Give some examples of everyday vibrat fi5w ).o:x.xnikdj (ping objects. Which exhibit SHM, at least approx i)x5jn:x(pof.kd i w.imately?

Is the acceleration of a simple harmonic oscillator ever zero? If so, whf :xp 3h;tm*by: ucew+ere?

Explain why the motion of a piston in a: ez -s l:3h09wcvpyhan automobile engine is approximately simple harmoniscw-h3al hy 09 :pevz:c.

Real springs have mass. Will the true period and frequency be larger or smallerhemn n;-m+ :k *5oqcac than given by the equations for a mass oscilq;enkham cn5m- +:co*lating on the end of an idealized massless spring? Explain.

How could you double the maximum speed of a simple harmon 4b yds em/ox)2za1y3qic oscillator (SHO)?

A 5.0-kg trout is at.hp:unkzv 9, c9 j*ykddxl53s g aon98tached to the hook of a vertical spring scale, and then is released. Describe the scale reading as a f 9 n*9a psoluhv:y3dcd9 k, j.g8zknx5unction of time.

If a pendulum clock is accurate(;n p f:p, mfom-ywck. at sea level, will it gain or lose time when taken to f:mc-mwp n.f k ;,(pyohigh altitude? Why?

A tire swing hanging from a branch reaches nearly to wva.1:h:*zqxgb4fa f the ground (Fig. 11–48). How could you estimate the height of the branch usiw: .:vf*1q4fxag bzahng only a stopwatch?

Why can you make water slosh back and forth in a pan only if you shake wv/a: .gnh3+; bjvwsathe pan at a certain frequency3hv vg+ jasa:w./bn;w ?

Give several everyday (yr.8u; x0w2oqyj -iodqs3bl examples of resonance.

Is a rattle in a car ever a resonance phenu,rrzxkcy , lt4i (t/;omenon? Explain.

Is the frequency of a simpl2er r0 ug0q67hf5ze gre periodic wave equal to the frequency of its source? Why or why noe6 2z0 e0fqgh75urg rrt?

Explain the difference between the speed of a transver d(d tpx5txylc:j pd*;.:kxz/se wave traveling down a cord an: pp:tld* c ;x(yd/xd5zx. tkjd the speed of a tiny piece of the cord.

Why do the strings used for the lowest-frequency notes on a piano normally-jc lg/xf jk fmmq::bd12 y(b0 have wire wrappe /k:bg0 q(mfjbx12ljm y-dcf:d around them?

What kind of waves do you think will travel dowqib3)m64 kzs fxb)yt7m hx60tn a horizontal metal rod if you strike its end (a) vertically from a60b4z yhx7 3itk )qtmbm)x s6fbove and (b) horizontally parallel to its length?

Since the density of air dev.d5 xexl axg p0iwy-6d2vgy5hcb0: 6creases with an increase in temperature, but the bulk modulus B is nearly independent of te6le0 acv.052:6xxpyh d-b5v ydgwgix mperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in amplitude as they trv8h ae mx44an g,f7-mhavel away from thh8g4 ,-m4mhanfavxe7 e source.

Two linear waves have the sameuo6 0j, -qafr/z:ph mk amplitude and speed, and otherwise are identical, except one has half the wavelength of the otherzmr:/ojh ku-6f qpa,0. Which transmits more energy? By what factor?

When a sinusoidal wave crosses the boundary betwew2,dv :ky tc2ben two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength ac2,k:b tw2d yvnd velocity do change). Explain why.

If a string is vibrating in three segments, are there any places(,zi+hy ck ;)onp6sv-vom:qj you could touch it with oyvczj kp;ovm(+)- ni:h,s6q a knife blade without disturbing the motion?

When a standing wave exists on a string, the vibrations of 2d 6vrkz(iqz: /2apxk incident and reflected waves cancel at the nodes. Does this mean that energy was destroyed? Explx:k(zpi 2kr2vq z/ad6ain.

