Could you go through the derivation of the Doppler effect for a source moving towards an observer?

(need a diagram showing situation). You know that the frequency emitted by the source is given by the velocity of the emitted source divided by the wavelength (f_s = v / wavelength). It is also known that frequency is equal to 1/T (where T is the period). Consider the source moving towards the observer at speed u, the observer will observe a wavelength shorter than the sources original wavelength. This is made much clearer by looking at the diagram. In a period of time T, the waves emitted from the source will travel a distance of (vT - uT) and hence the frequency observed will be f'= v/((v-u)T). We know 1/T = the frequency emitted by the source so the equation can be rewritten as f'= (v/(v-u))f_s. This is the formula that gives you the frequency detected by a stationary observer as a source is moving towards it.