To determine the frequency of each van as received by the others, we need to take into account the Doppler effect. The Doppler effect describes the change in frequency of a wave (in this case, radio waves) due to the relative motion between the source and the observer.
Let's assume the frequency emitted by each van is f0.
1. Frequency observed by Van 1 when receiving signals from Van 2:
Since Van 1 is moving towards Van 2, the frequency observed by Van 1 (f1) will be higher than the emitted frequency (f0) due to the Doppler effect. The formula for the observed frequency is given by:
f1 = f0 * (c + v) / c
where c is the speed of the radio waves and v is the speed of Van 1 relative to Van 2.
2. Frequency observed by Van 1 when receiving signals from Van 3:
Similarly, since Van 1 is moving away from Van 3, the frequency observed by Van 1 (f2) will be lower than the emitted frequency (f0). The formula for the observed frequency is:
f2 = f0 * (c - v) / c
3. Frequency observed by Van 2 when receiving signals from Van 1 or Van 3:
Since Van 2 is stationary, there is no relative motion between Van 2 and the other vans. Therefore, the frequency observed by Van 2 (f3) will be the same as the emitted frequency (f0).
4. Frequency observed by Van 3 when receiving signals from Van 1:
Since Van 3 is moving towards Van 1, the frequency observed by Van 3 (f4) will be higher than the emitted frequency (f0). We can use the same formula as for Van 1:
f4 = f0 * (c + v) / c
To summarize:
- Frequency observed by Van 1 from Van 2: f1 = f0 * (c + v) / c
- Frequency observed by Van 1 from Van 3: f2 = f0 * (c - v) / c
- Frequency observed by Van 2 from Van 1 or Van 3: f3 = f0
- Frequency observed by Van 3 from Van 1: f4 = f0 * (c + v) / c
Please note that these formulas assume the speeds of the vans are non-relativistic compared to the speed of light (c).