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Waves

Question
CBSEENPH11020384

A wave travelling along the x-axis is described by the equation y(x, t) = 0.005 cos (αx −βt). If the wavelength and the time period of the wave are 0.08 m and 2.0 s, respectively, then α and β in appropriate units are 

  • α = 25.00 π, β = π

  • α = 0.08/ π,  2.0/π

  • α = 0.04 / π , β =1.0/π

  • α = 12.50 , β =π/ 2.0

Solution

A.

α = 25.00 π, β = π

y = 0.005 cos (αx − βt)
comparing the equation with the standard form,
straight y space equals space straight A space cos space open square brackets open parentheses straight x over straight lambda minus straight t over straight T close parentheses 2 straight pi close square brackets
2 straight pi divided by straight lambda space equals space straight alpha space and space 2 straight pi divided by straight T space equals space straight beta
straight alpha space equals space 2 straight pi divided by 0.08
space equals space 25.00 space straight pi
straight beta space equals space straight pi