What is the ratio of the displacement amplitudes of two sound waves given that they are both5.0 kHz but have a 3.0 dB intensity level difference?

The ratio of the displacement amplitudes of two sound waves is 1.16.

Explanation:

Given that,

Frequency = 5.0 kHz

Intensity level difference = 3.0 dB

We know that,

The sound intensity is inversely proportional to the square of distance.

The sound intensity for first wave is

...(I)

The sound intensity for second wave is

...(II)

We need to calculate the ratio of intensity

From equation (I) and (II)

Put the value into the formula

We need to calculate the ratio of the displacement

Using formula of displacement

Put the value into the formula

Hence, The ratio of the displacement amplitudes of two sound waves is 1.16.

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