How to find a wavelength - and what to do with it
by Eddie Runner (NU5K)
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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.
So the speed of sound is different at sea level than it might be in the mountains. And
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 |
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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.
Use the chart above to help make sense of your
speaker mounting locations.
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