* rbvx6nu0.ge in amplitude as they travel away xnrh+. b0*e grg u6hv6from the source.

Two linear waves have the same amplia/9zcl0 svn( ptude and speed, and otherwise are identical, except one has half the wavelength of the other. Which transmits more energy? By what factor9ca vpz/0 s(nl?

When a sinusoidal wave crosses the boujw0a( atzxwy sy z5zyx8d,111ndary between two sections of cord as in Fig. 11–33, t810sjyaxzzt1a, dx w5 1w zyy(he frequency does not change (although the wavelength and velocity do change). Explain why.

If a string is vibra -ci (3z+pj/dke)ygvb ting in three segments, are there any places you could touch it with a knife blade withg+)dj b3p/(-k zy ievcout disturbing the motion?

When a standing wave exists on a string, the vibrafz1 8bl/awis l n0s:h ey4bu)*tions of incident and reflected waves cancel at the nodes. Does this mean that energy was destrn l b)lye0sz:b fu/i 4*81swahoyed? Explain.

If we knew that energy was being transmitted from one place t r*-sux q1dwu)o another, how might we determur* qdw sx1u-)ine 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 mf9 a hah4m9vk/ kpn2:p+es5*nt9tlv total distance it travels in one mt fvs 5p+lapk an:k*hev/499mnt92hperiod?    m

  An elastic cord is 65 cm longxha:no2v5tdw47. .wn r:q sco when a weight of 75 N hangs from it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” constant k of this elast.5 :wsn:wqxovoh4a c2.7r ndtic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg dr;tq+znh-l8r- a1bi c yr9 (sifiver gets into the driver’s seat. If the car goes hnciq1t-+yzs(fb8a r-;9rl i over a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches *d8j(itju (us39w4nf aa czx4 3.6 cm when a 2.7-kg fish hangs from it. (a) What is the spring stiffness constaa4f*4 t8s (azj(ucxj 3wi9d nunt $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a frequency of 3.0 Hz when a mass of upv j-zx 5gf(uxl ha8,h/8 ;ax0.60 kg is hung from it. What is its frequency if only 0.38 kg hanvl(-x8hpa;h8j,agu fx xu/ 5z gs from it?    Hz

Construct a Table indicating the position x of the mag+ylkid3oz3 80-z t ltss in Fig. 11–2 at times t = lzgo- y 3 zt3itdl0k+80,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 dz(hlhb 6zznzu 3eyg+2+9pog9t0f gqk 8if95in a spider’s web. The web vibrates predominately with a frequency of 4.e fhz9z(l 0o6fkn 5h z89yqz3gdb9pi+u+g t2g 0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a spring vibrates with a5+. kzn;4phb vfqwg(c- 5bwor frequency of 0.88 Hz. When an additio4w5cnk-o (gfzp+;bh .rb qwv5nal 680-g mass is added to m, the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a sprinyzbfl -6sqb92g vibrates 3.0 times per second with an amplitude o2b lsfq6 bz-9yf 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 vm)nlda*4ucm chhtbljk6h /1p 83e66 maximum valuechmlh 6dbh mac66p v)8lkn3/j ut1*4e?$\approx$    A

A mass attached to the end of a spring is stretch.l/mh5ghj3 jnlw(k0if e n;n ;ed a distance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretches a vertical spring 0.315 m. If the spring is s2 1m26a+qh 0b5ofqgktiikk.r tretched an additional 0.130 m and released, how long does it take to reach the (new) equilibrium position agaq2i5+bqkgr26kof k tm h0.a1i in?    s

  An object with mass 3.0 kg is attached to a spring with spring stiffo4pf+x4 mjpxg tn0,m ;ness constant k = 280 N/mnt x +4mjmo; gppx,f04 and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is moving with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compress the spring of a toy pume9 rpc ..zp+r7d1qg2wod6 l opgun 0.200 m to “load” a 0.180-kg ball. With what d+ u6m.cp. 9red7r2q l pg1owzspeed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is 5,5kclmr0qjbnm i-1ycfq2vz2f7oyu 5v: 1z g attached to one end of a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, the1u 22lfj5q:v zqy 0ckb5vrm5cngmi7z1y,o-f 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 accordin:cb)y h eqirnl.qg9dz 3n os4ceo7)-+g to the equation x = 0.45cos6.4t where x is in me)+-.o:4sd9c nhc 7bq one)3lqzryieg ters 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 from eqp*un56alejz9q * p;wu uilibrium is the energy of a SHO half KE and half PE?5uupp ;6jw*9aq e*nlz ±    A

