kean (msk955) – Homework 08 – yao – (56725) 1This print-out should have 25 questions.Multiple-choice questions may continue onthe next column or page – find all choicesbefore answering.001 10.0 pointsWhen a particular wire is vibrating w ith a fre-quency of 4.8 Hz, a transverse wave of wave-length 39 .6 cm is produced.Determine the speed of wave pulses alongthe wire.Correct answer: 1.9008 m/s.Explanation:Let : f = 4.8 Hz andλ = 39.6 cm .If the frequency is f and the wavelength isλ then the speed of wave isv = f λ = (4.8 Hz) (3 9.6 cm) ·1 m100 cm= 1.9008 m/s .keywords:002 10.0 pointsThe distance between two successive maximaof a certain transverse wave is 1.45 m. Sup-pose a maximum passes some point at t = 0,and eight more crests, or maxima, pass thatgiven point along the direction of travel in thenext 1 3.3 s.Calculate the wave speed.Correct answer: 0.87218 m/s.Explanation:Let : λ = 1.45 m ,t = 13.3 s , andn = 8 .The frequency of the transverse wave isf =nt=813.3 s= 0.601504 Hz .The wave speed then isv = λ f = (1.45 m)(0.601504 Hz)=0.87218 m/s .003 10.0 pointsEarthquakes produce two kinds of seismicwaves: he l ongitudinal primary waves (calledP waves) and the transverse secondary waves(called S waves). Both S waves and P wavestravel through Earth’s crust and mantle, butat different speeds; the P waves are alwaysfaster than the S waves, but their exact speedsdep end on depth and location. For the pur-pose of this exercise, we assume t he P wave’sspeed to be 8 520 m/s while the S waves travelat a slower speed of 5940 m/s.If a seismic station detects a P wave andthen 53.4 s later detects an S wave, how faraway is the earthq uake center?Correct answer: 1047.48 km.Explanation:Let : vP= 8520 m/s ,vS= 5940 m/s , and∆t = 53.4 s .Suppose the earthquake happens at time t = 0at some distance d. The P wave and theS wave are both emitted at the same timet = 0, but they arrive at different t imes, re-spectively tP=dvPand tS=dvS. The S waveis slower, so it arr ives later than the P wave,the time difference being∆t =dvS−dvP=d (vP− vS)vPvS.Consequently, given this time difference andthe two waves’ speeds vPand vS, the earth-quake center isd =vPvS∆tvP− vS=(8520 m/s) (5940 m/s) (53.4 s)8520 m/s − 5940 m/s·1 km1000 m= 1047.48 kmkean (msk955) – Homework 08 – yao – (56725) 2away from the seismic stat ion.004 10.0 pointsA transverse wave has a wave functiony = (0.2 m) sinn2 π(2 m−1) x − (2 s−1) t owhere x and y are in meters and t is in seconds.This wave i s1. a standing wave of maximal amplitude2 m, wavelength 0.2 m and frequency 4π Hz =6.28 Hz.2. a standing wave of maximal amplitude0.2 m, wavelength 0.25 m and frequency2π Hz = 3.14 Hz.3. a traveling wave of amplitude 0.5 m, wave-length 0.2 m and frequency 2 Hz.4. a standing wave of maximal amplitude0.4 m, wavelength1 m4π= 0.08 m and fre-quency 2 Hz.5. a standing wave of maximal amplitude0.2 m, wavelength 0.5 m a nd frequency2 H z.6. a traveling wave of amplitude 2 m, wave-length 0.4 m and frequency 60 Hz.7. a traveling wave of amplitude 0.2 m, wave-length 0.5 m and frequency 2 Hz. correct8. a traveling wave of amplitude 0.2 m, wave-length 0.5 m