Let's get one thing straight - sound does not travel at the speed of light. To be fair, I've only met one person who thought that it did. But even light doesn't travel at the speed of light, not when it's going through a medium other than a vacuum.
But light travels so fast that most of us can regard it as instantaneous for all practical purposes, no matter what the distance.
Not so with sound however. Sound is a real slow coach and travels at a mere 340 meters per second in air, on a good day. And since this is science, we'll stick to metric measurements. Confusion between metric and imperial measurements has ruined many a space mission. True.
Even so, this is a pretty fast pace compared to anything other than a supersonic fighter plane or the late Concorde. So does it matter in sound engineering?
Yes it does. Here are some examples...
In your recording studio control room, sound travels directly to your ears over the shortest path possible from the monitor loudspeakers. However, there might be a shorter air path between the monitors and the solid structure of your room.
Sound that takes this path will travel much faster in the solid material, and you could find that the room is radiating sound that you hear before the direct sound from the monitors.
The brain places great significance on time of arrival, so this can be confusing to say the least.
Another example... In a PA system, unless there are some loudspeakers close to the rear of the audience, the people there will not receive sound either loud enough or clear enough. But the electrical signal to those speakers travels much faster than sound through air, so the sound from the main loudspeakers at the front will be heard as a distracting and unpleasant echo. So the feed to the rear loudspeakers needs to be digitally delayed to compensate. Obviously the duration of the delay has to be adjusted according to distance.
Finally the Doppler effect, which is related to the speed of sound. This is where the sound of a police car's siren appears to rise in pitch as it approaches and falls as it goes past and recedes. (If the car stops, it's you they're after!)
There is a school of thought, though few experiments, that suggests that as the diaphragm of a loudspeaker drive unit moves forwards and backwards due to low frequency energy, higher frequencies are subjected to the Doppler effect, thus cyclically changing their pitch. This would be less of a concern with large low frequency drive units as they do not need to move so much to move enough air.
By the way, I said the speed of sound was 340 meters per second. This is on the fast side of average, but it is a nice round figure. The real-life figure, which depends on temperature, humidity and altitude, varies between around 330 and 350 meters per second.
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