IB Physics Sub-topic C5 Notes

The Doppler effect

In the HL syllabus, you are expected to quantify the observed frequency for sounds waves and mechanical waves. For this, the previous explanation are reviewed.

First, imagine a source moving with speed (u_s) and emitting a sound wave of frequency (f) and speed (v), as shown below:

1. At position A: As the source moves, a wave is emitted. Since the source is moving, the second wave starts further from the first wave. This decreases the frequency of the wave that A will observe, and the formula for this is:

   $f' = f\frac{v}{v+u_{s}}$

2. At position B: As the source moves, a wave is emitted. Since the source is moving, the second wave starts closer to the first wave. This increases the frequency of the wave thatBA will observe. The formula for this is:

   $f' = f\frac{v}{v-u_{s}}$

Second, imagine a source emitting a sound wave of frequency f and speed v, an observer A moving towards it with speed u_o, and an observer B moving away with speed u_o, as shown below:

1. At position A: As A moves, a wave is emitted. Since A is moving closer, the second wave is received earlier. This increases the frequency of the wave that A will observe, and the formula for this is:

   $f' = f\frac{v+u_{o}}{v}$

2. At position B: As B moves, a wave is emitted. Since B is moving further, the second wave is received later. This decreases the frequency of the wave that A will observe, and the formula for this is:

   $f' = f\frac{v-u_{o}}{v}$