Two loudspeakers are placed with a separation of 10 m, as shown in the figure. Both speakers are fed with an audio input signal of the same frequency with constant volume. [2026]

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Solution

Q.
Two loudspeakers $(L_{1} and L_{2})$ are placed with a separation of 10 m, as shown in the figure. Both speakers are fed with an audio input signal of the same frequency with constant volume. A voice recorder, initially at point A, equidistant to both loudspeakers, is moved by 25 m along the line AB while monitoring the audio signal. The measured signal was found to undergo 10 cycles of minima and maxima during the movement. The frequency of the input signal is ______ Hz.

(Speed of sound in air is 324 m/s and $\sqrt{5}$ = 2.23) [2026]

Ans.
(600)

$Point B will be 10^{th} maxima$

$Δ x = L_{2} B - L_{1} B$

$L_{1} B = \sqrt{20^{2} + 40^{2}} = 20 \sqrt{5} m = 44.6 m$

$L_{2} B = \sqrt{40^{2} + 30^{2}} = 50 m$

$Δ x = 50 - 44.6 = 5.4 m$

$Δ x = n λ$

$5.4 = 10 \times λ$

$λ = 0.54 m$

$V = f λ$

$f = \frac{324}{0.54} = 600 Hz$

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