Give some examples of everyday vibrating objects. Which exhibitseofint5bf2;0a*ggnf c 1)0 h SHM, at least approxi0s f5nh f*)g0e1oicbft2; gan mately?

Is the acceleration of a simple haz*9dwz jzuq / fz.8b(prmonic oscillator ever zero? If so, where?

Explain why the motion of a piston in an automx; zbz ,i8ail.obile engine is approximately simple har8lzi , ixb.a;zmonic.

Real springs have mass. Will the true perifc o jd):.4kiy.64kq3 vigkziod and frequency be larger or smaller than given by the equations for a mass oscillating on the end of an idealized madk.44j 6k: qociv3g)i f kzi.yssless spring? Explain.

How could you double the maximum speed of a simple hk2( xfzv ua14x 4v(k( q5w5ssiec1 ustarmonic oscillator (SHO)?

A 5.0-kg trout is attached to the hook of a vertical spring scale, wqq+e*-c-6pue-c xp czy6z 5rand then is releacrwxc- qp qeyz+6up6z c*-e -5sed. Describe the scale reading as a function of time.

If a pendulum clock is accurate at sea level, willdh2 chpz -nt:lszmd g(5a9zwrv)3h.; it gain or lose time when taken to high altitude?w5a-d s.(lz:zhnctpz hh; 2mv 3) 9rdg Why?

A tire swing hanging from a branch reaches nearly to the ground (Fig. 11–7mq6ivbn) h)- mqdo :t48). How could y-t6)dh) mi7 nb vq:omqou estimate the height of the branch using only a stopwatch?

Why can you make water slos:7huxpk x)xp9 aw-/g dh back and forth in a pan only if you shake the pan at a kdh9u 7xgx- wp :a/)xpcertain frequency?

Give several everyday examples of reso0poz t4nzyv4o.adk2 j . qz:m.nance.

Is a rattle in a car ever a resonance phenomenon? 32aa q d6kwx9xrpja(1jk-c .oExplain.

Is the frequency of a simple periodic wave equal to the frequency of its source?wj6p /,)k 8ykk* f 9b8opsycbd Why or why,wdsfkc k 8y6*98b)p o kjbp/y not?

Explain the difference between the speed of a transverse wave traveling down 7hal ewrjm,jurgm9q35;.p * qa cord and the speed of a tiny piece of tw; qm 9 , rlpm*.ge3q75rjuhjahe cord.

Why do the strings used for the lowest-frequency notes on a pikm*)vp x- utuihx,/;vb x44m lano normally have wireul,i hmtv)x;u xv mbx- kp4/4* wrapped around them?

What kind of waves do you thwx m3uuinp59 5g xvtx0k7+bxf5f (jf :ink will travel down a horizontal metal rod if you strike its end (a) vertically from above and (b) horizon9(5 jwtx7+:vbk 5 50xmpff3ixnfug uxtally parallel to its length?

Since the density of air decreases with an increase in o p58/jxzenl( temperature, but the bulk modulus B is nearly indep5jn eplo8/(zxendent 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 in am k 5ipr:*miq6xplitude as they travel away fr rikm6*pi5q: xom the source.

Two linear waves have the 6zv r.* -ybe6puyqsi;z 5e9j; meoxs8same amplitude and speed, and otherwise are identical, except one has half the wavelength of the other. Which trany8pe;ri-u. 6z9sj x*qys 5eebmz; v 6osmits more energy? By what factor?

When a sinusoidal wave crosses the boundary between twb-al a1j 9d1ucn 7j,bao sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocity do change1-d aabljc nuj1 7b,a9). Explain why.

If a string is vibrating in three segme d 3ph8sz6zgv-nts, are there any places you could touch it with a knife blade without disturbing thepvzz8 hs3d6g - motion?

When a standing wave exists on a string, the vibrations of incide7ql ltkeh6 ,7wsu9gy, nt and reflected waves cancel at the nodes. Does this me6uq ,ky7gswhl,7e9tl an that energy was destroyed? Explain.

