A wave disturbance in a medium is described by y ( x , t ) = 0.02 cos ( 50 π t + 2 π ) cos ( 10 π x ) where x , y are in meters and t is in second. Which statement(s) is/are correct?

cos 10 π x = 0 → Node 10 π x = n π + 2 π 10 π x = n π + 2 1 x = 0 , 20 1 m , 20 3 m cos π x = ± 1 → Antinode 10 π x = n π , x = 0 , 10 1 m , 10 2 m , 10 3 m wave speed ( v ) = k ω = 10 π 50 π = 5 m / s , k = 10 π , λ 2 π = 10 π , λ = 10 2 = 0.2 m

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Physics - Wave on String Question with Solution | TestHub

PhysicsWave on StringStandingMedium2 minPYQ_2025

PhysicsMediummultiple choice

A wave disturbance in a medium is described by $y (x, t) = 0.02 cos (50 π t + \frac{π}{2}) cos (10 π x)$ where $x, y$ are in meters and $t$ is in second. Which statement(s) is/are correct?

Options:(select one or more)

Answer:

A, B, D

Solution:

$cos 10 π x = 0 \to$ Node $10 π x = n π + \frac{π}{2} 10 π x = n π + \frac{1}{2} x = 0, \frac{1}{20} m, \frac{3}{20} m cos π x = \pm 1 \to Antinode 10 π x = n π, x = 0, \frac{1}{10} m, \frac{2}{10} m, \frac{3}{10} m wave speed (v) = \frac{ω}{k} = \frac{50 π}{10 π} = 5 m / s, k = 10 π, \frac{2 π}{λ} = 10 π, λ = \frac{2}{10} = 0.2 m$

Stream:WBJEESubject:PhysicsTopic:Wave on StringSubtopic:Standing

⏱ 2mℹ️ Source: PYQ_2025

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