If we knew that energy was being transmittfczo c bl 7lj:a29n-bv qzn44kn, t/p8ed from one place to another, how might we denzk a o4bbfl-8zlj 24,pn cv/t q:7cn9termine whether the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM withyjrj85 xn58vx5p71ncq g mj c- amplitude 0.18 m, what is the total distance it tr -pj85gy 1r7cjnxjq v ncxm585avels in one period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangu:po m5p.a qj( l,c-cgs from it but is 85 cm long when a weighto m.,:a(qcpc-jlg p5u of 180 N hangs from it. What is the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kolf1z l,7,ntv g driver gets into the driver’s seat. If the car goes over f ov,t,nlz17la 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) Wh qxw z5(8,fvud 6 tcb8p 6pgxz4q(3dtpat is the sp,zdd wp6b5(vux p3p (486 f tx8tqgqzcring stiffness constant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a frequency iy bd j8w7.mdsc+5q7y of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its freque7y d.iqd8ybm+s75wjcncy if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass i.(q qg*2k gca ur)t6xen Fig. 11–2 at times t =cg.r6(uge* qak )x2t 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 web. The web vibarle-yef3had1 b y31:rates predominately with a fre1yrle :d1ae ay3b3 -hfquency of 4.0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a spring vibrates with a frequency of 0.88 Hz. When anp(mkdh-c+ o: h additional 6po +dh (h:m-kc80-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 vb5pym:+ws tl lg57x694 ndv)8vspx 6w slh )owibrates 3.0 times per second with an amplitude of 0.13 m. Det slx)wmxs)pw8 n 96tys64+5obvwl hlvg:5d p7ermine
(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 s,r xnh )t+q8qypeed of a SHO half the maximum valuet,) xr+qn hyq8?$\approx$    A

A mass attached to the end of a spring is sc3oq;o3;6d,gb;c4nxpwopv i tretched 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 tp3bb +ywc9*+s*4smudx2 rkf jhe spring is stretched an additiom pc*kjsb+3 f+ *2wdurs4 xby9nal 0.130 m and released, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg i 4xlbn mb):eeu(i j5e)s attached to a spring with spring stiffness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrie5mie4ujnx(l :b)) beum 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 ldy4 wt)k0gmz 6v1 trvztaa/zc ,h: *.compress the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will t.,v lah6gztkw*1 :tv /4c)mz dtaryz0he ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surfv83.joo njo6 uace is 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 8ou.o ojjvn6 30.12 m. If the mass is released from rest with the spring compressed, the mass experiences a maximum acceleration of 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates according to the equatioc(y *lp 2;4vd (m/awg dy+nizdn x = 0.45cos6.4t where x is in meters2/day i zgw4vdd(pml;yc+n* ( 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 equilibriumtp.0-(h ax7a x+ren e(egej8u is the energy of a SHO half KE and half PE? x0e-8ep7gne(j .r +x(a hueat ±    A

  If one vibration has 7.0 timn2p /dq, wovm:e u3o /kot iniduk.+,(es the energy of a second, but their frequencies and masses are theu ,ide.k,m2(un qowi t / pn:k+3vod/o same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillates from a vertically hanging lig30( 3ue k7 rnt2st8szfo 90di(ffdn lnht spring once every 0.65 s.n e0(d k8r dl 0 9to(sifnzsffn73t2u3
(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 parallel vertical sgjo ;en )zvro*kcq/ 3;prings, each with spring stiffness constant k (Fig. ;orov* k) /zg3jc;neq11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equation x = 0.38sin6.5t where x is in mh+ z ddzib54e+eters +d h+z5d4zbie 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. /rlmf5u zclo-s)n g8 (For each, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on the end of a horizontal spring (k = 124 N/m) i6lu pj-jg7f*t2/ht+w dj xd3cs struck by a hammer, which j -cdwlhj2d3tjpu7/*g+xft6 gives the 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 305k x7a6en*z(lctofg6 u5* zr6 d N/m vibrates with an amplitude of 28.0 cm when 0.260 kg han 7z r*5f(ont6kcz66* xaludeg gs from it. The mass passes through the equilibrium point (x=0) with positive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two sprint1p *5-p4li eo .zglefgs, 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 )d3(hs ( up8 (ohwfeq*-s s7cr,sceqkspring whose spring stiffness cqd(ceh srpf*u s7h-q3c ek( sw(s,o )8onstant 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 reaching his h got+vo d56k/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 hgko/6 od+t 5vlength 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 vibratis8me shj xre,s*a. 7r7ons in exactly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it fvz;1ve5inu: is to make exactly one swing per second? (That is, one complete vibrativ5v : zne1iuf;on takes exactly 2.0 s.)    m

