Peak Power vs Average Power

[Physicslearner500039]

Homework Statement

An electric hair dryer is rated at 1500 W (the average power) at 120 V (the rms voltage). Calculate (a) the resistance, (b) the rms current, and (c) the maximum instantaneous power. Assume that
the dryer is a pure resistor. (The heating element acts as a resistor.)

Relevant Equations

P = $V_{rms}*I_{rms}$

It is an example problem and i could understand the solution and the answers are
$R = \frac {V_{rms}^2} {P_{av} } = 9.6 \Omega$
$I_{rms} = \frac {P_{av}} {V_{rms}} = 12.5 A$
$p_{max} = VI = 2P_{av} = 3000 W$
But main problem is the statement given by the author below the solution which says "Some unscrupulous manufacturers of stereo amplifiers advertise the peak power output rather than the lower average value". My understanding is something like the output power is a sine wave, since it is a pure resistance circuit the power keeps fluctuating from min value to max value and the user should actually feel the sound decreasing from min to max sine wave value. Is it correct? Can i clamp the output power coming from the speaker that is the audio to always generate Peak value (3000 W)? The manufacturer should specify the average power or the peak power? Please advise.

 

[Steve4Physics]

Hi. I notice you haven’t any replies yet. That’s unusual and I think I know why. What you have written contains major mistakes/misconceptions and it is hard to explain them. But let me have a go.

My understanding is something like the output power is a sine wave, since it is a pure resistance circuit the power keeps fluctuating from min value to max value and the user should actually feel the sound decreasing from min to max sine wave value. Is it correct?

No. Let's take a simple example of an audio system playing a single pure musical note (say an 'A' which has frequency of 440Hz). The voltage applied to the loudspeaker oscillates 440 times (cycles) each second. A single cycle take $\frac{1}{440}$s, which is 0.0023s approximately (this is the 'period').

Suppose the peak voltage is 5V. Each cycle, the voltage goes from 0V to 5V, then to zero, then to -5V and than back to 0V. The power depends on voltage squared so hits a maximum twice each cycle (for 5V and for -5V). Most of the time the power is less than the peak power. The power is oscillating between zero and Pmax 880 times each second.

The listener can't tell this is happening as these oscillations are far too fast to hear; the listener hears a smooth, steady note of power Prms (which Pmax/2)

Can i clamp the output power coming from the speaker that is the audio to always generate Peak value (3000 W)? The manufacturer should specify the average power or the peak power?

No. The power varies (many time per second) as explained above. To 'clamp' the output power you would have to apply a steady voltage (DC) which would produce no sound (and damage the speaker due to overheating).

3000W for an audio system is huge (rock-band level).

A manufacturer should include the following sort of information for a stated power:
- if the power is input (electrical) power or output (audio) power, as these are very different, as audio system efficiencies can be very small;
- if the power is peak power or rms power;
- to what frequency the power level figures apply.

This video should help understand rms and peak values better: