Principle of superposition of waves PYQs: JEE Mains Physics

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1. 1. 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 \(\sqrt{5}=2.23\) )
   2026 Hard
2. 2. The amplitude and phase of a wave that is formed by the superposition of two harmonic travelling waves, \(\mathrm{y}_1(\mathrm{x}, \mathrm{t})=4 \sin (\mathrm{kx}-\omega \mathrm{t})\) and \(\mathrm{y}_2(\mathrm{x}, \mathrm{t})=2 \sin \left(\mathrm{kx}-\omega \mathrm{t}+\frac{2 \pi}{3}\right)\), are \(:\)
   (Take the angular frequency of initial waves same as \(\omega\)) 2025 Medium
3. 3. Two waves are simultaneously passing through a string and their equations are : \({y}_{1}={A}_{1} \sin {k}({x}-v {t}), {y}_{2}={A}_{2} \sin {k}\left({x}-{vt}+{x}_{0}\right) .\) Given amplitudes \({A}_{1}=12\, {mm}\) and \({A}_{2}=5\, {mm}\) \({x}_{0}=3.5\, {cm}\) and wave number \({k}=6.28\, {cm}^{-1}\). The amplitude of resulting wave will be \(......\,{mm}\) 2021 Hard

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