IBDP Physics: 9.5 – Doppler effect : IB Style Question Bank:HL Paper 1

Ans: D

The equation for doppler effect may be generalised as

\(\nu _o=\nu_s(\frac{v\pm v_o}{v\pm v_s})\)

where, \(v\) = speed of sound in the medium.

\(v_o\) = speed of the observer with respect to the medium, considered positive when it moves towards the source and negative when it moves away from the source and

\(v_o\) = speed of the source with respect to the medium, considered positive when it moves towards the observer and negative when it moves away from the observer.

Here in the problem , when Train approached stationary observer ,  frequency of the sound measured by the observer is given by

\(\nu _o=\nu_s(\frac{v+ 0}{v- v_s})=\nu_s(\frac{v}{v- v_s})\)
Gien train is de-accelerating mean
\(v_s=v_{s0}-at\) or \( v- v_s = v-(v_{s0}-at)=v-v_{s0}+at\)
or
\(\nu _o =\nu_s\frac{v}{k+at}\) where k is \(v-v_{s0}\)
hence as \(t \uparrow \nu_o \downarrow\)

when Train approached leave observer ,  frequency of the sound measured by the observer is given by

\(\nu _o=\nu_s(\frac{v+ 0}{v+ v_s})=\nu_s(\frac{v}{v+ v_s})\)
Gien train is de-accelerating mean
\(v_s=v_{s0}-at\)  or  \(v+ v_s = v+(v_{s0}-at)=v+v_{s0}-at\)
or
\(\nu _o =\nu_s\frac{v}{k-at} \;where\; k \;is\; v+v_{s0}\)
hence as \(t \uparrow \nu_o \uparrow\)

This is in answer option D