My previous post about the Doppler effect provides a good explanation as to what the Doppler effect is and the properties of sound that cause it to exist. I decided to collect some data to try to provide a more tangible example of the Doppler effect at work in both a simple system and in a Leslie cabinet.
To get a simple measurement of the Doppler effect, working with Jon Bretan, we attached a battery to a simple buzzer so that it was constantly producing sound and tied some string tightly around these two objects. With the buzzer tied to one end of the string, we were able to spin it in a circle. We recorded the changes in sound pressure over the span of one second, and we also recorded the stationary buzzer to act as a control. This is our initial data set:
Both the uniformity of the sound pressure data and the thin band of frequencies on the fast Fourier transform show the purity of the tone generated by the stationary buzzer. In contrast, the complicated shape of the sound pressure data for the rotating buzzer reveals a much more complicated sound wave. The breadth of frequencies shown on the fast Fourier transform best illustrates the Doppler effect. Because the buzzer was moving relatively to the microphone, the microphone picked up many more frequencies than the central pitch generated by the stationary buzzer. The mix of frequencies appear to be fairly uniform, but they are not perfectly uniform due to aspects of the rotation that were not controlled, such as ensuring that the buzzer rotated in the same plane as the microphone. Despite this, the data set gives a very clear example of the Doppler effect at work. Using the same methodology, I recorded the frequencies produced by a popular piece of music equipment.
The Leslie cabinet, as I mentioned in my previous post about the Doppler effect, is an amplifier with a very unique way of producing sound. The cabinet is divided into two sections, the horn and the drum, which produce high and low pitches respectively. The speaker in each section has two speeds of rotation, fast and slow, and can also be stationary. I played a sine tone at 440 hertz through the Leslie cabinet and used a microphone to collect data for both the horn and the drum at both speeds. Additionally, I recorded sound produced by the stationary setting as a control.
The following data comes from the sound produced by the horn (higher pitch speaker):
The data appears similar to the simple Doppler generator as the faster rotating speaker produces a wider spread of frequencies. The logarithmic scaling of the Y axis reveals the incredible level of symmetry of the frequency spread. This reveals an important distinction between the simple spinning buzzer and the Leslie cabinet and suggests that the uniform rotation of the Leslie cabinet produces the uniform frequency spread that was recorded.
The following data comes from the sound produced by the drum (lower pitch speaker):
Looking at the full frequency range, we are able to see the very low pitch produced by the drum as well as the central tone of the 440 hertz sine wave. We are also able to see the frequency spread caused by the Doppler effect.
When we look at the same frequency range as the horn data, we are able to clearly see the Doppler effect:
When we look at the same frequency range as the horn data, we are able to clearly see the Doppler effect:
The similarities in frequency spread that correspond to speed of rotation are a clear indicator of the Doppler effect in the Leslie cabinet. Again, we are able to see near uniformity in the symmetry of the frequency spread, especially for the fastest speed of rotation.
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