Question

Two transmitters in space emit electromagnetic waves with frequencies that differ by 1MHz. How do the wavelengths of the waves compare?
The waves have the same wavelength because all electromagnetic waves travel at the speed of light.
A-The waves have the same wavelength because all electromagnetic waves travel at the speed of light.
B-A The wave with the higher frequency has the longer wavelength.
C-The wave with the higher frequency has the shorter wavelength
D-The wavelengths cannot be compared unless the specific frequencies of the waves are known.

Answer 1

Answer:

C-The wave with the higher frequency has the shorter wavelength

frequency= Speed of light/ wavelength

frequency is inversely proportional to wavelength

Answer 2

Given info : Two transmitters in space emit electromagnetic waves with frequencies that differ by 1MHz.

answer : option (C) The wave with the higher frequency has the shorter wavelength.

solution : let two transmitters A and are in space emit electromagnetic waves with frequency f₁ and f₂ respectively.

given, f₁ = f₂ + 1 MHz

it means, f₁ > f₂ ...(1)

we know, speed of light = frequency × wavelength of electromagnetic wave

⇒c = fλ

so, f = c/λ

∴ f₁ = c/λ₁ and f₂ = c/λ₂

now from equation (1),

f₁ > f₂ ⇒ c/λ₁ > c/λ₂

⇒λ₁ < λ₂

Therefore it is clear that the wave with higher frequency has shorter wavelength.