Question

At t=0, a transverse wave pulse traveling in the positive x direction with a speed of 2m/s in a wire is described by the function y=6/x^2, given that x not equal to 0 . It's velocity at x=2 m and t=2s will be

Answer 1

The velocity at x=2 m and t=2s will be Vt= −3 m/s

Explanation:

Given data:

• Wave velocity = 2 m/s.
• Equation of the travelling wave is   Y= 6 / X^2

The transverse velocity of the particle at X=2 m at t=2 sec. is

Vt = dY / dt = d / dt {6 / x^2}

Vt = d / dt{6x^−2} = 6 d / dt {x^−2}

Vt = 6(−2)X^−2−1 (dx / dt) = −12  / x^3(dx / dt)

Vt = (−12 2^3) (2)

⇒Vt = −12 × 28

⇒ Vt= −3 m/s

Hence the velocity at x=2 m and t=2s will be Vt= −3 m/s

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