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The physics of oscillations and waves - Part 2

(Placement, placement, placement)

by Elwood; Editing by Mac

In the last installment of our physics series we got our feet wet on a wide topic - Oscillations and waves. Though it may have appeared to be heavy stuff let's try to put our newly acquired knowledge to good use. Don't worry if you didn't read or understand the last article completely because last time we missed one of the most important facets which will be of great help for us this time. And I promise it'll be easier to understand (I hope) as we delve into what is perhaps the one physical parameter that affects all things acoustic: The speed of sound

At first glance it may sound a bit complicated if I say that the speed of sound is not dependent upon the amplitude (volume), frequency (pitch) or wavelength (lambda), but by the medium the sound is propagating through and that medium's temperature. But really it's easy enough: Last time we learned that sound travels through the air by moving the little molecules of air one by one in progressive fashion. By moving maybe up and down one molecule affects its neighbor molecule and transfers it's energy to the other with a slight time shift. One has to know that the molecules of a gas are always in random movement.

Of course we don't feel or even hear that movement because it is happening on a very very tiny area. Much smaller than the area of the movement caused by sound. If temperature is high the molecules move very fast. The higher the temperature the faster the movement and vice versa. At low temperature the molecules move slower. This can reach up to no movement at all which would be 0 °K (read: Kelvin) or -273.15 °C (Celsius). From this information we know that sound travels faster through air at warmer temperatures simply because the molecules can move more easily.

Of course there's also a formula which makes it simple for us to calculate the actual speed of sound:

v = 331.4+ 0.6T [m/sec]

Let's translate those numbers into human language:

velocity in meters per second is almost equal to 331.4 plus 0.6 times the temperature in Celsius.

Now several problems arise. This formula is great for 90% of the whole world but not for most of the US citizen. While in Europe temperature and distance are measured in Celsius and meters there are other conventions still being used in the US. (The “MKS” – Meters, Kilograms, Seconds and “cgs” – Centimeters, Grams and Seconds metric system is indeed used in the US today by nearly all scientists and engineers, the older “fps” or feet per second system is simply more cumbersome. –Ed.)

Firsthand one has to calculate the Celsius temperature by the Fahrenheit temperature. What's the difference you may ask? The difference is the reference temperatures.

When Celsius built his first quicksilver thermometer he took two temperatures as reference: The freezing point and the boiling point of water. He marked the first point, "0 °C" and the latter one was marked as, "100 °C".

Fahrenheit didn't use water as his standard, but chose to use the body temperature of man. It was very important to him to avoid negative numbers so he choose the temperature of the very hard winter 1708/09 in his hometown Danzig as 0 °F. His own body temperature would be 100 °F.

Later it was found that the average body temperature of a human being is rather 98,6 °F than 100 °F. He also found that the freezing point of water is approx. 32 °F and the boiling point approx. 212 °F. This also is not very correct and it's unknown whether he measured wrong or changed the numbers in order to get a difference of exactly 180 °F.

Ok, ok, 'nough said. How do we convert between Fahrenheit and Celsius? Look here:

F = (C * 1.8) + 32 [°F]
C = (F - 32) / 1.8 [°C]

Next problem is the conversion between meters and inch:

1" = 2,54cm
1cm = 50/127"

With CM being the distance in centimeters and IN the distance in inch the following formulas apply:

CM = IN / 2,54 [m]
IN = CM * 2,54 [in]


M = FT * 0.3048 [m]
FT = M / 0.3048 [ft]

(Note: The actual conversion requires many more decimal places to be as accurate as possible, using these constants will introduce an error known as “metric creep” in certain circles. For that reason alone it is better to think and work using the MKS metric nomenclature only when “plugging and chugging” any physical equations such as these. –Ed.)

After all that our speed formula would look like this:

v = ((331.4 + (0.6((F-32) / 1.8))) / 0.3048) [in/sec]

Wohoo, that's too complicated for me. Can't we do things easier? We can. And so we do. Actually that formula says that sound travels through the air at 331.4 m/sec when the air temperature is 0°C or 32°F. Most often we work with studio sound within the environment of a comfortable room. Standard room temperature is about 25°C or 77°F. So the most important number we have to remember after all that trouble is that sound travels at about:

346.4m/sec = 1136.48 ft/sec

in an average room. And these numbers are so important that it can't be a bad thing to tape them on the console. ;-)

Of course every room we encounter may be at a different temperature and things can change even worse if we're doing a live act outdoors. But this is where we leave the mathematical correctness alone and try without calculating until our ears say it's right. We would move that mic a few centimeters or play with that delay and it may surprise you how close to the calculations you can come by simply using your ears effectively. If you're doing sound very often outside and are keen enough you could calculate the speed of sound for your area at different seasons.

The headline reads “Placement, placement, placement“ and I promised you that we wouldn't be completely theoretical this time around so let's get to the nuts and bolts by thinking about the following: Many pro-consoles and most digital mixers offer built in time delay or phase control for every channel. With our new knowledge the reason is simple.

Let's say you mic a drum set or a guitar amp with several mics. Each mic has a different distance to the sound source. The farther each mic is away from the source the longer it takes for the sound waves to reach the mic. The effects are ugly delays which can lead to comb filtering and phase problems in the worst case. Of course we want to avoid this and so we use those included delays.

First of all we calculate the time it takes to reach every single mic. Then we attempt to adjust the delay time for each mic so that the sound of every mic reaches the speakers all at the same time. If it takes 2 ms to reach mic A and 7 ms to reach mic B we would delay mic A by 5 ms. Can you use the information already given in this article to calculate the ballpark distances between the single sound source and each of the two mics in both meters and in feet?

So here's the real-world example: John wants to mic his guitar amp using three mics. One 6" behind the amp, one 12" in front of the amp and a room mic 8 ft in the room. Because he carefully read the audiominds.com newsletter he taped a small paper on his console which reads: “346.4 m/sec = 1136.48 ft/sec“. His thermometer says the temperature is about 79 °F so those numbers appear good enough to him. The trouble is that it was nowhere told how to calculate the time the sound needs to travel to each mic.

Being an active car driver he can solve that task after some thinking, too. He thinks: "At 60mph I will have driven exactly 60 miles after one hour of driving, and of course it stands to reason that if I drove two hours then I would cover twice the distance. On the other hand it takes 1.5 hours to drive 150 miles at 100mph." (Don't try this at home, folks… --Ed.)

This leads to an easy formula which if you don't know it by heart should also be taped on your console:

d = v * t
distance = speed * time.


t = d / v
time = distance / speed.

The number on his console uses feet so he converts the inches to feet:

6" = 6" / 12 = 0.5 ft
12" = 1 ft

Now he's almost done. Using that t = d / v formula he knows that it takes 0.0004 sec (0.4mS) to reach the back mic, 0.0008 sec (0.8mS) the reach the front mic and 0.007 sec (7mS) to reach the room mic. The front and the back mic are too close together (under 1 mS difference) to be corrected by the console's delay. The room mic instead is 7 mS behind. So he delays the close mics by 6 ms. Voilà.

And how does his song sound now? I don't know but I think he may have undid the delay because he didn't like the sound of it either. ;-) But I'm sure he used it on the drums.

Ok, folks. This article turned out longer than I expected. Next time we will look at setting up speakers for an open-air concert and volunteer to tune the guitars. Unfortunately we will also then find out that our assistant forgot to pack the guitar tuner and why that won't deter us much if at all. After the gig is over we'll kick back and finish the physics series with a look at the tuning of our recording rooms for good sound.

See you then, and don't forget to spend a bit of time now and then “plugging and chugging” on these numbers. Do it often enough and one day you will discover an understanding of the whole process.



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