Write the equation of a simple harmonic progressive wave of amplitude

1.	Write the equation of a simple harmonic progressive wave of amplitude 0.05 m and period 0.04 s travelling along the positive xaxis with a velocity of 12.5 m/s.
Answer» Data : A = 0.05 m, T = 0.04 s, v = 12.5 m/s ∴ Equation of the wave travelling in the positive direction of the x-axis is y = A sin \(\frac{2\pi}T\)\((t-\frac{x}v)\) = 0.05 sin \(\frac{2\pi}{0.04}\)\((t-\frac{x}{12.5})\) meter OR v = \(\frac{\lambda}T\) \(\therefore\) \(\lambda\) = vT = 12.5 x 0.04 = 0.5 m \(\therefore\) The equation of the wave travelling in the positive direction of the x-axis is y = A sin \({2\pi}\)\((\frac tT-\frac x\lambda)\) = 0.05 sin \({2\pi}\)\((\frac t{0.04}-\frac x{0.5})\) meter

Write the equation of a simple harmonic progressive wave of amplitude 0.05 m and period 0.04 s travelling along the positive xaxis with a velocity of 12.5 m/s.

Answer»

Data : A = 0.05 m, T = 0.04 s, v = 12.5 m/s

∴ Equation of the wave travelling in the positive direction of the x-axis is

y = A sin \(\frac{2\pi}T\)\((t-\frac{x}v)\)

= 0.05 sin \(\frac{2\pi}{0.04}\)\((t-\frac{x}{12.5})\) meter

v = \(\frac{\lambda}T\)

\(\therefore\) \(\lambda\) = vT = 12.5 x 0.04 = 0.5 m

\(\therefore\) The equation of the wave travelling in the positive direction of the x-axis is

y = A sin \({2\pi}\)\((\frac tT-\frac x\lambda)\)

= 0.05 sin \({2\pi}\)\((\frac t{0.04}-\frac x{0.5})\) meter