Question

QUESTION 1 (SOUND) :

a) A person holds a rifle horizontally and fires at a target. The bullet has a muzzle speed of 170 m/s, and the person hears the bullet strike the target 1.10 s after firing it. The air temperature is 73°F. What is the distance to the target?

b) Sound propagating through air at 29 °C passes through a vertical cold front into air that is 3.8 °C. If the sound has a frequency of 2500 Hz, by what percentage does its wavelength change in crossing the boundary?

Answer 1

(a) Bullet muzzle speed Vb = 170 m/s

Time interval in person hear t = 1.10 s

Temperature T = 73 + 273 = 346 K

Velocity of sound at 73 oC is Vs = 331.5 (346/273)^1/2 = 373.2 m/s

the distance to the target is d = (373.2 + 170)x1.10/2 = 298.76 m

(b) Frquency of sound n = 2500 Hz

Velocity of sound at 29 oC is V₂₉ = 331.5 (302/273)^1/2 = 348.66 m/s

wavelength at 29 oC is ₂₉ = V₂₉ /n = 348.66/2500 = 0.139 m

Velocity of sound at 29 oC is V_3.8 = 331.5 (276.8/273)^1/2 = 333.8 m/s

wavelength at 3.8 oC is _3.8 = V_3.8 /n = 333.8/2500 = 0.1335 m

Now percentage change in wavelength in crossing the boundary d = (₂₉ - _3.8)100/₂₉

    d = (0.139 - 0.1335)100/0.139 = 3.96%

percentage change in wavelength in crossing the boundary is 3.96%