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

Answer:

option D

Explanation:

given,

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

increase the intensity by factor of 9

    I₁ = I₀

    I₂ = 9 I₀

now,

$\dfrac{I_1}{I_2}=\dfrac{A_1^2}{A_2^2}$

$\dfrac{I_0}{9I_0}=(\dfrac{A_1}{A_2})^2$

$(\dfrac{A_1}{A_2})^2=\dfrac{1}{9}$

$\dfrac{A_1}{A_2}=\dfrac{1}{3}$

      A₂ = 3 A₁

hence, amplitude increase with the factor of 3

so, the correct answer is option D

Answer 2

Answer:

3 times option (d) is correct

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.