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Number of beats per second from the equations of two sound waves

This type of question, asked 6 times: 4 May 2023 S1, 10 May 2023 S1, 21 Apr 2025 S1, 16 Apr 2026 S2, 18 Apr 2026 S1, 19 May 2026 S1. All 6 questions below, oldest first.

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  1. Question 1

    4 May 2023 S1

    8
    Two waves Y1=0.25sin⁡316tY_1 = 0.25\sin 316t and Y2=0.25sin⁡310tY_2 = 0.25\sin 310t are propagating along the same direction. The number of beats produced per second are

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  2. Question 2

    10 May 2023 S1

    25
    Two sound waves having displacements x1=2sin⁡(1000πt)x_1=2\sin(1000\pi t) and x2=3sin⁡(1006πt)x_2=3\sin(1006\pi t), when interfere, produce

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  3. Question 3

    21 Apr 2025 S1

    43
    Two sources of sound are emitting progressive waves y1=4sin⁡710πty_{1}= 4\sin710\pi t and y2=3sin⁡702πty_{2}= 3\sin702\pi t. The sources are placed close to each other. The number of beats heard per second and intensity ratio between waxing and waning are respectively

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  4. Question 4

    16 Apr 2026 S2

    122
    Two waves Y1=0.25sin⁡316tY_1 = 0.25\sin 316t and Y2=0.25sin⁡310tY_2 = 0.25\sin 310t are propagating along the same direction. The number of beats produced per second are

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  5. Question 5

    18 Apr 2026 S1

    121
    Two sources of sound are emitting progressive waves y1=4sin⁡708 πty_1 = 4\sin 708\,\pi t and y2=3sin⁡700 πty_2 = 3\sin 700\,\pi t. The sources are placed close to each other. The number of beats heard per second and intensity ratio between waxing and wanning are respectively

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  6. Question 6

    19 May 2026 S1

    122
    Two simple harmonic sound waves travelling in the same direction are given by y1(x,t)=Asin⁡(0.5πx−100πt)y_1(x, t) = A\sin(0.5\pi x - 100\pi t) and y2(x,t)=Asin⁡(0.46πx−92πt)y_2(x, t) = A\sin(0.46\pi x - 92\pi t) The number of times, a stationary listener can hear sound of maximum intensity in one second is

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