Finding the wavelength of a given frequency can be very useful to the SPL competitor and SQ enthusiast alike, both for tuning an SPL enclosure to form a quarterwave maturation at the mic location for competition, and for tuning a transmissionline enclosure, respectively, among other things.
When building an SPL vehicle, one means of maximizing efficiency of the system is to tune the box so that a quarterwavelength of your burping frequency will mature at the location of the judging mic at the dash. To do this, you need to know both the frequency you wish to tune your box to (or the cabin's sympathetic frequency) which you'll use to burp the system, and the length of that frequency's wave.
To find the wavelength, you'll need a few basic tools. Among these are:
a car audio system
a test tone CD or tone generator
a tape measure
your ears
In order to find the wavelength, place the test tone CD in the steeo, and play the test tone of the frequency you desire on the system, at burping volume.
Stand outside and in front of the car with the windows rolled down, and walk away from the vehicle, until you can no longer hear the stereo system.
Once the volume has decreased to an inaudible level, turn back and face the car, and measure the exact distance from where you're standing, to the speakers in the car, using the tape measure. When you can no longer hear the audio tone, you've reached the end of the waveform, where it runs out, and thus you are standing at the very tip of a full waveform.
Take that distance, and multiply it by 0.25, and you have the exact length of a quarterwave of your test frequency.
Now, build your speaker enclosure so that the port(s) of your box are exactly that distance from the dash, and you'll have a perfectly tuned SPL vehicle, ready to slaughter the competition!
Good luck in the lanes!
Just kidding.
OK Seriously, here's how you find wavelengths:
The relationship between Frequency & Wavelength
How to convert wavelength to frequency and to convert frequency to wavelength:
On a radio dial, stations are at positions measured in wavelengths by "metres" and in frequencies by "kilohertz" (KHz). Each particular spot on the dial has a wavelength and a corresponding frequency. There is a way to convert between frequency (f) and wavelength (l) which is as easy as the conversion between Fahrenheit and Celsius or between pounds and kilogrammes.
To convert any frequency to a wavelength, divide the speed of light by it.
So, it's: wavelength = 299792458 divided by frequency.
The formula works the other way round, like this:
frequency = 299792458 divided by wavelength.
To make it easier, it's possible to approximate the speed of light to 300 million. Also, wavelengths are always measured in metres in this formula, and frequencies are in Hertz. 1KHz (kilohertz) is a thousand hertz; 1MHz (megahertz) is a million hertz.
Example: What's the wavelength of Radio1 FM 9799 megahertz?
99 megahertz is 99 million hertz, so to get the wavelength, it's...
wavelength = 300 million divided by 99 million
= slightly more than 3 metres.
Another example: What's the frequency of BBC Radio4 long wave 1500 metres?
Ok, it's frequency = 300 million divided by 1500 = about 200,000 = 200 kilohertz
(The station is now on 198 kilohertz)
WHY? How come this works? You can see this by walking past a wall (at say 3 metres/second to make it conveniently one hundred millionth of the speed of light) and drawing a wave on the wall with chalk by moving the chalk up and down. If you move the chalk up and down at a frequency of three times a second that's 3 Hertz, and the wave you've drawn on the wall has a wave length (from peak to peak) of ONE METRE. Radio waves travelling at the speed of light and moving up and down at somany millions of times a second have a corresponding wavelength drawn in space. At 300 million metres per second, a radio frequency of 300 million cycles per second (300 megahertz) draws a line in space with peaks one metre apart.
Ok, so you can convert any* frequency to a wavelength. And any wavelength to a frequency.
* We're talking electromagnetic waves here, radio, microwave, light, etc. These all travel at the speed of light. For SOUND, and other mechanical waves, the calculations are a bit different, because they travel at the speed of sound. So, if you are calculating frequency versus wavelength for sound, you need to use the speed of sound in the equations rather than the speed of light. It's possible to have radio waves with frequencies as low as 10KHz, but their wavelengths are very much longer than those for sound waves of the same frequency.
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.
Wavelength of Radio Waves
by: Andrew Krause
The method for finding wavelength with radio is a bit different. To find radio wave lenghts, 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
