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14. waves and sound — Physics STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 SciencePhysics14. waves and sound1 Mark
MCQ
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
  • A
    $\frac{ u }{2 \lambda}$
  • B
    $\frac{ u }{\lambda}$
  • ✓
    $\frac{2 u }{\lambda}$
  • D
    $\sqrt{ u \lambda}$
✓

Answer

Correct option: C.
$\frac{2 u }{\lambda}$
c
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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