Question

By what factor must the amplitude of a sound wave be increased in order to increase the intensity by a factor of 9?a. 9 b. 2 c. 4 d. 3

Answer 1

3 times option (d) is correct

Step-by-step explanation:

Initial intensity = Io

final intensity = 9 Io

initial amplitude = A

Final amplitude = ?

let the final amplitude is A'.

Intensity of a wave is directly proportional to the square of the amplitude of the wave.

I ∝ A²

So, Io ∝ A² ... (1)

9Io ∝ A'² .... (2)

Divide (2) by (1)

9 = A'²/A²

A' = 3 A

So, the amplitude becomes 3 times.

Answer 2

option D

Step-by-step explanation:

given,

`intensity\ \alpha \ (Amplitude)^2`

increase the intensity by factor of 9

I₁ = I₀

I₂ = 9 I₀

now,

`(I_1)/(I_2)=(A_1^2)/(A_2^2)`

`(I_0)/(9I_0)=((A_1)/(A_2))^2`

`((A_1)/(A_2))^2=(1)/(9)`

`(A_1)/(A_2)=(1)/(3)`

A₂ = 3 A₁

hence, amplitude increase with the factor of 3

so, the correct answer is option D