Ch 17.1 #3

A flowerpot is knocked off a balcony 20.0 m above the sidewalk and falls toward an unsuspecting 1.75 m tall man who is standing below. How close to the sidewalk can the flower pot fall before it is too late for a warning shouted from the balcony to reach the man if the mans reaction time is 0.300 seconds.

v = Dx / Dt 343 = (20-1.75)/Dt tsound = 0.0532 sec treact = 0.3 sec tneed = 0.353 sec	d = ½ at^2 (20–1.75) = ½9.8t^2 tdrop = 1.93 sec	1.93 s–0.353 s = 1.58 s So the warning must be given within 1.58 sec for the man to respond in time.	The distance covered in 1.58 seconds is d = ½ a t^2 d = ½ 9.8 1.58^2 d = 12.2 m
So the pot is 20 – 12.2 meters above the ground = 7.82 meters

Ch 17.2 class

We’ve decided we want to create a sound wave in class that has displacement amplitude of 1 micron (10^-6 m). We don’t want the pressure amplitude to be greater than 2.00 N/m². What is the minimum wavelength?

ΔPmax = ρ v (ω) smax ΔPmax = ρv(2πv/λ) smax λ = 2π ρ v^2 smax /ΔPmax λ = 2π(1.17) 343^2 10^-6 / 2 λ = 0.432 meters

ω = 2π f ω = 2π(v/λ) note: density of dry air at 0°C is 1.29 kg/m^3, but then v = 331 m/s

Ch 17.3 baby

You are in a movie theater. The sound in one scene is at approximately 80.0 dB. There is a baby in the next row that crys at 76 dB because of this loud noise. (a) What sound intensity do you hear? (b)What is the sound level in dB?

β = 10 log (I / Io) 80 = 10log(Imovie/10^-12) Imovie = 10 x 10^-5 W/m^2	β = 10 log (I / Io) 76 = 10log(Icry/10^-12) Icry = 3.98 x 10^-5 W/m^2	(b) β = 10 log (I / Io) β = 10log(13.98 x 10^-5 /10^-12) β = 81.5 dB
(a) I = Imovie + Icry I = 13.98 x 10^-5 W/m^2

Ch 17.4 car

At a raceway you hear the frequency of a racecar as 600 Hz approaching toward you. After the car passes, the observed frequency of the siren is 400 Hz. What is the speed of the car?

From lecture notes f’ / v’ = f / v Toward: v ’ = v + vo Away: v ’ = v - vo

Toward: 600/(340+vo) = f / 340 Away: 400/(340-vo) = f / 340

600/(340+vo) = 400/(340-vo) 1.5(340-vo) = 340+vo 170 = 2.5 vo vo = 68.0 m/s

Ch 17.4 #47 A supersonic jet traveling at Mach 3.00 at an altitude of 20000 m is directly over a person at time t = 0. (a) How long will it be before the person encounters the shock wave? (b) Where will the plane be when it is finally heard? (Let speed of sound in air be 335 m/s.)
sin q = v / vs sin q = 335 / 3(335) q = 19.5°	tan q = h / x tan 19.5° = 20000 / x x = 5.66 x 10^4 meters		v = Dx / Dt 3(335) = 5.66 x 10^4 / Dt t = 56.3 sec

Ch 17.5 #49	Only two recording channels are required to give the illusion of sound coming from any point located between two “stereo” speakers. At the time of recording if the same signal is recorded in both channels, a listener will hear it coming from a single direction halfway between the two speakers. Each of the eight singers during the “Do-Re-Mi” recording from The Sound of Music (Columbia records) can be heard at eight different locations. The brain can sense the direction of the sound by noting how much earlier a sound is heard in one ear than the other. Model your ears as two sensors 19.0 cm apart in a flat screen. If a sound from a distant source is heard 210 μs earlier in the left ear than the right, from what direction does it appear to originate?
If the source is to the left at angle θ from the direction you are facing, the sound must travel an extra distance, d sinθ, to reach your right ear as shown, where “d” is the distance between your ears.		v = d sinθ / Δt 343 = 0.19sinθ/210x10^-6 θ = 22.3°