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Speed of Sound

Pay attention during any thunder and lightning storm and you'll be able to figure out that sound travels slower than light. Since the lightning and the thunder occur simultaneously and since the light flash arrives at you earlier than the clap of thunder (unless you're extremely unlucky...) then this must be true. In fact, the speed of sound, abbreviated $c$ is around 344 m/s although it changes with temperature, pressure and humidity.

Note that we're talking about the speed of the wavefront - not the velocity of the air molecules. This latter velocity is dependent on the waveform, as well as its frequency and the amplitude.

The equation we normally use for $c$ in metres per second is

$$c = 332 + (0.6 * t)$$ (4.7)

where $t$ is the temperature in $^{\circ }$C

There is a small deviation of $c$ with frequency shown in Table 3.1, though this is small and therefore generally ignored

Table 3.1: Deviation in the speed of sound with frequency.

Frequency	Deviation
100 Hz	-30 ppm
200 Hz	-10 ppm
400 Hz	-3 ppm
1.25 kHz	0 ppm
4 kHz	+5 ppm
10 kHz	+10 ppm

Changes in humidity change the value of $c$ as is seen in Table 3.2.

Table 3.2: Deviation in the speed of sound with air humidity levels.

Humidity	Deviation
0%	0 ppm
20%	+415 ppm
40%	+1136 ppm
60%	+1860 ppm
80%	+ 2590 ppm
100%	+3320 ppm

The difference at a humidity level of 100% of 0.33% is bordering on our ability to detect a pitch shift.

Also - in case you were wondering, ``ppm'' stands for ``parts per million.'' It's just like ``percent'' really, except that you divide by 1000000 instead of 100 so it's useful for really small numbers. Therefore 1000 ppm is $\frac{1000}{1000000} = 0.001 = 0.1\%$.