The sound level L is

Where

Q = Measured quantity of sound pressure or sound intensity

Q_{0} = Reference standard quantity of sound pressure

This question was previously asked in

UPSC ESE 2020 Paper 1

Option 3 : \({\log _{10}}\frac{Q}{{{Q_0}}}\left( {bels} \right)\)

CT 3: Building Materials

2962

10 Questions
20 Marks
12 Mins

The pressure level is a ratio of sound pressure to a base level.

**Sound pressure level (SPL)** is a logarithmic measure of the RMS sound pressure of a sound relative to a reference value (the threshold of hearing). It is measured in decibels (dB).

The formula to find the sound level is given by

\(SPL\left( {dB} \right) = 10\;{\log _{10}}{\left( {\frac{Q}{{{Q_0}}}} \right)^2}\)

\( = 20{\log _{10}}\left( {\frac{Q}{{{Q_0}}}} \right)\)

We have

\(1 decibel = 10 \times bels\)

So, in terms of bells,

\( L = 2{\log _{10}}\left( {\frac{Q}{{{Q_0}}}} \right)\)

Where

Q = Measured quantity of sound pressure or sound intensity

Q0 = Reference standard quantity of sound pressure

__Note:__

There is no correct answer, so we marked the official answer given by UPSC