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The Speed of Sound

How does temperature, humidity, and altitude affect the speed of sound?

Sound waves travel through solids, liquids and gasses. Sound waves travel faster through solids and liquids than gases because they're more dense. At sea level, the speed of sound is 1130 feet per second with 50% humidity.

How does temperature have on the speed of sound?
The higher the temperature, the faster sound travels.

How does humidity affect the speed of sound?
H umidity is a measure of the amount of water vapor in the air; the more humid the air is, the faster sound waves travel in it.**

How does the altitude affect the speed of sound?
Sound travels slower with an increased altitude (elevation if you're on solid earth). This is primarily a function of temperature and humidity changes.

A simple chart
the relationship between temperature, relative humidity, and the speed of sound (in feet per second

0% 10% 20% 30% 40% 50% 60% 70% 80% 90%
18.3 65 1123.3 1123.6 1124.0 1124.3 1124.7 1125.1 1125.5 1125.9 1126.2 1126.6
21.1 70 1128.6 1129.0 1129.5 1129.9 1130.4 1130.8 1131.3 1131.7 1132.2 1132.6
23.8 75 1133.8 1134.5 1134.8 1135.4 1135.9 1136.4 1136.9 1137.5 1138.0 1138.5
26.6 80 1139.1 1139.7 1140.4 1141.0 1141.6 1142.2 1142.8 1143.5 1144.0 1144.7

These figures were calculated with an online calculator which can be found here.

So What's this have to do with church audio? Plenty! How many times have you adjusted the sound system during rehearsal and everything sounded just right, but 15 minutes into the service, you're having trouble with feedback and things don't sound very good anymore? If the HVAC (heating, ventalation, air-conditioning) system wasn't designed or installed correctly, it won't keep up with the amount of humidity being added to the sanctuary during congregational singing. In 20 minutes of congregational singing, the humidity level can increase as much as 40%! This results in the sound waves traveling faster and a whole new set of feedback frequencies can appear to come from nowhere.

In winter, some churches sound very good, but when summer hits, they sound much too bright. Once again, this is due to the increased humidity in the room.

Here's an example: It's Sunday morning rehearsal, the temperature is 70-degrees and the humidity is 40%. Everything is just fine, though you needed to tweak your main parametric EQ by dropping 3616Hz 5dB to get rid of a feedback issue. Since you spotted it as a very narrow freuquency, you also adjusted the width of the filter so it was narrow. This, you figure, will ensure you're not loosing frequencies on either side of the 3616 mark. Now it's 30 minutes later, and 400 people are now in the room. They begin to sing. After about 10 minutes of singing, you're hearing a ringing sound from the audio system. You reach over to your parametric equalizer and begin to adjust the frequency once again. First you adjust down in frequency, and the feedback only gets more noticable. Then you adjust up, and at about 3640Hz, the feedback is once again gone. What happened? Not only did the humidity increase, but the temperature increased a few degrees as well. This is a great sign that's screaming out saying "the HVAC system is designed or installed wrong!" Rather than have adjusted the parametric equalizer with an extremely narrow filter, it would be better to make the filter a bit wider to "catch" problems like this.

While these differences seem small and insignificant, they can wreak a lot of havoc with you if you're not aware these issues exist.

04-2003, Blake A. Engel


** I was corrected on a statement made in this article; I had stated that the more humid air is, the more dense it is. Shawn Roberts wrote and corrected me on this.

From Shawn:
"Humidity is a measure of the amount of water vapor in the air; the more water vapor, the less dense the air is. The less dense the air is (more humidity), the faster the sound waves travel."

I know this may sound backwards but it is correct. The more humid that an air mass is, the less dense the air is because there are less molecules per cubic meter in that air mass. Sir Isaac Newton, first stated that humid air is less dense than dry air in 1717 in his book, Optics. The reason is that a fixed volume of gas, say one cubic meter, at the same temperature and pressure, would always have the same number of molecules no matter what gas is in the container. Now imagine a cubic foot of air that is at 0% humidity, it would contain about 78% nitrogen molecules, which each have an atomic weight of 28 and about 21% of the air is oxygen, with each molecule having an atomic weight of 32. Remember that molecules are free to move in and out of our cubic foot of air, so if we add water vapor molecules to our cubic foot of air, some of the nitrogen and oxygen molecules would leave because the total number of molecules in our cubic foot of air stays the same. The water molecules that replace nitrogen or oxygen have an atomic weight of 18. This is lighter than both nitrogen and oxygen. In other words, replacing nitrogen and oxygen with water vapor decreases the weight of the air in the cubic foot; that is, it's density decreases. These differences are small compared to the differences made by temperature and air pressure, humidity has a small effect on the air's density. But, humid air is lighter than dry air at the same temperature and pressure.