Robert Johnson's Delta Blues Inspire Physics

I really enjoy blues guitar and today my friend was telling me about how he had recently been listening to Robert Johnson. I told him that the quality of Robert Johnson's recordings bothered me, especially since I didn't think he had that great of a voice sans the lousy recordings (In case you don't know, Robert Johnson's music was recorded a long time ago with long out-of-date equipment). My friend then asked me if I had ever listened to his stuff slowed down and sent me this link.

For those of you too lazy to read it, like I would probably be, the guy says that he thinks Robert Johnson's music holds the proper pitch if you play it at 80% of the recorded speed. I listened to the slowed down recordings, and I do in fact like his voice a lot more in them.

This got me wondering why the speed at which audio is played back affects its frequency (and thus, pitch). I immediately thought of the equation v=f \lambda, but then I thought that didn't make sense, because it's not like we are actually changing the speed of sound.

So then I thought about this in terms of a casette and kind of took on the frame of reference of the microphone on it. I remember learning about how a casette player works from one of my high school physics teachers, but I don't remember much of it, so instead of talking about magnetic fields and all, I just decided to imagine the microphone read sine waves that describe the sound. Naturally, this is a ridiculous oversimplifacation, but hey, that's what physicists are known for.



So if I am a microphone, I see this sine wave printed onto this tape passing underneath me.


If we refer back to the equation v=f \lambda and this time think about v not as the velocity of sound in air, but as the velocity of this wave that is scrolling underneath the mic, things start to make sense. It's wavelength is constant, but if we increase the velocity at which it passes under the mic, its frequency will increase. Thus, hitting fast-forward will give us the chipmunk effect we all love to hate.

I'm not sure that what I said is an appropriate way to describe what is happening, but if it is, there are two things that are perplexing me.

1.) I would just assume that the two knobs on a casette player always turn with a constant rotational velocity, \omega, but to me, it seems like when the majority of the tape is on one side, that tape is coming off of the reel at a velocity, v=\omega r_2, which would be faster than the velocity at which the left reel could take in the tape when its reel radius, r_2L is smaller than r_2.

Am I viewing this wrong or are tapes just designed to compensate for this?


2.) I then imagined a record, as this is what Robert Johnson's music would have been recorded onto. I conceptually ran into the same wall. If a record spins around with a constant rotaional veloctiy, \omega, then the farther away from the center of the record, the faster the linear velocity, v, of any point. Thus, if we imagine these sine waves printed on the album as I did for the tape, it seems like the pitch would be higher on the outside. Does anybody know if this is something that they take into account when they record albums?


Going back to the Robert Johnson thing, the site says that a recording of a particular song sounds as though it is played in open G with a capo on the 4th fret, but it is believed that he played it in open G with a capo on the first fret (if you want to know why they think that, you can read the site.) this site shows the frequencies of musical notes. Having taken music theory and being a guitar player, I know that if it sounds like he is in open G with a capo on the fourth fret, then it sounds like he is in the key of B. Also, if it is thought to have been played in open G with a capo on the first fret, it is thought to be played in G#. The frequencies for B and G# are 30.87 and 25.96 Hz, respectively. Thus, returning to the good old formula v=\lambda f, we get
For all the above equations, the dots are decimals. The TeX is a little weird with that. But, this suggests that if Robert Johnson actually played in G# and the pitch of the album shows it to be in B, then his recording was sped up by a factor of about 1.19.

I immediately thought after I posted this, that with regards to the album having higher pitch on the outsides, I guess if you record it while it is spinning in a similar manner to when it is played, then this shouldn't be a factor.

Oh, I messed up again...I realized that the frequencies I used were actually for the lowest octave on a piano, which I believe is four octaves below what I was looking for. My bad.

In response to your questions, it depends on the technology. The tapes would have to require a constant linear velocity, since it's the speed of the tape going past the microphone that matters, since that's the point that's being measured. However for records and CDs, its a little more ambigous, so I looked it up (I love citing wikipedia, don't you):
Constant linear velocity
Constant angular velocity

In case you don't feel like clicking links (I often don't) LP records use constant angular velocity, because the technology when they first were produced wasn't capable of making fine enough adjustment in rotational speed, logically then the compensation must come from production. more modern data storage forms such as CDs and DVDs, use a constant linear velocity.

Hmmmm. That's interesting. Thanks.