If we knew that energy was being transmitted f7)uggk2wb6;g pcab 6i/oy 4ttrom one place to another, how might we determine wheth; 6bitay7kp tgo4g/6cug2b)wer 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 total disx3biq( . (voaitance it travels in one.aiqvb( 3ix(o period?    m

  An elastic cord is 65 cm long when 49 8g4x;zsna7- dl5nhs5j51dxt rd baa9fgwha weight of 75 N hangs from it but is 85 cm long when a weight of 180 N hangs 5 95g x5t4 zjdnasa -fd1b98xghwds7rn;a4l hfrom it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 6-l -zd xzshb 81*tegczvw .i5eg00qc(9 bvff48-kg driver gets into the driver’s seat. If the car goes over a bump, what will be the frequency ofive v01bzfl *0( -9wtf c egdx zc5gqzhs.8b-4 vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kgs6bujmn2r- u0x51ld,y3 lycy fish hangs from it. (a) What is the spring stiffness const 0x6,1uu2 m3jy cy5-lrsdy nblant $\approx$    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 vibrat1l*nqzi-uh68jq b+ rl,7ors h(mkg;ges with a frequency of 3.0 Hz when a mass of 0.60 kg is hung from 8l hgh7* ,q6qbs(lkioz;u m1g r+-rnj it. What is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. 11–2 at tg/ o9w-c/ hhiaq2c 4yd mjyt)1imes t = 0,ocwi4y ahdh9gc-my /j/q 1) 2tt = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,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 yzht;f q-g v-ruvbl9 j(6:p5wspider’s web. The web vibrates predominately with a q r5uz:j wb- vyvt-;flhg(6p9 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 vibrqobb+bv8g)l 6ates with a frequency of 0.88 Hz. When an additionalbob qb+)6lg8v 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 spring vibracg2,h06nxekice.z54ko9 w onq0k ne8tes 3.0 times per second with an amplitude of 0io2 c q e,c08n.5ee4zkg9kkoxn6hwn0.13 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 oftrq 36l6i ht*r a SHO half the maximum valuettr* rqih 36l6?$\approx$    A

A mass attached to the e,qj hcz54fgf *:e** szsrz +vhnd of a spring is stretched a distance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretches a vertical spring 0.315 m. If the sprirtn-xu- r ti 3kk9w3*oub6kzu) 2u0 orng is stretched an additional 0.130 m and released, how long does it take to reach th 2-0turb39ut)wi6rokx-k3 urnz k* ou e (new) equilibrium position again?    s

  An object with mass 3.0 hkj. 9b9x f,mx69bsc8 ebdt+oxo9i6zkg is attached to a spring with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. Whe b c6miod+9 z, jfkxt9 osx986hbex9b.n 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 sprue* bp:l;sqa2m. iar/ing of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will : blaar; q2*pi /.usmethe ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to x0obqy(cotgpa .t )ld(4hj 8*xc 7kb6one end of a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, the mass experienc4 (gd(6 oq atbkh x.pbxo)*ctl0 jy8c7es 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 wr21by2nb dvcojw g1-j/q- *tqhere x is in meters and 2c/yjq -g1*bdtn-wo1qv2rb j 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 equilibrium is the se8z4pk:/9cmh x7ult energy of a SHO half KE and half PE?/4txhcmp7lk98usez : ±    A

  If one vibration has 7.0 times the energy obsb )x r5r3a3af a second, but their frequencies and masses are the same, what is the ratio of their amplituderxb5ab )a3 sr3s?   

