Question

human beings can typically detect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount

Answer 1

Answer: 1.25

Explanation:

The ratio of the amplitude of the sound can be calculated using the wave intensity by squaring the amplitude of the two wave particles.

Let the sound level be S2 and S1 and intensities be I1 and I2

Difference in sound level(S) = S2 - S1 = 2dB

Using the relationship between difference in sound level and Intensity

S2 - S1 = 10log(I2 ÷ I1)

Note : Intensity is the square of the amplitude of sound

Therefore,

I1 = A1^2 and I2 = A2^2

Substituting the values into the equation:

S2 - S1 = 10log (I2 ÷ I1)

2dB = 10log (A2^2 ÷ A1^2)

2dB = 10log(A2 ÷ A1)^2

2 dB= 20log(A2 ÷ A1)

2÷20 = log (A2 ÷ A1)

0.1 = log (A2 ÷ A1)

(A2 ÷ A1) = 10^0.1

A2/A1 = 1.25