A Wave Is Represented By The Equation                                      Where x is In Metres And t in Seconds. The Expression Represents

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Question

 

A wave is represented by the equation  

                                  

Where x is in metres and t in seconds. The expression represents

Solution

Correct option is

A wave travelling the negative x-direction with a velocity of 1.5 ms–1. & A wave travelling in the negative x-direction with a wavelength of 0.2 m

 

Wave travelling in the positive x-direction is characterized by a function y= f (x – vt) and that in the negative x-direction by a function y = f (x + vt). Thus, the given wave is travelling in the negative x-direction. The wavelength of the wave is given by 

      coefficient of x in the argument of the sine function = 10π

Therefore, λ = 0.2 m. The wave velocity is given by

   coefficient of t in the argument of the since function = 15π

Which gives,    v = 7.5 λ = 7.5 × 0.2 = 1.5 ms–1.

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