The Lambda Effect

Wavelength is precipitated by frequency, instead of the other way around.

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After I published my article on big drivers and low frequencies, I got an email. In that email was a query about why bass drivers don’t have to move, say, 22.5 feet in order to produce a 50 Hz tone.

It’s a fair question, especially when you look at things like organ pipes. Making a low tone requires a big, long pipe, so why don’t bass drivers have to have a similarly long excursion – that is, forward-to-back movement measured in feet or meters?

We’re Trying To Do Different Things

The first part of the answer has to do with different technologies of sound production. In an organ or human-held wind instrument, we’re trying to produce a tone by setting up a vibration in an air column. The vibrating mass of air IS the “driver,” in a practical sense. With a conventional loudspeaker, the point is to produce a tone by vibrating a diapragm into free air. Although we may use all manner of horn-loading to create an acoustical impedance transformer, we’re not really trying to turn the loudspeaker into a flute or trumpet. We’re just trying to make the loudspeaker “play nice” with the surrounding atmosphere.

You might say that, in a wind instrument, air is the source AND the medium. With a speaker, air is really the medium only. A vibration is created and travels away from the source, and that’s the key to the second part of the answer.

Counting Cars

Let’s say that you have two parking garages full of cars. These parking garages are magic, because vehicles exiting them come out the exit ramp at a preset speed of 40 mph, and then hold that speed. Your task is to count how many cars come out of each parking garage every minute.

Parking garage #1 lets a car out every five seconds. Garage #2 lets a car out every 10 seconds. Garage #2 obviously has a lower frequency than #1: Over the course of a minute, #2 spits out 6 cars to #1’s 12.

Did you notice that measuring the distance between each car isn’t necessary for the “count how many cars exit each minute” objective? The frequency is what matters to you. The distance between cars is necessarily affected by the frequency that they exit the garages, but that’s not what you’re directly looking at. The slower garage has a larger distance between cars, of course, which is caused by it taking longer to disgorge an automobile. If all the vehicles are traveling at the same speed, then a lower exit frequency results in a longer space between each of those vehicles.

My example is definitely simplified. The speed of sound isn’t exactly the same everywhere, all the time. All kinds of interesting “lensing” phenomena can occur when sound waves travel across a temperature gradient and change velocity. At a coarse level, though, the principle is the same. Perceived pitch has to do with frequency, as opposed to wavelength. We don’t need a minimum amount of path length in order to hear a certain tone, which is why headphones can produce serious bottom end while being right up next to (or even inside) your ear canal. In any conventional, live-sound application I can think of, frequency precipitates wavelength instead of the opposite. A vibrating object creates pressure waves that travel outward at a certain speed, and so the disturbances caused by very fast vibrations don’t get very far before the next amplitude cycle begins.

(Even when encountering the Doppler effect, which is a special case of changing wavelength by moving the source or listener relative to each other, the thing that matters to our perceiving a drop in pitch is how often the positive and negative pressure fluctuations arrive.)

Wavelength matters a great deal to acoustics, but it doesn’t produce frequency as far as a driver sitting in a box concerns us. Rather, frequency produces wavelength. “F” is the cause, and “lambda” is the effect.