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 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~mathrmm/s and sqrt5=2.23)
Waves and Sound diagram for Q46 - JEE Main 2026 January Morning
Two loudspeakers setup with path difference for sound interference.

Numerical Answer Type:
Enter a numerical value Answer: 600 to 600 +4 marks

Solution & Explanation

### Related Formula Delta x = nlambda, quad v = flambda ### Core Logic
Solution geometry diagram for Q46 - JEE Main 2026 Morning
Two loudspeakers setup with path difference for sound interference.
Path difference at point B: L_1 B = sqrt20^2 + 40^2 = 20sqrt5 text m = 44.6 text m L_2 B = sqrt40^2 + 30^2 = 50 text m Delta x = 50 - 44.6 = 5.4 text m Delta x = nlambda implies 5.4 = 10 times lambda implies lambda = 0.54 text m f = fracvlambda = frac3240.54 = 600 text Hz ### Pattern Recognition Sees: Loudspeaker interference cycles along displacement line. Shortcut: Compute path difference at endpoint B, relate to total interference cycles to find wavelength, then frequency. Check: Numerical answer is 600 Hz. ✓ ### Chapter Mix Class 11 Physics: Waves and Sound

Reference Study Guides

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