A wavelength is the distance sound will travel while one cycle of the sound
occurs. The speed of sound varies a little depending on air pressure,
temperature, and humidity, so the speed of sound is different at sea level
than it might be in the mountains. That also means the wavelengths will be
longer or shorter depending on the air pressure. The speed of sound is a
very important variable when calculating wavelengths of sounds. For instance
if your listening to a bass note that's 40Hz, that means there are 40 cycles
per second, if the speed of sound where we are is 1127 feet per second then
we can figure out that each wavelength is 28.18 feet long. We do this by
dividing the speed of sound by the frequency, in this case 1127/40=28.18...
I like to do these calculations in a computer spread sheet so I can easily
change the speed of sound or the frequency and do many calculations quickly.
The following chart was done with a
spreadsheet and can be a handy reference. The speed of sound is assumed to
be 1127fps for the following calculations, the lengths are feet.
| Freq | Length | 1/2 length | 1/4 Length |
|
20 |
56.35 |
28.18 |
14.09 |
|
40 |
28.18 |
14.09 |
7.04 |
|
50 |
22.54 |
11.27 |
5.64 |
|
60 |
18.78 |
9.39 |
4.70 |
|
80 |
14.09 |
7.04 |
3.52 |
|
90 |
12.52 |
6.26 |
3.13 |
|
100 |
11.27 |
5.64 |
2.82 |
|
120 |
9.39 |
4.70 |
2.35 |
|
150 |
7.51 |
3.76 |
1.88 |
|
180 |
6.26 |
3.13 |
1.57 |
|
190 |
5.93 |
2.97 |
1.48 |
|
200 |
5.64 |
2.82 |
1.41 |
|
210 |
5.37 |
2.68 |
1.34 |
|
220 |
5.12 |
2.56 |
1.28 |
|
230 |
4.90 |
2.45 |
1.23 |
|
250 |
4.51 |
2.25 |
1.13 |
|
280 |
4.03 |
2.01 |
1.01 |
|
300 |
3.76 |
1.88 |
0.94 |
|
350 |
3.22 |
1.61 |
0.81 |
|
400 |
2.82 |
1.41 |
0.70 |
|
500 |
2.25 |
1.13 |
0.56 |
|
1000 |
1.13 |
0.56 |
0.28 |
|
2000 |
0.56 |
0.28 |
0.14 |
|
5000 |
0.23 |
0.11 |
0.06 |
|
8000 |
0.14 |
0.07 |
0.04 |
|
10000 |
0.11 |
0.06 |
0.03 |
|
14000 |
0.08 |
0.04 |
0.02 |
|
15000 |
0.08 |
0.04 |
0.02 |
|
18000 |
0.06 |
0.03 |
0.02 |
|
20000 |
0.06 |
0.03 |
0.01 |
Notice the low frequencies wavelengths are much longer than the high frequencies, with 20Hz being 56 feet long where as 20kHz is only 6 hundredths of a foot! (that's a little more than half an inch)...
Now the fun stuff comes when we start comparing mounting locations to wavelengths!
We all know if we mount two speakers near each other they will reinforce each other and make more sound than one! We also know that if we accidentally hook up a speaker backwards it will interfere with the other woofers because they are out of phase, cancellation will occur. The same cancellation will occur if we receive sounds from speakers that differ by 1/2 wavelength. If we mount speakers 1/2 wavelength apart the sound from one will cancel when it reaches the other. The good news is, in a car the distances are short and most bass sounds are constantly reinforcing each other. But when you get to the mids and highs of a system there is no way to keep the wavelengths nearly equal, cancellation at certain frequencies can cause big problems, and is a major pain to people seeking true audiophile reproduction
Use the chart above to help make sense of your speaker mounting locations.
by: Andrew Krause
The method for finding wavelength with radio is a bit different. To find radio wave lengths, divide the frequency in megahertz into 300. This is useful for determining antenna sizes, or just because you want to know.
Lambda, or the greek letter "l" is used to represent wavelength in formulas such as the one below.
Frequency in Megahertz = l x Wavelength
l = 300 / Frequency in Megahertz