Calculate the wavelength of each of the following frequencies of electromagnetic radiation.

Question

Calculate the wavelength of each of the following frequencies of electromagnetic radiation.

1. 104.7 MHz (typical frequency for FM radio broadcasting)
2. 1370 kHz (typical frequency for AM radio broadcasting) (assume four significant figures)
3. 894.5 MHz  (common frequency used for cell phone communication)

Answer 1

For electro magnetic radiation

λ = c/f

Where

c = speed of light = 3 x 10⁸ m/sec

λ = wavelength

f = frequency

Thus

1. For f = 104.7 MHz = 104.7 x10⁶ Hz

λ = 3 x 10⁸/ 104.7x 10⁶ = [3/104.7] x 10² m = 2.8 x10^-2x10² = 2.8 m

2. For f = 1370 khz = 1370 x10³ Hz

λ = 3 x 10⁸/ 1370 x 10³ = (3/1.37) x10 ² = 218.9 m

3. For f = 894.5 MHz = 894.5 10⁶ Hz

λ = 3 x 10⁸/ 894.5 x 10 ⁶ = 3/(894.5) x10 ² = 3.35 x 10^-3 x 10² = 0.335 m