A) \[n=\sqrt{n'n''}\]
B) \[n=\frac{n'+n''}{2}\]
C) \[n=\frac{2n'+n''}{n'-n''}\]
D) \[n=\frac{2n'+n''}{n'+n''}\]
Correct Answer: D
Solution :
When train approaches stationary observer, the apparent frequency \[n'=\frac{vn}{v-{{v}_{s}}}\] and when the train recedes away train the observer, the apparent frequency \[n''=\frac{vn}{v+{{v}_{s}}}\] or \[\frac{n}{n'}=1-\frac{{{v}_{s}}}{v}\] ? (i) and \[\frac{n}{n''}=1+\frac{{{v}_{s}}}{v}\] ? (ii) On adding Eq. (i) and (ii), we get \[\frac{n}{n'}+\frac{n}{n''}=2\] \[n=\frac{2n'n''}{n+n''}\]
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