A 3 dB gain in intensity indicates what change?

A 3 dB gain in intensity represents a doubling of intensity. This is based on the logarithmic nature of the decibel (dB) scale, which is commonly used in acoustics and electronics to express ratios of power or intensity.

When we refer to a gain of 3 dB, it signifies that the intensity has increased to twice its original value. This is derived from the formula for calculating decibels in relation to intensity, which is:

[

\text{Gain (dB)} = 10 \times \log_{10} \left( \frac{I_f}{I_i} \right)

]

In this case, (I_f) is the final intensity and (I_i) is the initial intensity. By rearranging this formula to find the ratio when the gain is 3 dB, it can be shown that:

[

\frac{I_f}{I_i} = 10^{3/10} \approx 2

]

This demonstrates that a 3 dB increase in intensity results in a doubling of the initial intensity. Hence, the statement that a 3 dB gain in intensity indicates a doubling is correct and aligns well with the principles of sound