  A pendulum has a period of g-usb11l ; 6+cpiidvpnef ux 5(m o54i0.80 s on Earth. What is its period on Mars, where the acceleration of gravity is about 0.37 that on Ea+ i( lnep1xv cm65;d-up ibg4s5u oi1frth?    s

  What is the period of ayf ww yt1)kb71 simple pendulum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple z9i hvx/3d3a*uqea 5z xv65ob pendulum is 0.760 m, the pendulum bob has a mass of 365 grams, and it6i33v bvau/ oz5x9 dz axq*eh5 is released at an angle of 12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’s pendulum has a b0t c:.x*xmp9,u t ze8.zi ruklength of 0.9930 m. If the clock loses half a minute per day, how should you adjust the length of the ppuztz8. *ix mt:uk0b x,rc9e.endulum? shortened by    mm.

Derive a formula for thehrr8 7x (k,af b7ko,sb 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 oyhnw2k(w/u5 xf 2.5 Hz. At it is released from rest starting at an angle wy2w/n5 x(khu of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wacefocdguq4dp25 6;9a ve crests pass the bow of his anchored boat every 3.0 s. He measures the distance between two crests to be 6.5 m. How fast are the waves traveco5 uap2efd4 9gqc;6 dling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with aaebg 8t7r x4o,ol(z,q-zt+xh e4b)ke speed of 343 m/s How far apart are elqo4br)g+-ztbz(te 4hkx,a,8x 7 oethe wave crests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz anim u6z kgiu0i(zu9z:bdxm4rpy:0 t 056fo1w yd 1600 kHz (kilohertz) and travel withm 96fd:y wxk46b p0 (ityu5i1r0:goizzz0 muu 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 long6*9 j rgz ;460qqs8ckvtonx qiitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have su-f:)vq21n gq7nab ld a-znpg8.jd5 the same elastic modulus, but one is twice as dense as the other. In-npz.v5 njq bf1g :ug s-8dq2a7adl) n which rod will the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched beaupe/. ,w6fjwfs955p qssq5n tween two supports 28 m apart. If the tension in the co usfwan5p6s 5psj5f,/e .w9qq rd 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 steel cablnq:. 6mv3xllc e of length 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps inm:lv cnl.36qx to the terminal and sends a wave pulse along the cable. It is observed that it took 16 s for the pulse to return.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

  A sailor strikes the side of his ship just below the surface oxt2p :; .ejvrc1/ dqbjf the sea. He hears the echo of the wave reflected from the oj b tpcq;:d2.j /r1xvecean 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 dj,s je8bzu ;ncw.p;0 vifferent speeds, and this difference helps in locating the earthquake “epicenter” (where v, .nw;jbze;8psjcu 0the disturbance took place).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced surface wave can be approximated by a sinusoidal transvenvwta9 3e xh (vaz+5r4rse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequench nrzex(wa395vtv4 a+ies), 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) theij8 fj5cu:lts)9 mp2r-wxkh, .g wy,d amplitudes, of an earthquake P wave t,)c -2ws:jif y5djrwk gm.p9 lh,8xu 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 papqpu +fq;zy4: ssing through the Earth is measured to be :up+q;qpzy4f$ 2\times10^{6 }J/m^2$ at a distance of 48 km from the source.
(a) What was its intensity when it passed a point only 1.0 km from the source?(round to one decimal place)$\approx$    $ \times10^{9 }W/m^2$
(b) At what rate did energy pass through an area of $5m^2$ at 1.0 km?    $ \times10^{10 }W$

  Two earthquake waves of the same frequency travel through the same port13:qlt hg m(xwion of the Earth, but one is carrying twice the energy. What is the rati3:qw1lxg(mht o of the amplitudes of the two waves?   

