Two loudspeakers L and L driven by a common oscillator and amplif… - Vidyadip

MCQ

Two loudspeakers $L$ and $L$ driven by a common oscillator and amplifier, are arranged as shown. The frequency of the oscillator is gradually increased from zero and the detector at $D$ records a series of maxima and minima. If the speed of sound is $330 \mathrm{~ms}$ then the frequency at which the first maximum is observed is

A
$165 \mathrm{~Hz}$
✓
$330 \mathrm{~Hz}$
C
$496 \mathrm{~Hz}$
D
$660 \mathrm{~Hz}$

✓

Answer

Correct option: B.

$330 \mathrm{~Hz}$

Path difference between the wave reachingat $D[\Delta x]=L_2PL_1P=\sqrt{40^2+9^2}-40=41-40=1 \mathrm{~m}$
For maximum $\Delta x=(2 n) \frac{\lambda}{2}$
For first maximum $(n=1)\Rightarrow 1=2(1) \frac{\lambda}{2}$
$ \Rightarrow \lambda=1 \mathrm{~m} \Rightarrow n=\frac{v}{\lambda}=330 \mathrm{~Hz}$

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