Is there an appreciable Doppler effect when the motion of the source is at right angles to a listener? Explain.
Solution 38E STEP 1: The Doppler effect depends on the relative motion of the source and receiver. So when 0 the source moves at an angle of 90 with the observer, we need to calculate the relativistic doppler effect. Suppose the source of light is moving at an arbitrary angle with the direction of the observer, the frequency change will be as follows, V fs= f 0 (1 + C cos )------------------------(1) Where = 1 is the Lorentz factor. 1V2 C2 STEP 2: When the angle between source and observer’s motion will be a right angle, then f = f (1 + V cos ) s 0 C V 0 f =sf 0(1 + Ccos 90 ) f =sf (1 + 0) 0 f =sf 0--------------(2) As the value of the lorentz factor is always less than unity for any velocity lesser than the speed of light, the frequency will be reduced. STEP 3: As it is true for light, it must be true for sound waves too. But the lorentz factor here we can neglect as the speed is very less compared to the speed of light. So, fs= f 0 Approximately same frequency. CONCLUSION: So, there will not be an appreciable doppler shift when the motion of the source is at right angles to the listener.