Question

Two identical sounds A and B reach a point in the same phase. The resultant sound is C. The loudness of C is n dB higher than the loudness of A. The value of n is ______.

Options

• 2

• 3

• 4

• 6

Answer 1

Two identical sounds A and B reach a point in the same phase. The resultant sound is C. The loudness of C is n dB higher than the loudness of A. The value of n is 6.

Explanation:

If a is amplitude of sound from A and B each, then I_A = I_B= ka², where k is constant.

Loudness due to C (i.e., A + B)

=I_C

=K(2a)²=4I_A, where K is constant.

Loudness due to C (i.e., A + B)

=I_C

=K(2a)²⁼ 4I_A

∴ n= 10 log₁₀ `("I"_C/"I"_A)`

= 10 log₁₀ 4

= 10 log₁₀ 4

=10 × 0.6

=6