  If one vibration has 7.0 times the energy of a second, but their frequencib18a7w3hbx pjo0kv *les and masses are the same, what is0bo1 8jb 7avhkx*pwl3 the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a ver2ey1e03nl7u1yq:b jd 11k pzmd9mwe- eqnx5ctically hanging light spring once every 0.65 s. -y201j zkm1eew 1y bde cnu79n5lqpdx13 q:em
(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 ideq84xfe u:xwv7sk;ba dca)e)/ntical parallel vertical springs, each with spring stiffness constant k (Fig. 11–49). What will be the freque4f8eu);q w7 )xcvd:kaes /xba ncy of vibration?

  A 300-g mass vibrates according to the equation x = 0.3v ql 5(juk2v(n8sin6.5t where x is in meters and t isuk5n2v l(j(qv in seconds. Determine
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows two examples of SHM, labeled A and oqqb5 +v u(zq,.k oeq4B. 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 a u.u)q, 6efka vd6(hz(k = 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.96m/s Determiah zv.dfe(,aq6 uk) 6une
(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 ampl g i+m)zqfa1z/e-9xhp itude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) withgh q mafe1zp)/9izx +- 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 t il9pi5twdy 0.o two springs, with spring stiffness constants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes a 0.600-kg block attached to a fixed horizontal spritw . 0hyza)s20 t:vajnng whose spring stiffnessa0j ahynv0t: w2z. st) constant is $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with mass 65.0 kg jumve :80 65krpyilgkv7rps from a high bridge. After reaching his lowest point, vg:kv7 ryre 8ilp56k0 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 vibrati: y8y2kth61 xwmqv xp+ons in exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly one swing pnvf3a c(coa7 1er second? (That is, one complete vibra73 o1v (ncaacftion takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its period on M c88 +a lkzml7l+8fqtrars, where the acceleration of gravrlmfl8zklt c++ a 87q8ity is about 0.37 that on Earth?    s

  What is the period of a simp,.oqb1 2; fnqzd8ecm ole pendulum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 m, the pendulum bob has a d1e zw7n ,/ gf,+cicrbu8 b rh2cu(ty9mass of 365 grams, and it is released at an angle of 12., f1gnut/c(h,9 ubyze7 rwcbd+8c2r i0 $^{\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 y5jxnwyq:)2i /f3w mm0.9930 m. If the clock loses half a minute per day, how should you adjust the leng:n 3wqjf)/wmim5yx2 yth of the pendulum? shortened by    mm.

Derive a formula for the maximum speed.-mxg7c+*bjf7u l hj qpgmss46a ; wm8 $v_{max}$ 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 frez+*pyyiq+ /+-19 4c rqght1fo*hq9 xvicxtbvquency of 2.5 Hz. At it is released from rest starting at an angle of 154y t1pyi+1tc z/9xr+-x qbhfigqh o+c *v9q*v $^{\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 cr4hl0mix +ep8iests pass the bow of his anchored boat every 3.0 s. He measures the distance between two crests to be 6.5 m. How fepxh i +4m08liast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz nswx,:t7jm u3 and travels with a speed of 343 m/s How far apart are the wave c:7xwjmust, n3 rests (compressions)?    m

  (a) AM radio signals have frjksss; 6o. 2meequencies between 550 kHz and 1600 kHz (kilohertz) and travel with a speed os eojsms2.k;6f $ 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 lon6 9mlhv*-u)o h(1c g cuecsxs,gitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but on tn3lcc8;p)o 60rd kpze is twice as dense as the other. In which rod will the speed of longitudiz3ldrk p8)c ;6cno0tpnal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched beru 5 /mu 5qgwwa-.,x:c-ytucztween two supports 28 m apart. If the tension iqcxmuu wtg-zr,/: 5.-w cau5yn 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 connev: rhhd 83rz+ ,g;7ngvipyl4 pcted to the top of a hill by a 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 :ilv,7 4 drnggphyzr3+8 ;h pvalong 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 jus xz/r,vcx;w lgyr 5j-td.e(r*t below the surface of the sea. He hears v;/(tz. -g5rrr*,dlx w jcyxethe echo of the wave 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 ep;piiyp .: kgxbvb .a4n*2(gdarthquake travel at different speeds, and this difference helps in locating the earthquake “epicentg*p.4;i xndgv( b.a pi yp2b:ker” (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 uo iss6lb12t-7 ff;jg 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 leave contact with the ground? [Hint: Set the acceleration aftjb2oi;s1 l-fg6 u7s>g]    m

