SATHEE: Waves - Result Question 14

Waves - Result Question 14

14. A transverse wave is represented by the equation $y = y_{0} \sin \frac{2 π}{λ} (v t - x)$

For what value of $λ$ is the maximum particle velocity equal to two times the wave velocity?

[1998]

(a) $λ = 2 π y_{0}$

(b) $λ = \frac{π y_{0}}{3}$

(d) $λ = π y_{0}$

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Answer:

Correct Answer: 14. (d)

Solution:

(d) $y = y_{0} \sin \frac{2 π}{λ} (v t - x)$

Particle velocity,

$\frac{d y}{d t} = y_{0} \times \frac{2 π}{λ} v \cos \frac{2 π}{λ} (v t - x)$

Maximum particle velocity $= y_{0} \times \frac{2 π ν}{λ}$

Wave velocity $= v$ [given]

So, $y_{0} \times \frac{2 π v}{λ} = 2 v$

$λ = π \cdot y_{0}$

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Waves - Result Question 14

14. A transverse wave is represented by the equation y=y0sin⁡2πλ(vt−x)

Answer:

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14. A transverse wave is represented by the equation $y = y_{0} \sin \frac{2 π}{λ} (v t - x)$