JEE Mains · Physics · STD 11 - Waves and sound
- JEE Mains 2026
- Hard
- Numerical
Two loudspeakers ( \(L_1\) and \(L_2\) ) are placed with a separation of 10 m , as shown in figure. Both speakers are fed with an audio input signal of same frequency with constant volume. A voice recorder, initially at point \(A\), at equidistance to both loud speakers, is moved by 25 m along the line \(A B\) 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 \(\sqrt{5}=2.23\) )
Pick an option to check your answer.
Answer & Solution
Correct Answer
(B) 600
Step-by-step Solution
Detailed explanation
Point B will \(10^{\text {th }}\) maxima
\(\begin{array}{l}\Delta x=L_2 B-L_1 B \\ L_1 B=\sqrt{20^2+40^2}=20 \sqrt{5} m=44.6 m \\ L_2 B=\sqrt{40^2+30^2}=50 m \\ \Delta x=50-44.6=5.4 m\end{array}\)
\(\begin{array}{l}\Delta x=n \lambda \\ 5.4=10 \times \lambda \\ \lambda=0.54 m \\ V=f \lambda\end{array}\)
\(f =\frac{324}{0.54}=600 Hz\)
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