Question

You hear the dishwasher with a loudness of 40 dB and a siren outside

Answer 1

Answer:

The ratio of the amplitudes of siren to dishwasher is 10.

Explanation:

loudness of dishwasher = 40 dB

loudness of siren = 60 dB

let the intensity of dishwasher is I an the intensity of siren is I'.

Use the formula of intensity and decibels.

$dB = 10 log\frac{I}{I_o}\\\\40=10 log\frac{I}{I_o}\\\\4 = log\frac{I}{I_o}\\\\I = 10000 I_o$

And

$60=10 log\frac{I'}{I_o}\\\\60 = log\frac{I'}{I_o}\\\\I' = 1000000 I_o$

The intensity if proportional to the amplitude.

$\frac{A'}{A}=\sqrt\frac{1000000}{10000}\\\\\frac{A'}{A}= 10$