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Physics Principles with Applications
Found in: Page 328
Physics Principles with Applications

Physics Principles with Applications

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

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Short Answer

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

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 \(14\;{\rm{W}}\).

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