John is listening to a horn. He knows the frequency of the horn is 300 Hz when both he and the horn are at rest. If he hears a pitch of 330 Hz, there are clearly several possibilities. For each of the following statements, indicate whether it is correct or incorrect.

Both can be moving in the same direction at the same speed.
Both can be moving and have the same speed.
Both can be moving and have different speeds.
Both can be moving, in opposite directions.
The distance between John and the horn is increasing with time.
John is moving towards the horn at rest.

Both can be moving in the same direction at the same speed. Correct, but they would need to be moving towards each other at a speed of 30 Hz.

Both can be moving and have the same speed. Incorrect, because for John to hear a higher pitch, he would need to be moving towards the horn, which means he would be moving faster than the horn.
Both can be moving and have different speeds. Correct, as stated in the previous statement, John would need to be moving towards the horn at a higher speed than the horn itself.
Both can be moving, in opposite directions. Incorrect, since for John to hear a higher pitch, he would need to be moving towards the horn, not away from it.
The distance between John and the horn is increasing with time. Incorrect, since John is moving towards the horn, the distance between them is decreasing with time.
John is moving towards the horn at rest. Incorrect, John is moving towards the horn, but he is not at rest.

To determine the correctness of each statement, we need to understand the concept of the Doppler effect, which explains the change in frequency of a sound wave due to relative motion between the source and the observer.

1. Both can be moving in the same direction at the same speed. - Correct. If John and the horn are moving in the same direction at the same speed, the relative velocity between them will be zero. As a result, there will be no change in the frequency heard by John, and the observed pitch will still be 300 Hz.

2. Both can be moving and have the same speed. - Incorrect. If both John and the horn have the same speed, there will still be a relative velocity between them. As a result, there will be a change in the frequency heard by John, and the observed pitch will not be 300 Hz.

3. Both can be moving and have different speeds. - Correct. If John and the horn have different speeds, there will be a non-zero relative velocity between them. This will cause a change in the frequency heard by John, resulting in a pitch different from 300 Hz.

4. Both can be moving, in opposite directions. - Correct. If John and the horn are moving in opposite directions, there will be a relative velocity between them. This will cause a change in the frequency heard by John, resulting in a pitch different from 300 Hz.

5. The distance between John and the horn is increasing with time. - Correct. If John hears a pitch higher than the rest frequency (330 Hz), it means that the horn's source frequency is higher than what John is hearing. This could occur if John is moving away from the horn, causing an increase in the distance between them.

6. John is moving towards the horn at rest. - Incorrect. If John was moving towards the horn at rest, he would experience a higher frequency (pitch) than the rest frequency (300 Hz). However, since he hears a pitch lower than the rest frequency (330 Hz), it suggests that either John or the horn is moving away from each other or both are moving away relative to each other.

To determine the possibilities, we need to consider the Doppler effect, which explains how sound waves change when there is relative motion between the source of the sound and the listener.

1. Both can be moving in the same direction at the same speed - Incorrect: If both John and the horn are moving in the same direction at the same speed, the frequency John hears would be the same as the frequency emitted by the horn when they are at rest. Therefore, the pitch would still be 300 Hz, not 330 Hz.

2. Both can be moving and have the same speed - Incorrect: Similar to the previous statement, if both John and the horn have the same speed, then the relative motion between them would not cause a change in frequency. Therefore, the pitch would still be 300 Hz, not 330 Hz.

3. Both can be moving and have different speeds - Correct: If John and the horn are moving relative to each other, with different speeds, this relative motion will cause a change in frequency. John hearing a pitch of 330 Hz implies that he is moving either towards the horn or the horn is moving towards him. The difference in speed between them would determine the change in frequency.

4. Both can be moving, in opposite directions - Correct: If John and the horn are moving in opposite directions, this can also result in a change in frequency. The magnitude of the change would depend on the speed of each of them and the direction of motion.

5. The distance between John and the horn is increasing with time - Correct: Since John hears a higher frequency (330 Hz) compared to the frequency emitted by the horn at rest (300 Hz), it indicates that the distance between John and the horn is increasing with time. This would be the case if John is moving away from the horn while the horn remains stationary.

6. John is moving towards the horn at rest - Correct: Since John hears a higher frequency (330 Hz) compared to the frequency emitted by the horn at rest (300 Hz), it implies that John is moving towards the horn. The relative motion causes a compression of sound waves, resulting in an apparent increase in frequency.

1. False.

2. F.
3. T.
4. T.
5. F.
6. T.