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Resultant amplitude of two superposed waves with a phase difference

This type of question, asked 5 times: 2021 Paper 19, 14 Jun 2022, 25 Jul 2022, 29 Jan 2023, 31 Jan 2023. All 5 questions below, oldest first.

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  1. Question 1

    2021 Paper 19

    21
    Two waves are simultaneously passing through a string and their equations are : y1=A1sin⁡k(x−vt),y2=A2sin⁡k(x−vt+x0)y_{1}=A_{1}\sin k(x - vt),y_{2}=A_{2}\sin k\left( x - vt +x_{0} \right). Given amplitudes A1=12 mmA_{1}= 12\text{ }mm and A2=5 mmA_{2}= 5\text{ }mm, x0=3.5 cmx_{0}= 3.5\text{ }cm and wave number k=6.28 cm−1k = 6.28{\text{ }cm}^{- 1}. The amplitude of resulting wave will be ______ mmmm.

  2. Question 2

    14 Jun 2022

    12
    The equations of two waves are given by:
    y1=5sin⁡2π(x−vt)cmy2=3sin⁡2π(x−vt+1.5)cm\begin{matrix} & y_{1}= 5\sin2\pi(x - vt)cm \\ & y_{2}= 3\sin2\pi(x - vt + 1.5)cm \end{matrix}
    These waves are simultaneously passing through a string. The amplitude of the resulting wave is

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  3. Question 3

    25 Jul 2022

    117
    Two waves executing simple harmonic motion travelling in the same direction with same amplitude and frequency are superimposed. The resultant amplitude is equal to the 3\sqrt{3} times of amplitude of individual motions. The phase difference between the two motions is ____\_\_\_\_ degree.

  4. Question 4

    29 Jan 2023

    23
    Two simple harmonic waves having equal amplitudes of 8 cm8\text{ }cm and equal frequency of 10 Hz10\text{ }Hz are moving along the same direction. The resultant amplitude is also 8 cm8\text{ }cm. The phase difference between the individual waves is_____ degree.

  5. Question 5

    31 Jan 2023

    120
    The displacement equations of two interfering waves are given by y1=10sin⁡(ωt+π3)cm,y2=y_{1}= 10\sin\left( \omega t +\frac{\pi}{3} \right)cm,y_{2}= 5[sin⁡ωt+3cos⁡ωt]cm5\lbrack \sin\omega t +\sqrt{3}\cos\omega t\rbrack cm respectively. The amplitude of the resultant wave is ____cm.