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Resultant amplitude of two superposed waves with a given phase difference

This type of question, asked 6 times: 9 May 2023 S1, 9 May 2023 S2, 16 May 2023 S1, 9 May 2024 S1, 14 May 2024 S2, 20 Apr 2026 S2. All 6 questions below, oldest first.

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  1. Question 1

    9 May 2023 S1

    7
    Two sound waves having same amplitude AA and angular frequency ω\omega but having a phase difference of π2\frac{\pi}{2} are superimposed. The maximum amplitude of the resultant wave is

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  2. Question 2

    9 May 2023 S2

    50
    The equations of two waves are given as y1=asin⁡(ωt+ϕ1)y_1 = a\sin(\omega t + \phi_1), y2=asin⁡(ωt+ϕ2)y_2 = a\sin(\omega t + \phi_2). If amplitude and time period of resultant wave is same as the individual waves, then ϕ1−ϕ2\phi_1 - \phi_2 is

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  3. Question 3

    16 May 2023 S1

    36
    Two sound waves each of wavelength 'λ\lambda' and having the same amplitude 'A' from two sources 'S1S_1' and 'S2S_2' interfere at a point P. If the path difference, S2P−S1P=λ/3S_2P - S_1P = \lambda/3 then the amplitude of resultant wave at point 'P' will be [cos⁡120°=−0.5\cos 120° = -0.5]

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  4. Question 4

    9 May 2024 S1

    36
    The equation of a simple harmonic progressive wave is given by y=1asin⁡ωt±1bcos⁡ωty = \frac{1}{\sqrt{a}}\sin\omega t \pm \frac{1}{\sqrt{b}}\cos\omega t. Then the resultant amplitude of the wave is (cos⁡90∘=0\cos 90^\circ = 0)

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  5. Question 5

    14 May 2024 S2

    7
    When two light waves each of amplitude AA & having a phase difference of π2\frac{\pi}{2} superimposed then the amplitude of resultant wave is

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  6. Question 6

    20 Apr 2026 S2

    121
    Two sound waves each of wavelength λ\lambda and same amplitude AA interfere at point QQ. If the path difference is λ4\dfrac{\lambda}{4}, the amplitude of the resultant wave at point QQ is [sin⁡π2=1,cos⁡π2=0]\left[\sin\dfrac{\pi}{2} = 1, \cos\dfrac{\pi}{2} = 0\right]

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