Doppler's Principle

Abstract

IN answer to a correspondent who has met with a difficulty in the consideration of Doppler's principle, I may say that I think I fairly solved the difficulty in a paper delivered last year before the University College Chemical and Physical Society. In cases (1) and (2) of your correspondent, viz. approach or recession of observer, source and medium being at rest, the correct formula is and in cases (3) and (4), viz. approach and recession of source, observer and medium at rest, it is, n′ = the new, and n the old frequency of vibration of the note heard. It should be remarked, however, that in all practical cases, the two formulæ give very nearly the same result; but if the velocity v is very great, the case is entirely different. Suppose, for instance, in cases (1) and (2) that v = velocity of sound a, then n′ = 2n for approach, and O for recession of the observer. The correctness of these results is obvious without the aid of any formula. Again, in cases (3) and (4) suppose v = a, then n′ = ∞ for approach, and for recession of the source of sound. The effect of an infinite number of waves striking the ear at the same moment would be simply that nothing would be heard. It would be interesting to notice the change in pitch of the whistle of a rifle-bullet passing near an observer. Ganot's formula is correct for cases (1) and (2), and Prof. Everett's for cases (3) and (4); the proofs are very simple, and may be easily thought out. When the observer and the source of sound both move, the two formulæ should be applied separately when a, very accurate result is desired. These conclusions have been confirmed by Dr. Fison, of University College. I had not considered the effect of the motion of the medium, but it appears to me, after a little reflection, that this would increase or diminish the velocity of the sound, and the wave-length, in the same proportion, leaving the pitch unaltered; the velocity of the medium should therefore be added to or subtracted from a in the formula.