Can you clear my misconception?

Question

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

Suppose there are two balls of unequal sizes placed touching each other, the bigger one on the left and the smaller one on the right. At a particular moment, let the smaller ball start moving towards the right at velocity w and at that moment let the bigger ball move towards the right at velocity v. In such a case, the length of the smaller ball does not decrease. It remains the same. But then in Doppler Effect, why does the wavelength of the waves moving in the same direction of the source decrease?  

Answer 1

The source is moving in the direction of the wave that it is releasing while maintaining its frequency. That means that it is catching up to the waves that it is emitting and shortening the distance between the wave peaks resulting in a shorter effective wavelength by a factor of (vsound - vsource)/vsound. This means that the frequency, which is inverse with the wavelenght will increase by the ratio vsound/(vsound - vsource). When a listener is moving towards the source, that affects the frequency directly f' = f(vlistener+vsound)/vsound.

The overall doppler equation for sound is f' = f(v+v_L)/(v-v_s) where v is vsound and the source and listener velocities are >0 if they are moving towards each other. Note that source or listener causes f'>f when moving towards each other, but they do it in different ways.