• :00Days
• :00Hours
• :00Mins
• 00Seconds
A new era for learning is coming soon

Suggested languages for you:

Americas

Europe

12-75GP

Expert-verified
Found in: Page 328

### Physics Principles with Applications

Book edition 7th
Author(s) Douglas C. Giancoli
Pages 978 pages
ISBN 978-0321625922

# 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?

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

See the 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 $$14\;{\rm{W}}$$.