  A 2.00-kg pumpkin oscillates from a vertically hanging light spring once evex-, n4svurvg+l zd86 kry 0.65 d8rvnz6v l g+usk4x-,s.
(a) Write down the equation giving the pumpkin’s position y (+ upward) as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. y = (   m)cos($\frac{2\pi t}{0.65s}$)
(b) How long will it take to get to the equilibrium position for the first time?    s
(c) What will be the pumpkin’s maximum speed?    m/s
(d) What will be its maximum acceleration, and where will that first be attained?   $m/s^2 $

A block of mass m is supported by two identiij(1oh)xd:w8v8g 3 evszmsw0cal parallel vertical springs, each with spring stiffnz31v)w(o8j 0sx8wimge hsd : vess constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t whet93lcv1 my.pt re x is in mey1tc 9t3pl v.mters and t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows two examples of SHM, labeled A and B. For each, what iswgv* b3a23/nq5uz b ga
(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 t46pk;gz ,wru w:xon;spring (k = 124 N/m) is struck by a hammer, which gives the mass an initzt wop ;u6rw:xkn ,g4;ial 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 wit f9gz(1lv*vp;v7b gsb3c1o jrh an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) with posit*zl 1bfv ;vo cv791(sgpr 3bjgive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two springs, with spring stiffness constants nm6bkef39a) t $k_1$ 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 attaccw boa1/)jky 9hed to a fixed horizontal spring whose spring stiffness way o kc1j)9/bconstant 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 high bridge. After(*ws 8shx1d1wfrs-qzu 4x tc 1 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 the unstretched lengtw1 d(1 s- xqzh xfsr14scuw8t*h of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrations in exactly 60 s. What is itxk o/cg 0lwa6*s
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly one swing per secon m4l7fh1dcfn:8y uff8d? (That is, one complete vibration takefl 8m 1fy7df:c4u8fnhs exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s o+tfst(9 zn .ron Earth. What is its period on Mars, where the acceleration of gravity is about 0.37 that on Earth(+r9 .tnszo tf?    s

  What is the period of a simple pendulum1vh - xr pd8fa -d,(yi.bzokj: 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 mass of 365 t;c5yd,p 1h cfgrams, and it is released at an angle of 1ctd ,;f hpc15y2.0 $^{\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 soh7o tj88tr; u;vg9uqz/ b8v of 0.9930 m. If the clock loses half a minute per day, how should you adjust the length of the pendulum? shortus;9u 7v8qb/ ;hojrgtt vzo88 ened by    mm.

Derive a formula for the-87r mkyd2a71tmc*zp iui 4fh maximum speed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at a frequency of 2.5 Hz. At it is f s5 ,mi.xfyz;released from rest starting at an angle of 15,;.s mzfiyfx5 $^{\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 bowceo ua.(j 5 ;hdcm:mb z99kik8 of his anchored boat every 3.0 s. He measures the distance between two crests to be 6.5 m. Howm9hbc.: jo ed8i9ac z (k;mku5 fast are the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with a speed of 343 m( mco*-/s s3 em9hxdqp/s How far apart are the wave crests/ 3 ss( mq9cxed-ohpm* (compressions)?    m

  (a) AM radio signals havjj23 17 1ninslxxb/ vorsz 6u/a/gr5 me frequencies between 550 kHz and 1600 kHz (kilohertz) and travel wv6/ xmaub2ji /s75z3lg11r jnn/o xrsith a speed of $ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

  Calculate the speed of longi5bydesb (l.t2tudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, but one is twice as dense as thoglo47e dey3/ cj f*w.e other. In which rod will the e fc *de 3g7.4yoojw/lspeed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m aph y2acx2 l.0jky 7j2kwart. If the tension in the cord is 150 N, how long will it take a pulse to travel fw2 y70 ckajx2.hk2lyj rom one support to the other?    s

