Mystery Aircraft and Beat Frequencies

Antonov An-12BK. Image courtesy Richard Vandervord via Wikimedia Commons. CC BY-SA 4.0 International.

Didn't manage to get the camera out in time, but I noticed the distinctive beat frequency of multi-prop engines. (Quite loud for the altitude). I checked with FlightRadar24 and it was an Antonov An-12BK cargo aircraft, flying at 22,000 feet on a flight from Porto to Prestwick and operated by Ukrainian Cavok Airlines. The AN-12BK is a four-engine turboprop military transport aircraft, dating from the Soviet era.

What are beat frequencies?

 

When two sound waves of different frequencies interact, the waves add together and the variation in amplitude results in a tremolo effect; a periodic rise and fall in volume. (Basically the peaks or troughs combine and reinforce or cancel each other out. ) The phenomenon is sometimes noticed when two musical instruments with different pitches are played together. Beat frequencies also occur with radio waves, electrical signals and coherent light waves.

The animated GIF below show a red and green sound wave, initially at the same frequency and in phase. The two waves add together to form a blue sine wave that's greater in amplitude. As the frequency of the green wave slowly changes, the resultant blue waveform changes in amplitude, modulated by a beat frequency. See link also in the comments to a YouTube demo, showing the phenomenon with two tuning forks.

Anyone who's doing their Junior Cert will probably be able to do the maths and find the resultant of two sine waves of different frequencies added together, requiring the trigonometric identities at the end of the maths tables to do the calculations (Are these still available from the Government Publications Sales Office?)

 

More information on beat frequencies here:
https://en.wikipedia.org/wiki/Beat_(acoustics)

 

Beat frequency. The blue waveform is the sum of the red and green waves. Animated GIF courtesy Adjwilley via Wikimedia Commons. CC BY-SA 3.0 Unported.