  Two waves traveling along a stretched syxhid8(/ p5lstring have the same frequency, but one transports three times the power of the other. What is the rati (8yhx dis/5lpo of the amplitudes of the two waves?   

  A bug on the surface of a pond is ob nhkoym3/agna icm.57rie( 79served to move up and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm, by what factoha(ni 7gka7.ycoe /r n53mm9i r does the bug’s maximum KE change?   

The two pulses shown in uf.em1nkvc8*ta26v f,aox ssr (6xh1Fig. 11–52 are moving toward each other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments ,ac.e1m6 *v ah 68frxsuks(vxnfo 12tlater. (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 frequecs .x lm1h*))9qfxsfvncy, what are the freq)s xvf) 1xsmf9c.*hlquencies of the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfpk ow2 f/7+lnde2(m8avvbk x5ingered. At what frequency will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds ofevv o a+pn2(bd85 m7kf lx2/wk the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequency ws)(* exeth cijo9p15of 280 Hz. Name at least three other frequencies at wpwxehe1 (j*tci9)o 5s hich it will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string i6qp.-klld g9go 4me1i s 92m/s If the frequency of standing waves is 475 Hz, how far apart are ql. kgd m49p-o1eigl 6two adjacent nodes?   m

  If two successive overtones of a / slk25o.wfqr gh*2j7bshni5tho *4 mvibrating string are 280 Hz and 350 Hz, what is lh42g5 7j2.*mo bhr q*k hf/iswstn5othe frequency of the fundamental?    Hz

  A guitar string is 90 cm long and has a mass of 3.6 g.jw7 ci;0) kgg8 c3lnqk 2guel, The distance from the bridge to the suppor;cg2073g)gq nlkc ,iejuw k8lt post is L = 62cm and the string is under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrlygur j3 5j11 hru(h:kate at 200 Hz, but it is measured to vibrate at 205 Hz. By w 1:3gkrhj5uuh1r ( ljyhat 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 vib;8::wmoln03vs6m ce o no* pjarate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequeo8 03*je n:s6:;comapln mw voncy? decreased by    %

