Sound propagation

How fast does an aeroplane have to fly in order to travel faster than sound? Well, that depends. Because the speed of sound is not constant. Sound spreads out from its source. Molecules knock into other molecules, creating bands of compressed air, followed by bands of less compressed air -- rarefactions.

Just how fast these waves of compressions and rarefactions move through a medium depends on how quickly the molecules can bump their neighbours, making them move too. In air, there is plenty of space between the molecules. So each molecule needs to travel a bit, before it hits its neighbour. Because air contains so much empty space between its molecules, this slows down the speed of sound. But in water, the molecules are much closer to each other.

And unlike air, water cannot be compressed. So sound waves travel more than four times as fast in water, compared to air. Steel is harder still than water. Here, the atoms are firmly bound to each other, and each movement is immediately passed onto the next. Sound travels 17 times faster in steel than in air, at nearly six thousand metres per second.

The speed of sound is different in different media. It even differs in the same medium. Sound travels faster in air that is hot and humid, as opposed to air that is cold and dry. The speed of sound in dry air at 20 degrees Celsius is 340 metres per second. We illustrate sound as a wave, like this.

A peak is a compression, and a trough is a rarefaction. The distance between two peaks, or two troughs, is the wavelength. But the wave doesn't stand still. It moves through the medium, and the number of peaks that pass any fixed point in one second, is the frequency. Listen carefully.

Here's a bass tone with a frequency of 170 Hertz. Each wave is two metres long, from peak to peak. Two metres per wave. Times 170 waves per second. Equals...

340 metres per second! Here's a higher pitched tone. Its wavelength is five centimeters. That's zero-point-zero-five metres. And it travels at 340 metres per second.

What's its frequency? Well... 340 metres divided by waves of 0.05 metres equals 6800 waves per second. The frequency is 6800 hertz. Wavelength times frequency equals speed.

Or if you prefer... Speed Divided by frequency Equals wavelength. When a sound hits a wall, or some other object which is much harder than the medium it travels through, it can bounce off, and come back. This is an echo. The distance to the mountain is 680 metres.

It takes two seconds for the sound to get there, and two seconds to travel back. So you'll hear the echo after a delay of four seconds. In a room, the sound of your voice bounces off the walls when you talk. This kind of echo that is all around you, and without any noticeable delay, is called reverberation. A little bit of reverberation makes the sound 'softer', and it's easier to understand what someone says.

But too much of it, and the sound gets garbled and muddy. Acoustics is the study of how sounds are reflected and reverberated. If you work in the field of acoustics, you may be designing a room, selecting surface materials, and working on the distances and angles between the walls. Acoustic engineering would be very hard if you didn't know the speed of sound.