  A ski gondola is connected to the top9a )e(kbd6q4julv: xy 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 along the cable. Ibl)x (day6 :94k juqevt 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 justpg1x*bbzvh s js)c c0n6/1p) wr//xho below the surface of the sea. He hears the echo of the wavcb *sh)sw10xhz p p vn/oc/)/1g6bxr je 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, and this3v(ktax+i u 9t074utkifm ut pf8,1z s difference helps in locating the earthquake “epicenter” (where the disturu0 it m1 9fs( uu37xa,ftk+vt8 it4zpkbance took place).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced surface wave can be approximated bya7vl0bx*,h h r a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitu7 rh0,* xalhbvde 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, 5 4)iybg,a ysf kuj-ckmu2k ). uym7)nand (b) the amplitudes, of an earthquake P wave passing through the Earth and detected at ) ym csbygm5uk)74i)yu2n,-ukj.fka two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passje8p 97p ,pk pw c2u1h+5jnnlying through the Earth is measured to be upy,5 pnlp+knjp78 c1jw e9h2$ 2\times10^{6 }J/m^2$ at a distance of 48 km from the source.
(a) What was its intensity when it passed a point only 1.0 km from the source?(round to one decimal place)$\approx$    $ \times10^{9 }W/m^2$
(b) At what rate did energy pass through an area of $5m^2$ at 1.0 km?    $ \times10^{10 }W$

  Two earthquake waves of the same frequency travel through the samedf7yj m,1 82 ojqe(a7wb9t o;*nxpmdq portion of the Earth, but one is carrying twicb2 *joe8at qo(,7xnjfqpd1dy m7 w9m;e the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same frequency, butn2 7hgd847r3cbdhey o one transports three times the power of the other. What is the ratio of th y3gnhdb7 2hocdre47 8e amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move up and down a total verticalsyzab5xbdk xu)73 ( 6j 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 buk57ajd)z xxbb6u(y3 s g’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each otheiwht vjr)6qtcj,17t/z s h3d tx98(y ir. (a) Sketch the shape of the string at the moment they directly overl ijt/ h3z7 6dr itv qy89swcx(t,jh)1tap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrate x/- zj/:2lwyps 7nf-d0gd uxos at 440 Hz as its fundamental frequency, what are the frequencies of the first fourx 27dyf/o0-w:/x -ugzln js dp harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At whpt8h-1 s1xx vxat frequency will it vibrhp 8txxvx11- sate if it 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. Name at qgb,0k:gqq 6n0. di87vu ( totjlbl)y least t b8j:tn,bdy(.qk6iglq)qlv7 0uo0 tg hree 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 frequency ofvrwq7u5imx /-;gcn w4 standing waves is 475 Hz, how far apart are two adjac;mxqrn/7u4 v5 wg-iw cent nodes?   m

  If two successive overtones of a vibrating string are 280 Hzk3 8lu(tbve /x and 350 Hz, what is the frequency of the fundamental? ek/bu xvl3 (t8   Hz

  A guitar string is 90 c7 93aqdxr/f99 vqqdy jt7 pw4vm 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 the frequenciq9 94avx93f/ jyd w qpt7dqrv7es of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, but it is measurul2v s+amml7 tj( tt37ed to vibrate at 205 Hz. By what percent should the tension in the string be changed 2 mta ml7sj7u+vtt3 (lto 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 ic;qllc1ut)ot ab- 8i+s measured to vibrate at 205 Hz. By what ulq ct18) ia+l-o;ct bpercent should the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attached to a lr3fr2+ e eni;small-amplitude mechanical 60-Hz vibrator. The string’s mass per un 2r 3e;rinelf+it 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 ma.vy9uu- 1doonm 4r*m zy be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many di.-y uoz vr9o1nmumd 4*fferent standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water ba4f 7i2rrw4vqx ck and forth in a tub at just the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. What is the r2 ir7 vxf44wqspeed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundary withi x8jh dqakr7wn40: 5y b5i(nlan the Earth between two kinds of material. If it approache8 kyj rq4xd5ba0an nwh7li5 (:s 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 “sh8+g.zz h3lekki j 4.tquzr w vd1.e)q,elf” where the velocity changes from 2.8 m/s to 2.1 m/s I84+ q.3lr,t1k ezhid.zwg.v kj) zeu qf 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, dense: v64,6 t3ezmhd ijhcn air. If the sound wave hits the cold airvd : 6z6h3 m,ejtnhi4c interface at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave strikes a boundary betwee s rev57aju6el/ (t1wan two types of rock at a 3e6jsvt1 u75 ea(war/l 8 $^{\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 the5i9dr22mt3m aj:7s1wn,s isesq b3f r user’s manual, the dish has to be poin aitsss snef23mdmwr13i925b:7q,jrted 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 25o:7kdsa(b6* kaom7m )yg *diusneh 7-0 km and velocity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. A*k()d *dsm 7o:k - 6aua 7ihmsgn7beoypproximately 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 bu li0ch/k)tr3gai6z0dh9 x -yg mper 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 (approximately 5 mi/h). [Hint: Use conservation of energ9z-d6h/0 3ctx glriih ag) y0ky.]    m

