Verified Solution • 2025–26 Session moderate

QAIPM-2012-Ph-1674: NEET 2012 Physics - Class 11 AIPM-2012-Ph-1674 Solution: The equation of a simple harmonic wave is given by \(y = 3 {…

The equation of a simple harmonic wave is given by y=3sin⁡π2(50t−x)y = 3\sin\frac{\pi}{2}(50t-x) where x and y are in metres and t is in seconds. The ratio of maximum particle velocity to the wave velocity is 2π2\pi 32π\frac{3}{2}\pi 3π3\pi 23π\frac{2}{3}\pi

Multiple Choice Options

  • A 2 π\pi �
  • B 32π{3 \over 2}\pi 2 3 _ �
  • C 3π3\pi 3 �
  • D 23π{2 \over 3}\pi 3 2 _ �

Step-by-Step Verified Solution

y = 3 sin _ � 2 ( 50 t _ x ) y = 3 sin _ ( 25 � t _ � 2 x ) on comparing with the standard wave equation y = a sin _ ( _ t _ k x ) Wave velocity v = _ k = 25 � � / 2 = 50 m / sec The velocity of particle v p = � y � t = 75 � cos _ ( 25 � t _ � 2 x ) v p max = 75 � then v p max v = 75 � 50 = 3 � 2

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