Since sound is a longitudinal wave, energy travels in areas of compression and rarefaction. The density of those areas will determine the intensity of the sound. In other words, the more dense the compressions are, the louder the sound will be. Intensity is actually a measure of the pressure per unit of area, so as sound moves out from a source, the intensity of the sound decreases. Watch this video to find out more about sound intensity.
Sound intensity is another thing we're going to talk about here, and this is the rate at which energy is transferred through an area. The formula is intensity equals power divided by 4 pi r squared. And r is the distance from the point source. So you're looking at a distance there.
And the units are watts, which are the units of power, over meters squared. And then oftentimes you'll hear people refer to sound intensity in decibels. And that's just a relative intensity that really puts the scale a little bit easier for us to recognize. And you'll notice that in some of your readings.
So let's do an example problem of intensity. If a saxophone is 4.3 meters away, what is the intensity of the sound wave produced by a saxophone that has a power output of 0.17 watts? Assume the sound waves are spherical.
So we identify our givens. And of course, we're looking for intensity. Intensity equation is power divided by 4 pi r squared. Plugging in our numbers, be careful to only square the r. This is the only thing squared in this algebraic equation. And then we get our intensity to be 7.32 times 10 to the negative 4 watts per meter squared.
Question
What are the units of sound intensity?
The units of intensity are watts per square meter. Usually, sound intensity is translated into a relative intensity called a decibel. Relative intensity relates the sound intensity relative to the threshold of hearing. So, 0 decibels is barely audible. Each increase in 10 decibels is equivalent to 10 times the intensity of the previous rating. It is a logarithmic scale similar to that of intensity of earthquakes. Examples of relative intensity are:
- whisper = 30 dB
- vacuum cleaner = 70 dB
- pain threshold = 120 bB
- jet airplane engine = 150 dB
Question
How does distance from the source effect the sound intensity?
The intensity of sound decreases as the distance from the source increases. In fact, since the distance factor is squared, if you double the distance, the intensity decreases by a factor of 4 (2 squared). If you triple the distance, the intensity decreases by a factor of 9 (3 squared).
