The Acoustics of the Dubstep-as-a-series-of-records video
So, this video has been making the rounds today, and it’s just incredible, you need to watch it. In short, a very clever producer of music videos has cut a series of records to match the waveform of a dubstep song, and arranged them on a pole in time with the music.
I sent this video to my undergraduate phonetics class today, and one student emailed me back, asking “How accurate would that representation of the waveform be? What would it sound like if you played it back?”. Well, I have a conference call to prepare for, and I don’t want to be doing that right now, so I decided to go full nerd and do a bit of analysis instead and answer that question.
Let’s assume that the records were cut extremely carefully, and that every record represents the amplitude at that moment perfectly. A stretch, but they seem to have done their homework. We’re also assuming (as seems to be the case) that the records are cut to a flat edge (rather than representing additional detail. Even with that assumption, does this represent the sound well? Let’s do the math.
The first record goes on at 27 seconds, the last at 1:52. That’s 85 seconds of audio. Those 85 seconds are represented by 960 vinyl records. This is a new record representing a slice of the waveform roughly every 0.088 seconds (the period). Using our frequency formula (f=1/0.066), that’s a record addition rate (sampling rate) of roughly 11 Hz. Bam.
So, we have a new amplitude sample 11 times per second. Now, we’re basically treating this as a digital audio file, which samples amplitude repeatedly at a given rate. The Nyquist theorem (which is awesome) states that the highest frequency captured accurately by a given sampling rate (the “Nyquist Frequency”) is 1/2 of the sampling rate.
For your average CD, your sampling rate is 44,100 Hz, which has a nyquist frequency of 22,050 Hz. This means that the highest frequency captured accurately in the recording is 22,050 Hz. Higher than humans can hear, but your pet dolphin isn’t impressed by your “Hi-Fi” stereo.
In this video, our sampling rate is only 11 Hz (11 records per second of audio). This means that the Nyquist frequency would be 5.5 Hz. Which means that if you were to “play back” the waveform here by pulsing the amplitude shown by the next record every 0.088 seconds, it’d be completely inaudible to humans (who can only hear 20Hz and above) as periodic sounds, and would just sound like a series of bursts of noise.
In effect, they’re representing a zoomed-out version of the waveform, which is incredibly awesome looking, but not a very good way to store audio information for playback. But that doesn’t take away from the fact that this is one of the more creative things done in a music video in a long time. So, I’d still chalk this one up as a victory for the producers of this video.
Alright, alright. I’ll go prepare for my conference call.