Q.The displacements of two sinusoidal waves propagating through a string are given by the following equations: y₁ = 4 sin(20x − 30t), y₂ = 4 sin(25x − 40t), where x and y are in centimeter and t is in second.

When two waves of the SAME frequency $\omega$ but generally different amplitudes $A_1$, $A_2$ and a fixed phase difference $\phi$ superpose at a point, $y_1=A_1\sin\omega t$ and $y_2=A_2\sin(\omega t+\phi)$, the principle of superposition combines them into a single resultant simple-harmonic oscillation of the SAME frequency, $y=A\sin(\omega t+\theta)$, whose amplitude works out (by expanding the compound-angle term and then squaring-and-adding to eliminate the new phase $\theta$) to $A=\sqrt{A_1^2+A_2^2+2A_1A_2\cos\phi}$.

This single formula captures BOTH extreme interference cases seen with wave pulses: when $\phi=0$ (the waves are exactly in phase), $A=A_1+A_2$, the LARGEST possible resultant amplitude -- constructive interference; when $\phi=\pi$ (exactly out of phase), $A=|A_1-A_2|$, the SMALLEST possible resultant amplitude (zero, if $A_1=A_2$) -- destructive interference. Since intensity is proportional to the square of amplitude, the corresponding maximum and minimum intensities are $I_{max}\propto(A_1+A_2)^2$ and $I_{min}\propto(A_1-A_2)^2$: intensity is greatest wherever two interfering waves arrive in phase, and least wherever they arrive out of phase -- the physical basis for locating points of maximum/minimum loudness between two sound sources.

This superposition-of-waves result comes from the NCERT Class 11 Physics chapter on Waves, and constructive/destructive-interference numericals built on it are a recurring feature of CBSE boards, JEE Main and NEET. Students searching "resultant amplitude formula superposition of waves" or "constructive and destructive interference class 11" land squarely on this concept.