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Wave Optics question

2025 · Shift 1 · Q39
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Wave Optics question

2025 · Shift 1 · Q39

JEE AdvancedPhysicsWave OpticsMultiple correct+4 / −2
Consider a system of three connected strings, S1,S2S_1, S_2S1​,S2​ and S3S_3S3​ with uniform linear mass densities μkg/m,4μ kg/m\mu\mathrm{kg} / \mathrm{m}, 4 \mu \mathrm{~kg} / \mathrm{m}μkg/m,4μ kg/m and 16μ kg/m16 \mu \mathrm{~kg} / \mathrm{m}16μ kg/m, respectively, as shown in the figure. S1S_1S1​ and S2S_2S2​ are connected at the point PPP, whereas S2S_2S2​ and S3S_3S3​ are connected at the point QQQ, and the other end of S3S_3S3​ is connected to a wall. A wave generator 0 is connected to the free end of S1S_1S1​. The wave from the generator is represented by y=y0cos⁡(ωt−kx)cmy=y_0 \cos (\omega t-k x) \mathrm{cm}y=y0​cos(ωt−kx)cm, where y0,ωy_0, \omegay0​,ω and kkk are constants of appropriate dimensions. Which of the following statements is/are correct: JEE Advanced 2025 Paper 1 Online Physics - Wave Optics Question 2 English
  1. A
    When the wave reflects from PPP for the first time, the reflected wave is represented by y=α1y0cos⁡(ωt+kx+π)cmy=\alpha_1 \mathrm{y}_0 \cos (\omega t+k x+\pi) \mathrm{cm}y=α1​y0​cos(ωt+kx+π)cm, where α1\alpha_1α1​ is a positive constant.
  2. B
    When the wave transmits through PPP for the first time, the transmitted wave is represented by y=α2y0cos⁡(ωt−kx)cmy=\alpha_2 y_0 \cos (\omega t-k x) \mathrm{cm}y=α2​y0​cos(ωt−kx)cm, where α2\alpha_2α2​ is a positive constant.
  3. C
    When the wave reflects from QQQ for the first time, the reflected wave is represented by y=α3y0cos⁡(ωt−kx+π)cmy=\alpha_3 \mathrm{y}_0 \cos (\omega t-k x+\pi) \mathrm{cm}y=α3​y0​cos(ωt−kx+π)cm, where α3\alpha_3α3​ is a positive constant.
  4. D
    When the wave transmits through QQQ for the first time, the transmitted wave is represented by y=α4y0cos⁡(ωt−4kx)cmy=\alpha_4 y_0 \cos (\omega t-4 k x) \mathrm{cm}y=α4​y0​cos(ωt−4kx)cm, where α4\alpha_4α4​ is a positive constant.
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