  One end of a horizontal string is attached to a 01tc qn k*+alesmall-amplitude mechanical 60-Hz vibrator. The stri+c lkeaqnt*01 ng’s mass per unit length is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of the string2*p.gai9 iby)v o wm*u may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave pa 9)a.g *2*ibupiv wymotterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water back and forth in cd-uud jk;;l-;,m,hf fu.bb sa tub at just the right frequency, the water alternately rises an ;dkuh -bmj-bdl,u; ,usfc f;.d 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 water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a boundary within fo0,pj4ms 9ntlov 0w( th s7x5the Earth between two kinds of material. Ifjhfpotlto ,0vm9w4 57xns 0s( 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 velocityxmp6e w,mm) c9 changes from 2.8 m/s to 2.1 m/s If the incident wave ep 6,9wmc)xmmcrests 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 hits6ep gr2n7e8 ywr3m.uh a layer of cold, dense air. If the sound wave hits the cold air interface 7y8hp3e.mgw6rnr e2u at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave strikes a boundary between two ty0 t45gjoo j*i)pe(c uapes of rock at a 38*uj5t4j (0ac)geiopo $^{\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 di1w4md9 ff(.w opj:wf aameter. According to the user’s manual, the dish has to be pointed in the direction of the satellitf4(fwpaw odf. 9w1 :mje, 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 velb5 afpsbl.fr.9gd-; j ocity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level ipfr- l;afbbdsg5 9..jn 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 1 /wmbg:nere9+q+6 g9 wshbfy:sgl 1nspring stiffness constant of 550 kN/m Find the maximum compression of the bumper if the car, wiw :n6 bgws:meg e+9+qy /nh9 1lsfgr1bth mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps frbo2 qn kw31y0l:prg 5t/xuca:om a window to a fire net 18 m below, which stretches the net 1.1 m. Assume that the net behaves like a sil5rbq :o 0/tp:1 u3n gwayxc2kmple 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 6 yd)x ruib: hnnww4:e,6/ltts9d,c zfreely hanging spring. The mass then falls 33 cm before it stops and begins to rise. What is tu4hi6teyz / n6x :rsln,w) dtd9b cw:,he frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 11–54), comp yyg(hxv 92zb pgyl9l2:8 /cunressing the spring lny ygh:9 (zu/29lx v2ygpcb85.0 m. (a) What is the spring stiffness constant of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of coffee (diameter 8 cm) at just the right pace of /1kz 2 xrivga7hev k.2about 1 step per seh2/gv i21 a.vkxzr7 kecond, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the c7h)xfq ok--dz enter of a 33-rpm phonograph record have af kxz o7-)-hdq wavelength of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the epju 4+n deq36r3 m.wie2qex, dquation x=0.650cos7.40t where x is in meters and t in seconds. +qx.e 2ji4e6 wdqd ru3nep,m3Determine
(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 oscilla u-v9 *bophi/ates with frequency f. What is its frequency if it accelerates at 0.50g (a) upwi v9opu-a/h*b ard,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When alu *l) bdke-/q 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When u*e/lb)d -lqk 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 instrumksqbeu+1bf (q(d8ji/ent are tuned to play at 392 Hz (G) and 440 Hz (A) +(sb/(kujei 1qqbd f8.
(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:w+ p+;xct gxe 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 tpx:;cgw+e+ x 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 e 9wp3jw6m3k ztc:n8r pach prong moves 1.8 mm to either sid8: tj9wm63 nzkw3prpc e 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 simpl wjilz1d 2c.4le 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 th1zdi2cj 4l.lwat 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 can t(rxu r+zk.-3 e/tgpk slide without friction on a vertical pole (Fig. 11–57). Determine the wavelengths of the resonanpkre t-.tx+zk /rg3u(t vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — v;x-sraq7ph - each one-way swing takes 1.;rpq as-v7x -h000 s.
(a) What is the length of a seconds pendulum in Austin, Texas, where $g=9.793\mathrm{m/s}^{2}$    m
(b) If the pendulum is moved to Paris, where $g=9.809\mathrm{m/s}^{2}$ by how many millimeters must we lengthen the pendulum?    mm
(c) What would be the length of a seconds pendulum on the Moon, where $g=1.62\mathrm{m/s}^{2}$    m

A mass hanging from a spring can oscillate z/9 x7 sh vhqep7kpc8t-qr,+hk m55ug )0ukri in the vertical direction or can swing as a pendulum of small amplitude, but not both at tk hzkqe /m5xhrig-u9c775k pq0rh p t+u)s,v8 he 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 az:;c bhyqpu+r-o7b/oowx(4 lsv io,1 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 fi hosz xu-y4 bov(l ,ro:+; /cwio1b7pqrst meet?    m

A block of mass M is suspend2)yzxp +xor ,yed from a ceiling by a spring with spring stiffness constant k. A penny of mass m is placed on top of the block. Wha ,px)r x2zoyy+t 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 junkyard. The steel crane cable is 22 mm92eh bt/ 8rse 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? [ e2mrh s9et/b8Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 1s 7enwwy wq qtqje6x,ds8(vp):e8j1 4 1–58 (which 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 w(jen1d4:e s7qes 6xw)vyjq8,t8 pqw 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