Time Delay: Not Just for Einstein and Interstellar
There is an interesting phenomenon that occurs during any live performance that has its sound amplified or enhanced. It’s particularly noticeable, and particularly a problem, at large outdoor concerts with lots of people and lots of speakers inhabiting a large area. As you already know, sound waves move a lot slower than light particles/waves (light is weird).
When the sound from the stage is converted into an electric signal it reaches the speakers, for our purposes, instantly. If the speakers are a quarter mile away from the stage, then you can see how there’s a problem. The audience at the back of the house is hearing the sound before it gets there from the stage. This causes distortion, echo, and produces a generally less enjoyable experience for your audience.
Sound engineers have been accounting for this delay since the beginnings of electric amplification, but when a few milliseconds can make the difference between a good concert and a great concert, it requires the right know-how and equipment to get things just right. Picture a huge outdoor venue like Woodstock in upstate New York or Bonnaroo south of Nashville. Now put yourself at the back, look at the tiny stage up front and the rows and rows of stacks and speakers between you and the band. Each set of speakers has to be carefully delayed so that, together, they produce a uniform, pleasing sound.
This effect is accomplished delaying the output of each speaker according to their distance from the stage; with the furthest speakers delayed the most and the closest delayed the least. How we calculate the delay required to produce this uniform sounds is where the engineering in sound engineering comes from. It takes a little math.
First, the speed of sounds is not a constant. Since sound, unlike light, requires a medium through which it must move, the speed of sound is dependent on that medium. For example, the speed of sound at sea level is around 343 m/s with variations due to atmospheric forces like temperature and humidity. At 30,000 feet the speed of sound is closer to 303 m/s and gets slower and slower until you reach the vacuum of space through which sound cannot travel.
Once we have an accurate speed of sound for set conditions, the time delay at any given distance can be calculated in milliseconds by putting the distance in meters over the speed of sound in meters per second. As a general rule, it takes 3 milliseconds for a sound wave to travel one meter (1/343=.002915). The equation is simple (Δt=r/c; where r is distance and c is the speed of sound and Δt is our delay) but the sound engineering it takes to put on an excellent show certainly isn’t.