Question

Radio waves are used to transmit information on various channels. What is the wavelength of a radio wave having the frequency of 5.40 × 1010 Hz?

1. Analyze the Problem

ν = and c = Unknown: λ =

You know that because radio waves are part of the electromagnetic spectrum, their speed, frequency, and wavelength are related by the formula c = λν.

Answer 1

5.56×10¯³ m

Step-by-step explanation:

From the question given above, the following data were obtained:

Frequency (v) = 5.4×10¹⁰ Hz

Wavelength (λ) =?

The velocity of electromagnetic wave, frequency and wavelength are related according to the equation:

Velocity (c) = wavelength (λ) × frequency (v)

c = λv

With the above formula, the wavelength of the radio wave can be obtained as follow:

Frequency (v) = 5.4×10¹⁰ Hz

Wavelength (λ) =?

Velocity (c) = 3×10⁸ m/s

c = λv

3×10⁸ = λ × 5.4×10¹⁰

Divide both side by 5.4×10¹⁰

λ = 3×10⁸ / 5.4×10¹⁰

λ = 5.56×10¯³ m

Thus, wavelength of the radio wave is 5.56×10¯³ m