"a railroad locomotive is at rest with its whistle shrieking, then starts moving toward you. does the frequency of sound that you hear increase, decrease, or stay the same?"

This effect is called Doppler effect- it occurs when a source of a wave is moving relative to an observer. As a result, the apparent frequency of the sound (as seen by the observer) changes, because the wavelength of the wave appears shortened/lenghtened. In particular, we have two different situations:

- When the source of the wave is moving towards the observer, the apparent frequency as seen by the observer is higher than the real frequency

- When the source of the wave is moving away from the observer, the apparent frequency as seen by the observer is lower than the real frequency

The general formula to calculate the frequency shift due to the Doppler effect is:

[tex]f' = (\frac{v+v_o}{v+v_s})f[/tex]

where

f is the real frequency

f' is the apparent frequency

v is the velocity of the wave

[tex]v_o[/tex] is the velocity of the observer relative to the wave

[tex]v_s[/tex] is the velocity of the source of the wave relative to the observer