signal clipping
At low volumes, the square wave should be louder because it basically has more overall amplitude over the entire wave cycle. If you are using your amp to maximum potential however, you will find that the sine wave should be louder, unless you are burping well below your note.
Very few people realize that a square wave is actually a higher frequency than a sine wave oscillating with the same period. This is due to the nature of the way a square wave is constructed.
If you look at a sine wave you find a single peak every period. If we take the period as 2pi, we find that the slope is equal to one at 0 and pi, with the peak occuring at 0.5pi. To turn this signal into a square wave, we must do two things:
1. Extend the peak to cover an entire half period at the same amplitude on both sides of the x-axis
2. Increase the slope at 0 at pi to infinite in order to have an instantaneous change
If we take our sine wave and add a signal with 1/3 the magnitude and 1/3 the period { (1/3)sin(3X) } we find our graph now has two peaks for each half period and the slope has increased in order to reach the maximum sooner. Now if we add (1/5)sin(5X), we find 3 peaks and an even greater slope.
If we continue to take this series to infinite, we eventually find ourself with a square wave. This mean that if you have a square wave at 100 hz and 1000 watts of power are going into the 100 hz portion of the signal, you are also putting 333 watts into a 300hz tone, 200 watts into a 500 hz tone, 145 watts into a 700 hz tone, and so on.
We can see this result by using a spectrum analyser to take the Fourier transform of each signal (plotting it vs. frequency rather than time)
For a clean sine wave we find one pulse at 100 hz, while the square wave will produce a series of pulses at the odd frequencies as well. These odd frequencies are essentially wasted power because they will not produce maximum output in a properly tuned enclosure.
Amplifiers are also more attuned to sine waves due to their continous nature. A sine wave is considered to be the most continuous oscillating signal because its derivitaves are simply a time-domain shift of the original signal. This makes it every easy for the amp to get the signal to the speakers with very little disortion.
If we look at a square wave, it has a derivitave of 0 at all points expect 0 and pi, where the derivitive is momentarily infinite. This gives a square wave a discrete component, which, when analysed by an analog system such as an amplifier, creates further distortion.
So, in summary, if your box is louder with a square wave, you are either not tuned properly, not played the right frequency for you set-up, or you are not getting full power out of your amp with the sine wave.
[ March 29, 2005, 02:28 PM: Message edited by: seege ]
Very few people realize that a square wave is actually a higher frequency than a sine wave oscillating with the same period. This is due to the nature of the way a square wave is constructed.
If you look at a sine wave you find a single peak every period. If we take the period as 2pi, we find that the slope is equal to one at 0 and pi, with the peak occuring at 0.5pi. To turn this signal into a square wave, we must do two things:
1. Extend the peak to cover an entire half period at the same amplitude on both sides of the x-axis
2. Increase the slope at 0 at pi to infinite in order to have an instantaneous change
If we take our sine wave and add a signal with 1/3 the magnitude and 1/3 the period { (1/3)sin(3X) } we find our graph now has two peaks for each half period and the slope has increased in order to reach the maximum sooner. Now if we add (1/5)sin(5X), we find 3 peaks and an even greater slope.
If we continue to take this series to infinite, we eventually find ourself with a square wave. This mean that if you have a square wave at 100 hz and 1000 watts of power are going into the 100 hz portion of the signal, you are also putting 333 watts into a 300hz tone, 200 watts into a 500 hz tone, 145 watts into a 700 hz tone, and so on.
We can see this result by using a spectrum analyser to take the Fourier transform of each signal (plotting it vs. frequency rather than time)
For a clean sine wave we find one pulse at 100 hz, while the square wave will produce a series of pulses at the odd frequencies as well. These odd frequencies are essentially wasted power because they will not produce maximum output in a properly tuned enclosure.
Amplifiers are also more attuned to sine waves due to their continous nature. A sine wave is considered to be the most continuous oscillating signal because its derivitaves are simply a time-domain shift of the original signal. This makes it every easy for the amp to get the signal to the speakers with very little disortion.
If we look at a square wave, it has a derivitave of 0 at all points expect 0 and pi, where the derivitive is momentarily infinite. This gives a square wave a discrete component, which, when analysed by an analog system such as an amplifier, creates further distortion.
So, in summary, if your box is louder with a square wave, you are either not tuned properly, not played the right frequency for you set-up, or you are not getting full power out of your amp with the sine wave.
[ March 29, 2005, 02:28 PM: Message edited by: seege ]
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