and frequency 0.5 H z.9. a traveling wave of amplitude 0.2 m,wavelength 4π m = 12.5 m and frequency2π Hz = 6.28 Hz.10. a traveling wave of amplitude 0.2 m, wave-length 2 m and frequency 2 Hz.Explanation:Let : A = 0.2 m ,ω = 2 π2 s−1, andk = 2 π2 m−1.The wave in question has the formy(x, t) = A sin(k x − ω t)so it is a traveling wave. The frequency isf =ω2 π=2 π2 s−12 π= 2 Hzand the wavelength i sλ =2 πk=12 π (2 m−1)= 0.5 m .005 (part 1 of 2) 10.0 pointsA steel piano wire is 0.7 m long and has amass of 70 g. It is stretched wi th a tension of400 N.What is the speed of transverse waves onthe wire?Correct answer: 63.2456 m/s.Explanation:Let : F = 400 N ,L = 0.7 m , andm = 70 g = 0.07 kg .The speed of transverse waves o n the wire isgiven byv =sFµ=vuutFmL=rF Lm=s(400 N) (0.7 m)0.07 kg=63.2456 m/s .006 (part 2 of 2) 10.0 pointsTo reduce the wave speed by a factor of 2without changing the tension, what mass ofcopper wire would have to be wrapped aroundthe steel wire?Correct answer: 210 g.Explanation:kean (msk955) – Homework 08 – yao – (56725) 3Let : v = 2 v′andm = 70 g = 0.07 kg .The new wave speed will bev′=rF Lm′∝r1m′, sovv′= 2 =rm′mm′= 4 m .The amount of copper w ire required is∆m = m′− m = 3 m = 3 (0.07 kg)=210 g .keywords:007 10.0 pointsA point source emits sound waves with apower output o f 140 W.At what distance will the decibel reading be130 dB, w hi ch is noise level of a loud indoorrock concert?Correct answer: 1.0555 m.Explanation:Let : I0= 1 × 10−12W/m2,P = 140 W , andβ = 1 30 dB .From the definition of decibelβ = 1 0 logII0I = I010β/10.At a distance r from the source point, thesound i ntensity isI =P4 π r2P = 4 π r2I = 4 π r2I010β/10r =rP4 π I010−β/10=s140 W4 π (1 × 10−12W/m2)10−13=1.0555 m .008 10.0 pointsA typical decibel level for a buzzing mosquitois 40 dB, and normal conversation is approxi-mately 50 dB.How many buzzing mosquit oes will producea sound intensity equal to that of normalconversation?Correct answer: 10.Explanation:Let : βmos= 40 dB ,βcon= 50 dB ,Imos= 1.0 × 10−8W/m2, andIcon= 1.0 × 10−7W/m2.n Imos= Iconn =IconImos=1.0 × 10−7W/m21.0 × 10−8W/m2=10 .009 10.0 pointsHeard at a certain distance, a car horn emitsa sound with a loudness of 50 dB.If instead there were 100 i dentical cars allsounding their horns at this certain distance,how loud would the sound b e?1. 90 dB2. 500 dB3. 70 dB correct4. 5000 dB5. 150 dBkean (msk955) – Homework 08 – yao – (56725) 46. 100 dB7. 5 dB8. still 50 dBExplanation:The sound level in the case of one car isβ = (10 dB) logII0= 50 dB .Thus when 1 0 0 identical cars sound theirhorns, the loudness becomesβ′= (10 dB) log100 II0= (10 dB)log(100) + logII0= (10 dB) log 102+ (10 dB) logII0= (10 dB) 2 + 50 dB = 70 dB .010 10.0 pointsTwo separated sources emit si nusoidal trav-eling waves that have the same wavelength λand are in phase at t heir respective sources.One travels at a distance ℓ1to get to theobserva tion point, while the other travels adistance ℓ2. The ampli tude is at a minimumat the observa tion point if ℓ1− ℓ2is:1. a mult iple of π2. a mult iple of λ3. an odd multiple of12π4. an odd multiple of12λ correct5. an odd multiple