When two sound waves with a phase difference of π/ 2 and each having amplitude A and frequency ω

step 1 The given situation of the question is when two sound waves with a phase difference of pi by two

When two sound waves with a phase difference of π/ 2 and...

When two sound waves with a phase difference of $\pi / 2$ and each having amplitude $A$ and frequency $\omega$ are superimposed on each other, then the maximum amplitude and frequency of resultant wave is $\quad$ [MP PMT 1989] (a) $\frac{A}{\sqrt{2}} ; \omega / 2$ (b) $\frac{A}{\sqrt{2}} ; \omega$ (c) $\sqrt{2} A ; \frac{\omega}{2}$ (d) $\sqrt{2} A ; \omega$

When two sound waves with a phase difference of $\pi / 2$ and each having amplitude $A$ and frequency $\omega$ are superimposed on each other, then the maximum amplitude and frequency of resultant wave is $\quad$ [MP PMT 1989]
(a) $\frac{A}{\sqrt{2}} ; \omega / 2$
(b) $\frac{A}{\sqrt{2}} ; \omega$
(c) $\sqrt{2} A ; \frac{\omega}{2}$
(d) $\sqrt{2} A ; \omega$

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Key Concepts

Superposition Principle

This concept explains that when two or more waves overlap, the resultant displacement at any point is the algebraic sum of the individual displacements. It is fundamental in wave theory and is applicable to all types of waves, including sound, light, and water waves.

Phase Difference

Phase difference refers to the difference in the phase angle between two waves. It determines how two waves interfere with each other, leading to constructive or destructive interference. A phase difference of ?/2 radians, for instance, leads to partial constructive interference where the peaks of one wave correspond to the midpoints of the other.

Phasor Addition

Phasor addition is a mathematical technique used to combine waves of the same frequency by representing them as rotating vectors (phasors) in the complex plane. The resultant amplitude can be determined by vector addition of the individual amplitudes, taking into account their phase differences, making it easier to calculate the maximum amplitude of the superimposed wave.

Frequency Invariance in Wave Interference

While interference affects the amplitude of the resultant wave, the frequency remains unchanged during the superposition process. This is because the frequency is a property of the source and is not altered by the linear addition of the waveforms.

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