I am looking for formula and easy explanation for calculating the wavelength of a sine wave. So far I have not been able to calculate the example I want to do as I could not understand the resources I've found from Google.
What is the wavelength of sine wave? Given frequency, distance and time.
For instance, a 0.42 MHz sine wave takes 3.3 µs to travel 2500 meters.
I am asking for patience I know this might look amateur for some but I am learning basics and I struggle to find the answer.
$$speed = \frac{distance}{time \; to \; traverse \; it} $$
$$= \frac{2500}{3.3 \times 10^{-6}} \cdot \frac{[m]}{[s]} = 7.58 \times 10^8 m/s$$
That's physically impossible - it's faster than the speed of light (\$3 \times 10^8 m/s\$). Check again what the speed of the signal should be.
anyway, once you find it:
$$wavelength = \frac{speed}{frequency}$$
The wavelength is $$\lambda = \frac{v}{f}$$
where \$v\$ is the velocity of the wave and \$f\$ is the frequency. Here you have $$v = \frac{2500\text{m}}{3.3\mu\text{s}}$$
Just be sure to convert \$v\$ to m/s and \$f\$ to Hz so the units work out. \$\lambda\$ is in meters.
Using λ=v/f
assuming it is a standard electromagnetic wave (not a sound wave):
300/.42=714.2857142857143m, or 809.5238microns (peak-to-peak or crest-to-crest)
Where v is the velocity of the wave (default is velocity of light in vacuum: 300.000 Km/s).
[This answer is technically more correct (v=299,792,458 m/s): 713.79m]
Expanding on Answer #1 above
or if you're going through some odd medium (Jello maybe?):
Using λ=v/f
λ=(2500m/0.0000033sec)/420000Hz=1803.7518m
1 meter = 1 000 000 000 nanometers (1,803,751,800,000nM)
