What does a reading of -3 dB indicate?

A reading of -3 dB indicates that the intensity has decreased by half. The decibel (dB) scale is a logarithmic measurement used to quantify sound intensity, signal power, or other related concepts, where a negative value signifies a reduction in the parameter being measured.

In terms of intensity, the decibel change can be calculated using the formula:

[ \text{dB} = 10 \log_{10}\left(\frac{I_2}{I_1}\right) ]

where (I_2) is the final intensity and (I_1) is the initial intensity. A -3 dB change specifically indicates that:

[ -3 = 10 \log_{10}\left(\frac{I_2}{I_1}\right) ]

Through algebraic manipulation, this leads to the result that when intensity is reduced by 3 dB, it is half of the original intensity:

[ \frac{I_2}{I_1} = 10^{-3/10} \approx 0.5 ]

This computation directly shows that the intensity is halved. Therefore, a -3 dB reading unequivocally points to a