Question

Loudness of sound from a point source at
a distance R is 50 dB. If
the distance in doubled
then the new loudness value is
a) 25 dB 6) 125 dB c) 100dB
d) 44 dB​

Answer 1

Given :

Loudness of sound at distance R = 50 dB

To find :

Loudness value when the distance is doubled .

Solution :

Let the loudness at 2R be x .

The difference in loudness of sound = 10 × ㏒₁₀ $\frac{I_1}{I_2}$

where , I$_1$ and I$_2$ are intensities .

Intensity ∝ 1 / $R^2$

where , R is distance .

now ,

50 - x =  10 × ㏒₁₀ $\frac{4R^2}{R^2}$

=> 50 - x = 6      {approx.}

=> x = 44 dB     {approx.}

Loudness value when the distance is doubled is 44 dB approx .