# How much energy has square wave and sinewave of X Hz?

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#### tellMeDaBasix

##### Member level 1
energy of sine wave

I confused. Say I have both square wave and sinewave of X Hz.

Now I see both have area unders curve the same.

However, in all experiments I do, I see square wave seem to have more power!

Basics tell me square wave have not only sinewave of X Hz but also odd harmonics of X?

Am I right? Is that why square wave of X Hz seem to have more power than sinewave of X Hz?

energy sine wave

If you actually mean same area under the curve, the sine wave has a higher power.If the square wave has an amplitude of 1, the sine wave must have a peak amplitude of pi/2 for same area. Square wave's power is 1.0 but sine wave's power is 1.11 then.

You don't have to refer to spectral components to calculate the power, simply evaluate the integral of squared amplitude.

square wave power

a square-wave has exactly twice as much power as a sine-wave if they both have the same p-p voltage.

The harmonics of a square-wave add to produce exactly as much power as the fundamental.

The square-wave is basically a switched DC voltage so its power is V peak squared/R load.

square sine wave

Audioguru, what you say match with meter output but I still confused. FvM know a lot and he say something other.

What is correct? Wikipedia entry not show anything :-(

sine wave squared

I based my calculation of the square wave fourier series, listed in any profound mathematical handbook. It's (for a squarewave amplitude of h):

$f(x) = \frac{4h}{\pi}(sin x + \frac{1}{3}sin 3x + \frac{1}{5}sin 5x...)$

For a square wave with an amplitude of 1, the fundamental is 1.27, so it's relative energy share is 81%.

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### tellMeDaBasix

Points: 2
energy in sine wave

A one line solution is to speak in terms of area under the curve of v square plot for comparison of such situations.
This is subject to
2. Same frequency of square and sine waves. Else long time integration.
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energy of square wave

tellMeDaBasix,
Consider a sine wave voltage with a peak amplitude of 1V driving a 1 Ohm load. The RMS value of the sine wave is .707V. The power = V^2/R = 0.5W. The average value of the sine wave is 2/pi = .637.
.
Now consider a square wave with the same average value of .637. The RMS and average values of a square wave are the same (.637 in our case). The power dissipated by the 1 Ohm load is V^2/R = (.637^2) = .406W.
.Conclusion: The sine wave has more power.
Regards,
Kral

### tellMeDaBasix

Points: 2
area of sine wave

OK.. but let me tell you whay I say square have more power.

I connect speaker to electret mic. Mic connected to opmp and then to dso.

1. Now when I feed 5Vpp sine wave I get 2Vpp on DSO.

2. Now when I feed 5Vpp square wave I get 3.2Vpp on DSO.

You see my troubles :-(

power of square wave same as power of sine wave

A speaker connected to an electret mic does not do anything without an amplifier.
A speaker cannot be driven by an opamp.
What is a"DSO"?

energy of sine

TellMeeDaBasix,
In your original post, you were considering a sine wave and a square wave with equal areas (average values). In your last question, you are considering a sine wave and a square wave with equal peak to peak values. In this case, the square wave has a higher RMS value and hence more power will be delivered to the load (speaker).
Regards,
Kral

square wave squared

DSO is a digital storage oscilloscope.

Like a CRO but has an function to save and modify waveforms/signals. It also has a facility to connect to computer and get pre stored waveforms.
It has 3 modes of operation.
1. Free running mode.
2. Store
3. auto store... or something I dont exactly remember the modes

calculating the energy of a sine wave

Your acoustic signal chain adds an arbitray frequency characteristic to your setup. If you get a higher microphone signal level, this hasn't to do with "power" of the squarewave. Apparently the signal chain is preferring the harmonics to the fundamental.

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