V.5 No 1

49

Classical transverse Doppler-effect

In the view of classical conception, the particular expression for frequency received by moving observer, with central mutual motion, can be yielded on the basis of (9) either (10) by additional stipulation

The only, in transition from (9) to (12), we have to account additionally that the difference in the square brackets of denominator is alternating in sign.

At 0 / 2

and the bracket is positive.

At  / 2

(where ₁ = - / 2) and the bracket is negative.

Noting this change of sign in transition from positive x to negative, we yield the solution as follows:

The calculation after (10) gives us the same result, given the above sign-alternating square root at small aimed distances.

Basically, yielded solutions do not essentially differ from the known. "Let the speed between the source of sound and receiver be v. Then the observed frequency, with moving source of sound and stationary receiver, is

with stationary source of sound and moving receiver

Note, to compare with their results, relativists use (2) fully coinciding with (15). While in classical physics there is used the regularity coinciding with general solution only for quadratic terms, which, naturally, can bring considerable discrepancy with the experiment in studying the sublight-speed motion of objects. This is the defect of particular calculations, not of the classical conception as the whole. As we could see, general solution has the form (9).