Why did the magnitude of the doppler shift increase as the velocity of the sound source increased?

The Doppler effect happens as the result of a source of waves having relative motion to observers somewhere else consider that if something is producing a wave of wavelength W and it is moving relative to the waves then as the waves spread out it seems to chase one side and run away from the other side there for wavelengths produced on the scale it is chasing will be less than W on the side it is running away from the apparent wavelength will be greater than W so using this knowledge if the source of the Waves moves faster than it will chase one of the more closely and run away from the other more quickly there for making the short wavelength even shorter and the long wavelength even longer can turn you in and tell you have gone all over the speed of wave creating boom when dealing with sound this is what causes a sonic boom this lengthening of the long wavelengths and the shortening of the short wavelengths is referred to as being a greater Doppler shift