Question

four of your neighbors are all mowing their lawns using identical "Super-Silent" mowers. When they are each 20 m from your open bedroom window, what is the intensity level of the sound in your bedroom? You can neglect any absorption, reflection, or interference of the sound. The lowest detectable intensity is 1.0 × 10-12 W/m2. The intensity level of a "Super-Silent" power lawn mower at a distance of 1.0 m is 100 dB. You wake up one morning to find that four of your neighbors are all mowing their lawns using identical "Super-Silent" mowers. When they are each 20 m from your open bedroom window, what is the intensity level of the sound in your bedroom? You can neglect any absorption, reflection, or interference of the sound. The lowest detectable intensity is 1.0 × 10-12 W/m2. 40 dB 400 dB 104 dB 50 dB 80 dB

Answer 1

Answer:

The 80 dB option is correct.

Explanation:

The sound intensity level is converted to sound intensity with the formula

[D] = 10 log (I/I₀)

I₀ = 10⁻¹² W/m²

[D] = 100 dB

100 = 10 log (I/I₀)

Log (I/I₀) = 10

(I/I₀) = 10¹⁰

I = I₀ × 10¹⁰ = 10⁻¹² × 10¹⁰ = 10⁻² W/m²

But sound intensity varies inversely as the square of the distance of the sound.

I ∝ (1/d²)

I = k/d²

At d = 1 m away, I = 10⁻² W/m²

0.01 = k/1

k = 0.01 W

At d = 20 m, we solve for I

I = 0.01/20² = 2.5 × 10⁻⁵ W/m²

4 people mowing their lawns at the same time,

I = 4 × 2.5 × 10⁻⁵ = 10⁻⁴ W/m⁻²

The sound intensity level in decibels is given as

[D] = 10 log (I/I₀)

[D] = 10 log (10⁻⁴/10⁻¹²)

[D] = 10 log (10⁸)

[D] = 10 × 8 = 80dB