December 2016 Newsletter: The Heart Shaped Bass

While everyone is in a holiday mood and waiting for the release of Star Wars-Rogue One, we would like to introduce a mysterious Force of a different sort: the Heart-Shaped Bass.  In physics class we learned that low frequency sounds have very long wavelengths.  They tend to propagate in all directions in a spherical shape unless there is a very large object to block or direct their progression.  Read on to learn more about how we harness the Force to transform the shape of the bass.
The wavelength of a 100 Hz tone is approximately 11 feet.  To direct a sound wave of this length, an object must have comparable dimensions to the wavelength of the sound.  For example, if a barrier is only 1 foot high, a 100 Hz sound wave would easily go around the barrier as if it wasn’t there.  Eleven feet doesn’t seem like much when we think about a highway

 sound barrier; however, in the world of audio systems, does this mean a loudspeaker, or more specifically the subwoofer, has to have a dimension of 11 feet to generate a directional 100 Hz tone?

Why do we want to control the directivity of low frequency sound? As an example, a subwoofer mounted at the proscenium of an auditorium would generate higher sound levels at the orchestra pit and stage than in the seating area simply because of the distances involved.  The graphic below is the predicted sound levels produced by a single
proscenium-mounted subwoofer.

 

A sound system like this is not favorable as the majority of the sound energy does not extend to the farthest seats.  Furthermore, if microphones are in use, they will likely cause low frequency feedback.

Do we really need a huge subwoofer to obtain directivity of low frequency sound energy?  Actually, no.  By taking advantage of the physics of waves, we can fight fire with fire, so to speak.  We can place a second subwoofer slightly behind the first one and generate the same sound, but out of phase and slightly out of synch with the first.  The two sound waves interact, and the superposition of their combined output creates a louder sound for the audience and cancellation at the stage.

The graphs below are the polar response of the subwoofers, with and without the Force.  The “sphere” has same sound level in all directions, but the “heart” is 20 dB higher in the front than at the back.  For reference, a 20 dB increase is perceived as 4 times as loud.

The formal term of this Force is called Cardioid Array.  With this technique in the same auditorium model, we get the following sound level plot:

Several other subwoofer steering techniques also use additional devices with proper placement and time alignment to take advantage of wave interference to create the desired directivity.  The Force doesn’t seem so mysterious once the behind-the-scene mathematics are revealed, but it’s still really cool.  May the Force be with you!

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