Two stationary sources each emitting waves of wave length $\lambda$. An observer moves from one source to other with velocity $u .$ Then number of beats heared by him
AIPMT 2000, Diffcult
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For $1^{st}$ source
$n _{1}= n \left(\frac{ v - u }{ v }\right)=\left(1-\frac{ u }{ v }\right) n$
for $2^{nd}$ source
$n _{2}= n \left(\frac{ v + u }{ v }\right)=\left(1+\frac{ u }{ v }\right) n$
Beat freq. $=\left| n _{1}- n _{2}\right|= n +\frac{ nu }{ v }- n +\frac{ nu }{ v }$
$=\frac{2 nu }{ v }=2 \frac{ u }{\lambda}\left[\because v = n \lambda \quad \therefore \frac{1}{\lambda}=\frac{ n }{ v }\right]$
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