  What is the ratio of (a) the intensities, and (b) the amplitudec5 ib: i m *ws/waq/do3uzwzd,puxg95 i*b8b7s, of an earthquakz//bw:b du* i75*bdigw,c w3 xo8p5qasz u9ime P wave passing through the Earth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing :uv(+*;egs u d7pb:msrdrqd) through the Earth is measured to be b:du*s vg7d;) pd(+qs re:urm $ 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 naofmz,*a g m3rb2 rn7*i,e 5athe same frequency travel through the same portion of the Earth, but one is carrying twice the ene,3n mb,*znaa mer* 7a2ofi5rgrgy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the sanqm1l0d )eo2p me frequency, but one transports three times the power of dlpn me210 o)qthe other. What is the ratio of the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to movdpg7gz;p3kao ge i v1 dl:a+sw i/2x7,e up and down a total vertical distance of 6.0 cm, from the lowest to the highest pointa2i/lgdv7:as edpw7;+ p gz,o3 i1kxg, as a wave passes. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are 6cv+ep ksww: +moving toward each other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass e+p6:+vswkewc ach other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 4406zn:l;, stouwi. tz)b Hz as its fundamental frequency, what are the frequencies of the first four harmonics?tonbsw)z6; tzu, .i:l$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what frequency will i tkcmx ++iuo;bdi .d5,t vibrate if itbco5m,t+d;i+i k .ud x 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 fhq-w o lu(pqiu1g6a5 ;)7czljour loops at a frequency of 280 Hz. Name at least three other frequencies at which it wil-pwuji ago(6 1)uqq5h l7c;l zl 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 st o dazgwh-y0-xp-fr+ 3anding waves is 475 Hz, how far apart are tdpw+-gf 3-ao 0y xhr-zwo adjacent nodes?   m

  If two successive ov8zpi bmqm9;q4 ertones of a vibrating string are 280 Hz and 350 Hz, what is the frequm8bqz9q ; 4pimency of the fundamental?    Hz

  A guitar string is 90 9qmdgpjg./x k/ej 5 y/cm long and has a mass of 3.6 g. The distance from the bridge to the support post is L = 62cm and the string is under a tension of 520 N. What are tjqg.p/xyj5/g/9 d k emhe frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is fimv6o2m0fcj/ an* i 8supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent shom 0faj/n6* cmfi2 o8viuld 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 meatque/,a -m;p 8 ovp0uksured to vibrate at 205 Hz. By what percmqvepo, p /0ak;-8t uuent 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-amplidd6iy-xp e8mhp1, z9o*ig(hetude mechanical 60-Hz vibrator. The string’s massph*y eom,hi-d 6ex idg(918zp 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 zi*a:+jdlapi6j7 p0 xfncu.8 of the string may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying L :z0iixn+ufap8c*dl .6 7j pa jbetween 10 cm and 1.5 m?   

  When you slosh the water back and forth in a tub at just the right frequencv8k9 tjo(o/prl a.vv 5y, 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. What is the speed of the wa5/ avr.oo(tkj 9 vvpl8ter wave?    m/s

