Xander's walkie-talkie sends out a radio wave 2.5 m long. What is the wave's frequency?
The wave is 2.5 m long, and it travels at the speed of light, 3.00 × 10⁸ m/s. No new physics is needed: c = fλ already ties those two numbers together; this lesson rearranges it for whichever one is missing.
This is the same calculation you ran with v = fλ for sound and water waves; for an electromagnetic wave, v is always c.
So for any electromagnetic wave in a vacuum: c = fλ, with c = 3.00 × 10⁸ m/s.
Frequency unknown: f = c ÷ λ.
Wavelength unknown: λ = c ÷ f.
The walkie-talkie wave: f = c ÷ λ = (3.00 × 10⁸ m/s) ÷ (2.5 m).
Divide the front numbers: 3.00 ÷ 2.5 = 1.2. The power of ten is untouched by that divide, so f = 1.2 × 10⁸ Hz.
A sense check: 2.5 m is a long wavelength, and 1.2 × 10⁸ Hz is a low frequency for an electromagnetic wave. Long pairs with low, exactly as c = fλ requires.
A ship's radio sends waves with wavelength 1.5 m. Calculate the frequency.
Write down the values:
λ = 1.5 m, c = 3.00 × 10⁸ m/s, f = ?
Write down the equation:
f = c ÷ λ
Substitute in the values, and calculate:
3.00 ÷ 1.5 = 2.0, and the 10⁸ is untouched, so f = 2.0 × 10⁸ Hz.
The frequency is 2.0 × 10⁸ Hz.
A TV satellite transmits at a frequency of 1.0 × 10⁹ Hz. Calculate the wavelength.
Write down the values:
f = 1.0 × 10⁹ Hz, c = 3.00 × 10⁸ m/s, λ = ?
Write down the equation:
λ = c ÷ f
Substitute in the values, and calculate:
3.00 ÷ 1.0 = 3.0, and 10⁸ ÷ 10⁹ leaves 10⁻¹, so λ = 3.0 × 10⁻¹ m = 0.30 m.
The wavelength is 0.30 m.
A rescue beacon's radio wave has wavelength 6.0 m. Enter the wave's frequency, in Hz.
An FM station broadcasts at a frequency of 1.00 × 10⁸ Hz. Enter the wavelength of its waves, in m.
A microwave oven runs at a frequency of 2.4 × 10⁹ Hz. Enter the wavelength of its waves, in m.
Green light has a frequency of 6.0 × 10¹⁴ Hz. Enter its wavelength, in m.
An AM station's radio waves are 500 m long. Enter their frequency, in Hz.
A door sensor sends out microwaves with wavelength 0.060 m. Enter the waves' frequency, in Hz.