Question

If the amplitude of a sound wave is increased to 4 times, then by how many times the intensity change?

Answer 1

Answer:

As another example, changing the amplitude from 1 unit to 4 units represents a 4-fold increase in the amplitude and is accompanied by a 16-fold (42) increase in the energy; thus 2 units of energy becomes 16 times bigger - 32 units.

Explanation:

Answer 2

Given:

The amplitude of a sound is increased by 4 times.

To Find:

Number of times of the change in intensity.

Solution:

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

Let the initial intensity be i and the final intensity after the amplitude is increased by 4 times be I.

$i \: \alpha \: {a}^{2}$

The amplitude is to be increased four times.

Therefore,

$I = ( {4a)}^{2}$

$I = 16 {a}^{2}$

$\frac{I}{i} = \frac{16 {a}^{2} }{ {a}^{2} }$

$\frac{I}{i} = 16$

$I = 16i$

The final intensity is 16 times the initial intensity.

Thus, if the amplitude of a sound wave is increased to 4 times, then the intensity changes by 16 times.