Placed at a large distance from an observer, a source emits a sound of frequency . The source begins traveling towards the observer with a uniform acceleration a . Determine the frequency heard by the observer corresponding to the wave emitted just after the source starts. The speed of sound in the medium is given as v .

Step-by-step solution

The time period of the emitted sound is T = 1 . Let the source emit the first wave crest at t = 0 . The position of this crest at time t is x₁ = vt . The second wave crest is emitted at t = T . During this time, the source moves a distance x_s = 1 2 aT^2 . The position of the second crest at time t (where t > T ) is x₂ = x_s + v(t - T) = 1 2 aT^2 + v(t - T) . The apparent wavelength ' is the distance between the first and second crests: ' = x₁ - x₂ = vt - [ 1 2 aT^2 + v(t - T) ] = vT - 1 2 aT^2 The frequency ' hear