How Tall is B Flat?

I like nonsense questions: how thick is 36, how cold are pickles; what's the temperature of math; how tall is B flat; what's the pitch of your mom?

As it happens though, I've been reading Asimov on Physics, and, if you allow for a little bit of logical wiggle room, those last two questions are sort of answerable.

If you read anything at all about acoustics and musical instruments, you eventually begin to hear wavelengths and frequencies tossed about. We've all probably heard of 'concert A'. That's the A above middle C. Most likely, we have heard that that is 440 HZ, and we know HZ has something to do with frequency: which we think of as a fancy word for pitch. And so, if we think about it maybe a minute more, we might guess that the frequency of B flat is more than 440... and if we think about it a minute more, we'd remember that wavelength has something to do with frequency and allow that wavelength of B flat is not the same then as the wavelength of A, and then mostly we decide we don't have more minutes to think about such things. But, if you do, continue musing along such lines, perhaps to avoid thinking about your taxes or avoid doing the laundry or practicing scales, you might begin to ask yourselves how to find out the wavelengths of musical pitches and if those wavelengths equate to anything real you can think about easily.

Happily enough, I can figure this all out without straying too far from my Basic Algebra Comfort Zone (BACZ) which is nice because I am very fond of my BACZ, and am always glad to see it accomplish mighty things!

I know that concert A has a frequency of 440 HZ. that means, its wave has time to repeat itself 440 times each second. I know how fast it's moving: it moves at the speed of sound.

So, what's the speed of sound? You know sound travels more slowly than light because you see lightning before you hear the thunder. Lightning and its thundre happen at the same place at as close to the same time as makes no difference, but light from lightning arrives at your eyes long before the sound of thunder makes it to you. Light is so fast that, in the distances we're talking about here, itmight as well be infinitely fast.

To calculate the speed of sound, I could set off a tornado warning siren in downtown Bowling Green as soon as I see the funnel cloud at precisely 3:00 PM, and you could note, standing in our classroom, (a bit more than a mile from downtown or 1.7-ish KM) exactly when you hear the siren (which will be about five seconds later. Divide the precise distance from the siren to our classroom by the exact time delay and you get the speed of sound. (Luckily for you, tornados travel even more slowly that sound does, ... around 27 MPH according to so you still have probably around two and a half minutes to get off the fourth floor and go cower in the stairwell by the ACS office before the building is flattened, but that's beside the point.)

The speed of sound works out to 331.5 meters per second ... at sea level... at 0 degrees C. Both of those qualifiers have to do with the behavior of air (the medium through which sound must move if it wants to get from the siren to your eagerly waiting ear. (You really do need air to propagate sound waves... in space, you can't even hear even William Shatner scream ... as much as you might want to.) (Thanks to Matt's Movie sounds for that.)

At any rate, roughly ... the speed of sound depends both on the density of the air (how close the molecules are to one another and thus how far they must travel before bumping into one another) and the temperature which is how quickly they are moving.

Don't confuse speed of molecule movement with speed of sound: sound is waves, motion of one molecule banging into the next and that one into the next and that one into the next... not the speed at which that first or second or 17,000th molecule its lonely self is moving... Isaac Asimov ('s book) tells me that an air molecule at sea level need move only a millionth of an inch before it thwacks into a neighbor. That means, if I yell TOOOOORNAAAADOOOOO!!!" an uncomfortably-close 2 inches from your ear, over 2,000,000 air molecules may participate in transferring that message to your ear... and that's if they all go in a straight line, which they most assuredly do not.

Here in Ohio, I'm as close to sea level as makes no difference, especially here in the Black Swamp . Unfortunately, for my equation (only) though, it's no where near 0 degrees C in my living room or our classroom just now. Double-unfortunately, I have read a variety of figures about exactly how much speed of sound increases with ambient temperature, and I like it around 20C at least. For no better reason that its the number used by the website on which I found my particular set of piano pitches/wavelengths on, I'll use a speed of sound of 345 meters per second instead of 331.5: you don't want to be that cold anyway.

So here is the equation I'd use to figure out how 'tall' B flat is: that is, the wavelength of B flat:

wavelenth = speed of sound divided by frequency:

W = 345/F

If I know the wavelength and want frequency, I'd use:
f = 345/w

There is a nifty table of frequencies of musical notes. here. For what it's worth, that page also clearly explains how to generate this table, (and the explanation doesn't violate the BACZ), but it was more fun to write the perl script involving a look up table than to just plug in the equation, so that's how I did it.

My handy table tells me that B flat has a frequency of 466 HZ.

Remember that all of this is in meters not feet:

W = 345/466
W = .74
74 CM
or about the height of a tallish one-year old girl!

Given all that, here comes the program which will enable me to take the height (or length) of any object you like: (you, your piano, your cat's tail, your house, yonder tree, said tallish girl, the Star Ship Enterprise) and give you the name of the musical note whose wavelength is just that tall/long. (What good this will do you, I am not sure, but there it is.)

Object, please:
My Input is Given in Feet/Inches
I'm cool: I use the metric system