Question

The sound level L is

Where

Q = Measured quantity of sound pressure or sound intensity

Q₀ = Reference standard quantity of sound pressure

1. \({\log _{10}}\frac{{{Q_0}}}{Q}\left( {bels} \right)\)
2. \(20{\log _{10}}\frac{Q}{{{Q_0}}}\left( {bels} \right)\)
3. \({\log _{10}}\frac{Q}{{{Q_0}}}\left( {bels} \right)\)
4. \(20\frac{Q}{{{Q_0}}} + {\log _{10}}\frac{Q}{{{Q_0}}}\left( {bels} \right)\)

Answer 1

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

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