  An earthquake P wave traveling at k.0 km/s st,xzq st1og./wbb)+er rikes a boundary within the Earth between two kinds of material. If it approaches the boundary at /ogsz1btx, b)e. qr +wan 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 velocity y b22:w8s plkgchanges from 2.8 m/s to 2.1 m/sk8yw bg:2slp2 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 layer of cold,*8m9 ua0umrwf dense air. If the sound wave hits the cold air interface at an w um af9rmu08*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 types6tt0 ma1pr8om of rock at aom a0trmt8 16p 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/-.akq, / epcz87 2xymqht lks.5 m in diameter. According to the user’s manual, the dish has to be pointed in the directihs qqzck-at7/k2.pe lm,x/y 8on of the satellite, but an error of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 250 km and velocity 53+1tcq +6/ yb)v0tn ts(pjclofjkzi750 km/h travels across the Pacific Ocean. As it approaches Hatpjzc6+i+tkjb)(5yf t3 /cln1 sq0 vowaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness constant of 550 kNubgtx;/).oi -( ,o;djyra 1ma/6tiu n6wgx sh/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collides with ig bg /.-6/rom)watjh;y;dn s1xit6,(oxuaua wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a firer7us4ohi:p*y t tg6-a net 18 m below, which stretches the net 16yt4pu stoa*i h 7-:gr.1 m. Assume 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 onkigi*r3m;z35 hnx-/yya v:yy the end of a freely hanging spring. The mass then falls 33 cm before it stops and begins to rise. What is the frequency ofnzm:yi rih -v3x ;yy5k*3/gya the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 2 s dj,oq.jc6c,2 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the springso,q d6,c j.cj 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 (dia8 g2 x(mfsc,i) oik -hryrw(*zmeter 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 over the top (Fig. 11–55). Estimate the speed of waves ih *k(i(w z 8sx2fo)yrc, -mgrin the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the center of a 33-rpmww6 umdmvnlvt qwa r0cn1+c8:s /980h phonograph record have a r+n6uh09vwvctw/ m1n0ld:m wq8sc 8a wavelength of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates accor cpe5f)m y2p02lk/j aiding to the equation x=0.650cos7.40t where x is in meters and t in secondsm lfpy2a/2p5ei)ck 0j. Determine
(a) the amplitude,    m
(b) the frequency,(round to two decimal place)$\approx$    Hz
(c) the total energy,(round to one decimal place)$\approx$    J
(d) the kinetic energy and potential energy when x=0.260 m.(round to one decimal place) PE$\approx$    J KE =    J

  A simple pendulum oscillates with frequency f. What is itsb+z 1czk)v1e q frequency if it acceleezz b11)qvck +rates at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man )y5ojoo )bkyocs* )3cstands on the raft, it siyj*)sco5 oo kyob3))c nks 4.0 cm deeper into the water. When he steps off, the raft vibrates for a while.
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a musical instrument are tun(s uyx+e5 owv *)bw:,k8wwut fed to play at 392 Hz (G) and 440 Hz (Aty(ku, +w*boxuwws:e8f5v w) ).
(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-part cord of Fig. 1q; ;egx b8olm(1–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the light gm;b(x8q; oeler section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the tip of each prong +3 sz 86qu:obmf;xibx moves 1.8 mm to either sidq:u3xs x+bm;oz i6 fb8e 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 w1 uv:ut3n*q0s ev32j kgdy/reith 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) will not lose contact with the board during t*0rq syj1u g ek3:d/uv3e2vtnhe oscillation?

A string can have a “free” en04xpyn 04n(ba3ys*g aoe:2 td fza l7fd if that end is attached to a ring that can slide without friction on a vertical pole (Fig. 11–57). De(pf:3ot 74 af ba 0dxns2ly* 4gzynae0termine the wavelengths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each one-way swing tak pj3ch6 eph qcef-4bmc5;,1cac(w5vses 1.000 s. 1f 6 4c3q hsc5,c5jmec v-;pawhcpbe(
(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 k*;/ 2rnfcg320uyepdi. bq0xxf f u/ xoscillate 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 of the vertical oscillations or the period of the horizontal swings, and by what amount? [Hintfb i0e2ugc kxfxruf/dyq.0 /* p2xn3;: 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 q( /lp4dks c */djf99lhx :eplunder a tension of 255 N. A pulse is generat/s hjx (4l9k c9qd*llf pe:/dped at one end, and 20.0 ms later a second pulse is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spring with spring stiff(kv2wgzqra (* h 5+ q,)/7rfw jrdujqjness 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 blocv* r5zaqrrhujjw(/f, gqjkw7q 2+d () k? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. t hqr+mq zxr8sb f/*d/:*e6rg 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 9–1g /*ftd8hr: rq6/r *m +qbzesx.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (which dbs:ks5o cq (1io 5ec7also gives the dimensions of the block). You push it sideways as sh75 q( ocokdsbi:5cse1 own, 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