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Standard XII

Physics

Differential Equation of Wave

The equation ...

Question

The equation of simple harmonic progressive wave is given by $Y = 0.05 sin π [20 t - \frac{x}{6}]$ , where all quantities are in S.I units. Calculate the displacement of particle at $5 m$ from origin and at the instance $0.1$ second.

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Solution

Given, $x = 5 m$ , $t = 0.1 s$
$Y = 0.05 sin π [20 t - \frac{x}{6}]$
$∴$ Displacement $Y = 0.05 sin π [20 \times 0.1 - \frac{5}{6}]$
$= 0.05 sin π (2 - 0.833) = 0.025 m$

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The equation of simple harmonic progressive wave is given by Y=0.05sinπ[20t−x6], where all quantities are in S.I units. Calculate the displacement of particle at 5m from origin and at the instance 0.1 second.

Given, x=5m, t=0.1sY=0.05sinπ[20t−x6]∴ Displacement Y=0.05sinπ[20×0.1−56]=0.05sinπ(2−0.833)=0.025m

The equation of simple harmonic progressive wave is given by $Y = 0.05 sin π [20 t - \frac{x}{6}]$ , where all quantities are in S.I units. Calculate the displacement of particle at $5 m$ from origin and at the instance $0.1$ second.

Given, $x = 5 m$ , $t = 0.1 s$
$Y = 0.05 sin π [20 t - \frac{x}{6}]$
$∴$ Displacement $Y = 0.05 sin π [20 \times 0.1 - \frac{5}{6}]$
$= 0.05 sin π (2 - 0.833) = 0.025 m$