Can you clear this misconception of mine?

Question

In Doppler Effect, I have a misconception regarding one thing which I have explained below:

In the Doppler Effect, the wavelength of the waves travelling in the same direction of the source decreases and the frequency of those waves with respect to the medium increases. In the Doppler Effect, the wavelength of the waves travelling in the opposite direction of the source increases and the frequency of those waves with respect to the medium decreases. But in the Doppler Effect, the wavelength of the waves travelling in the direction perpendicular to the direction of travel of the source remains the same. So what happens to the frequency of those waves with respect to the medium?

Answer 1

When you say "same direction" you mean the source and observer and traveling towards one another. As you correctly stated, the wavelength will decrease and the frequency increase. This is because of the relative velocity between the moving object and the source. Understanding this will help you understand the constant frequency and wavelength perpendicular to the source.

If we consider a stationary observer and a moving source emitting sounds waves, which each passing moment a wave compression (or think of it as a crest) leaves the source. As the source moves towards the observer it is also moving towards he compression just released as it releases another compression. This makes the wavelength shorter compared to if the source was stationary. In other words, the source is chasing the wave pulse it just released. You can also recall that perpendicular vectors are independent of each other, so the portion of the wave front moving perpendicular to the source velocity doesn't change.