What is (-3) and divide(-2) plus 8?

Answer 1

Wavelength, λ, and Frequency, f, are inversely proportional. Their product is a constant, the wave velocity.

For lightwaves, their product is the speed of light, c:

c = λ * f = 299,792,458 m/s,

~= 3.00 * 10**8 m/s, 0.300 m/ns, 30.0 cm/ns,

~= 186,000 mi/s, 11.811 in/ns, 0.984252 ft/ns;

Where ns = nanoseconds, or 10**-9 seconds.

Frequency, f, and Wavelength, λ, describe simple values that can be measured on a moving wave, if it contains a constant signal or, at least, a clearly repetitive waveform.

So, as the wave moves past a reference point like a microphone, or radio receiver, find some repetition in the wave, measure the shortest interval of time, t, that marks the entire repetition. The frequency, f, is simply[1] the reciprocal of that time interval:

f = 1 / t

The wavelength is the measured distance between two identical areas of the waveform (like peaks, troughs, or blips), in adjacent copies of a repeating waveform. Whereas the interval measurements required one wave sensor, plus a fast timer, the wavelength measurements require two wave sensors, accurate distance measurements, but no timer. As the sensors are separated, the two signals will diverge until, at one wavelength separation, the two signals become identical again (difference is minimal).

Sometimes, it is hard to be highly accurate about where, exactly, a single interval starts and stops. However, if you can flawlessly count a large number of repetitions, just do your best to start and stop the timer in the same place on the first and last repetition. Now you get to multiply your accuracy! Divide the total time, Δt, by the number of intervals, n, this average is an improved measurement of interval!

t = Δt / n

If you divide the count by the time interval, you get an improved frequency measurement.

[1] Frequency is a counted number, n, of full waveform repetitions divided by the total elapsed time, Δt.

f = n / Δt