  A 65-kg person jumps from a window to joih;pl7 :.hta fire net 18 m below, which stretches the net 1.1 :h. tj loip7;hm. 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 on the end of a freely hanging spring. The mass then nvs ,bg geok8;es,:6gfalls 33 cm before it stops and begins to risevs 6bs;:eg,ok, g8eng . What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spriv 75tp er8w3 )mi;zwstng at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffness constant of the springs53rt ;z8e7wpm w vt)i?    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) v6 jmed)+j q .isbww79cij.gk -mq ;(lat 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).wmqi .iwsldb(;9jke 6+-vq7 cgj.j)m Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certt njgn1frh /4rz5)j,)ee*ce hy+ 8yhaain groove 10.8 cm from the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequency of the sound rhta5 4y+h /* r eefjhn8,jng )yz)e1cemitted?    Hz

  A 2.00-kg mass vibrates accoafmmqs2d3be p)it,/;q v5/ odrding to the equation x=0.650cos7.40t where x is in 2da;/ iqv)mp,5 3m /oq sdbeftmeters 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;zsml5jflo m/ so ;e86 f. What is its frequency if it accelerates at 0.50g (a) upward,lss/8zoje 5;;f lm om6    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. Wh .xk 3e/2tov-9t*ougft zb.rxen a 75-kg man stands on the raft, it sinks 4.0 cm deepertg 2xuo-v9k.e.3 brf*ot xz/ t 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 tuned to play at 392 /usb jo-.1aebd. h7,v lihq9fHz (G) and 440 Hz (A). /hesaq lbd7v-. 91oi j.uh,bf
(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 stretchen or w/1+evnju:t u0,xd 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 thew+0neu ,xuv:/tr 1onj 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 theo fz9aa s*)6 o7s43nn+ooc cbr tip of each prong moves 1.8 mm 3 oaa7zsonf +c*6)nbors4co9to either 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 with simple harmonic motion of frequency 1.5 cyc g:sxbi y6;5q9xjym b)les per second. What issbj :xq iy6)yg 9x;b5m 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 oscillation?

A string can have a “free” end if that end is attached to a ring that canouv-ifj m . qu(tf 1ecks8/b,p (qp/x3 slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with one end fmv3,(k-siqu op f ex( q1c/t.u8bpjf/ ixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each one-way swing takchix6am1an(a+ 5a cs ygo.65f es 1.000 s.5aaac6xsc+ig ha5. 6fm(n 1y o
(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 verticalyrog1b,9)o ip dqr ,r0s2d/fv direction or can swing as a pendulum of small amplitude, but not both at 0rord, )r9dy /fp q,vso1i2 bgthe 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 is stretched under a oxuva4a/i1m xx 5 y (l6:dcg)htension 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 t/v5 yag4x: i d)uxh6omc( l1axwo pulses first meet?    m

A block of mass M is suspended from a ceiling by a spring with spring stir7 xjqm* 1e8td5ugswmyk--n7 ffness constant k. A penny of mass m is placed on top of the block. What is the m-smjmu7-dr g1t kxe8wyn *7q5aximum 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 junkyard. The 96n ysi*;wc1c odsdxl+7fk qn/3idm+steel crane cable is 22 m long and has a diamef nk61+ cc+9l;s3dyi7nx/* dsqm iw doter 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 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (wmo,elc * 4yy-bhich also gives the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this vibration, given that the shear modulus (Section 9–5) of jy yc,* mbl-o4eello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz