Question

A stereo amplifier is rated at 225 W output at 1000 Hz. The power output drops by 12 dB at 15 kHz. What is the power output in watts at 15 kHz?

Short answer

The ouput at 15 kHz is \(14\;{\rm{W}}\).

Step-by-step solution

Determination of power output

The power output subjected to a particular frequency can be determined using the equation of sound level. The intensity of the sound is proportional to the logarithmic ratio of power.

Given Information

Given data:

The rating of amplifier at 1000 Hz is \({p_{1000}} = 225\;{\rm{W}}\).

The level of sound is \(\beta = 12\;{\rm{dB}}\)

Evaluation of power output at 15 kHz

The value of ouput at 15 kHz can be calculated as:

\(\begin{aligned}{c}\beta &= 10\log \frac{{{p_{15}}}}{{{p_{1000}}}}\\ - 12 &= 10\log \frac{{{p_{15}}}}{{\left( {225\;{\rm{W}}} \right)}}\\ - 1.2 &= \log \frac{{{p_{15}}}}{{\left( {225\;{\rm{W}}} \right)}}\\{10^{ - 1.2}} &= \frac{{{p_{15}}}}{{\left( {225\;{\rm{W}}} \right)}}\\{p_{15}} &= 225\left( {{{10}^{ - 1.2}}} \right)\\ &= 14\;{\rm{W}}\end{aligned}\)

Thus, the ouput at 15 kHz is \(14\;{\rm{W}}\).