Question

You are trying to decide between two new stereo amplifiers. One is rated at 75 W per channel and the other is rated at 120 W per channel. In terms of dB, how much louder will the more powerful amplifier be when both are producing sound at their maximum levels?

Short answer

The sound level produced by both amplifiers at their maximum levels is \(2.04\;{\rm{dB}}\).

Step-by-step solution

Understanding the concept of sound level

The logarithmic ratio between sound intensity and threshold intensity gives the sound level.

Given data

The intensity of sound produced by amplifier 1 per channel is \({I_1} = 75\;{\rm{W}}\).

The intensity of sound produced by amplifier 2 per channel is \({I_2} = 120\;{\rm{W}}\).

Evaluating the sound level produced by both amplifiers

The sound level produced by both amplifiers at their maximum levels is calculated below:

\(\beta = 10\log \left( {\frac{{{I_2}}}{{{I_1}}}} \right)\)

Substitute the values in the above equation.

\(\begin{aligned}{c}\beta = 10\log \left( {\frac{{120\;{\rm{W}}}}{{75\;{\rm{W}}}}} \right)\\\beta = 2.04\;{\rm{dB}}\end{aligned}\)

Hence, the sound level produced by both amplifiers at their maximum levels is \(2.04\;{\rm{dB}}\).