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Waves question

2014 · Shift 1 · Q50
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Waves question

2014 · Shift 1 · Q50

JEE AdvancedPhysicsWavesMultiple correct+3 / −1
One end of a taut string of length 3 m along the x-axis is fixed at x = 0. The speed of the waves in the string is 100 ms −-− 1. The other end of the string is vibrating in the y-direction so that stationary waves are set up in the string. The possible waveform(s) of these stationary wave is (are)
  1. A
    y(t)=Asin⁡πx6cos⁡50πt3y(t) = A\sin {{\pi x} \over 6}\cos {{50\pi t} \over 3}y(t)=Asin6πx​cos350πt​
  2. B
    y(t)=Asin⁡πx3cos⁡100πt3y(t) = A\sin {{\pi x} \over 3}\cos {{100\pi t} \over 3}y(t)=Asin3πx​cos3100πt​
  3. C
    y(t)=Asin⁡5πx6cos⁡250πt3y(t) = A\sin {{5\pi x} \over 6}\cos {{250\pi t} \over 3}y(t)=Asin65πx​cos3250πt​
  4. D
    y(t)=Asin⁡5πx2cos⁡250πty(t) = A\sin {{5\pi x} \over 2}\cos 250\pi ty(t)=Asin25πx​cos250πt
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