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Question

A standing wave y=A sin (20πx3)cos (1000 π t) is set up in a taut string, where x and y are in metre and t is in seconds. The distance between first two successive points oscillating with the amplitude A2, from the fixed end will be equal to
  1. 10 cm
  2. 15 cm
  3. 2.5 cm
  4. 4 cm


Solution

The correct option is A 10 cm
For the standing wave represented by 
y=A sin (20πx3)cos (1000πt)


A particle on string in a standing wave execute SHM with amplitude of  
Ax=A sin (20πx3)
Putting Ax=A2
sin (20πx3)=12
(20πx3)=π6,5π6
x=140,18 m
So, distance between two consecutive points having amplitude A2 is 18140=110 m=10 cm

 

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