Question

John is listening to a horn. When the horn and John are both at rest, the frequency of the horn is 300 Hz. If he hears a pitch of 330 Hz, there are clearly several possibilities. State which of the possibilities are correct.

1. Both can be moving and have the same speed

2. John is moving towards the horn at rest

3. The distance between John and the horn is increasing with time

4. Both can be moving in opposite directions

5. Both can be moving and have different speeds

6. John and the horn are both moving in the same direction but John is behind and moving faster than the horn

Answer 1

The Doppler equation for sound wave is given as

where f' is the observed frequency, v is the velocity of sound waves, v₀ is the velocity of observer, v_s is the velocity of the source, f is the actual frequency.

Now here, for case 1, both are moving in same speed and in same direction then v₀ is (+)ve and v_s is (-)ve, so denominator and numerator are same in quantity so there will be no change in frequency.

For case 2, john is moving but horn is rest then v₀ is (+)ve and v_s is 0, so numerator is greater than denominator hence frequency increases.

For case 3, the distance between john and horn is increasing with time which implies the frequency should decrease.

For case 4, both can be moving in opposite direction which implies both v₀ and v_s are (+)ve quantity. So, the frequency increases.

For case 5, both can be moving and have different speed. Here are two possibilities they are separating or the are coming closer. If they are separating then frequency decreases and if they are coming closer then frequency increases.

For case 6, v₀ is (+)ve and v_s is (-)ve but v_o is greater than v_s. hence, frequency increases.