# Calculating wavelength of sine wave

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:

$$wavelength = \frac{speed}{frequency}$$

• I guess its just example for getting use to formulas, there was never tought put into it – corkalom Nov 19 '14 at 20:52
• 1804m/s I totally confused I was used to work with nano meters – corkalom Nov 19 '14 at 21:09

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]

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)