A transverse wave is described by the equation y = y 0 s i n 2 π f t - x λ .The maximum particle velocity is equal to four times the wave velocity if

d y d t = y 0 cos ⁡ 2 π f t - x λ × 2 π f ∴ maximum particle velocity = d y d t m a x = 2 π f y 0 × 1 Wave velocity = f λ As 2 π f y 0 = 4 f λ , ∴ λ = 2 π y 0 4 = π y 0 2

Physics - Wave on String Question with Solution | TestHub

PhysicsWave on StringEquation/graphEasy2 minPYQ_2020

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A transverse wave is described by the equation $y = y_{0} s i n 2 π [f t - \frac{x}{λ}]$ .The maximum particle velocity is equal to four times the wave velocity if

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Answer:

Solution:

$\frac{d y}{d t} = y_{0} \cos 2 π [f t - \frac{x}{λ}] \times 2 π f$

$∴$ maximum particle velocity $= {(\frac{d y}{d t})}_{m a x} = 2 π f y_{0} \times 1$

Wave velocity $= f λ$

As $2 π f y_{0} = 4 f λ$ , $∴ λ = \frac{2 π y_{0}}{4} = \frac{π y_{0}}{2}$

Stream:NTA_ABHYAS_NEETSubject:PhysicsTopic:Wave on StringSubtopic:Equation/graph

⏱ 2mℹ️ Source: PYQ_2020

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