Question

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3. What is the intensity level in decibels for an intensity sound wave of (a) 10-10 W / m2 and (b) 10-2 W / m2?

4. While an ambulance is traveling east on a highway at a speed of 33.5m / s (75mph), its siren emits sound at a frequency of 400Hz. How often will a person traveling in the car ride west at 24.6m / s (55mph) (a) while the car approaches the ambulance and (b) while the car moves away from the ambulance?

Answer 1

3) The decibel intensity of a sound of intensity I is given by I(dB) = 10.log₁₀( I / I₀ ), where I₀ = 10^-12 W/m²

a) for I₁ = 10^-10 W/m², I(dB)₁ = 10. log( 10^-10 / 10^-12 ) = 20 decibels.

b) for I₂ = 10^-2 W/m², I(dB)₂ = 10.log( 10^-2 / 10^-12 ) = 100 decibels.

4) Here we use the Doppler's effect formula, Apparent freqeuncy F = [ (C+V_l) / (C+V_s) ] * f_o , Here V_l is the speed of the listener and it will be negative when he is moving away from the sound source, V_s is speed of source and it will be negative when source is moving toward the listener. C is speed of sound i.e 343 m/sec

Here we are given V_s = 33.5 m/sec due east, V_l = 24.6 m/sec due west, and originbal frequency f₀ = 400 Hz,

a) So when car approaches ambulance apparent frequency will be F₁ = [(343+24.6) / (343 - 33.5)] * 400 = [367.6 / 309.5] * 400 So F₁ = 475.1 Hz

b) When car is moving away from ambulance, F₂ = [(343-24.6) / (343 + 33.5)] * 400 = [318.4 / 376.5] * 400 So F₂ = 338.27 Hz