The equation of a plane progressive wave is given by y = 5 cos π (200 t - x/150) where x and y are in cm and t is in second. The velocity of the wave is _______ m/s.

The correct answer is Option 4. Full mathematical solution steps and hints are accessible in the interactive StemCET workspace.

Physics Q35 – JEE-MAIN 2026

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The equation of a plane progressive wave is given by

y = 5 \cos π (200 t - \frac{x}{150})

where

x

and

y

are in cm and

t

is in second. The velocity of the wave is _______ m/s.

Clue 1 of 3: Standard Wave Equation

Recall the general form of a progressive wave equation, $y = A \cos (ω t - k x)$ , and identify its components from the given equation.

🧠 Full Solution Path

Step 1: Identify Wave Parameters✦ Active

The given equation of the plane progressive wave is $y = 5 \cos π (200 t - \frac{x}{150})$ . Expand the equation to match the standard form $y = A \cos (ω t - k x)$ :

y = 5 \cos (200 π t - \frac{π x}{150})

Comparing this with the standard form, we identify the angular frequency $ω$ and the wave number $k$ :

ω = 200 π rad/s

k = \frac{π}{150} rad/cm

Step 2: Calculate Wave Velocity○ Expand

The velocity of the wave $v$ is given by the ratio of the angular frequency to the wave number:

v = \frac{ω}{k}

Substitute the values of $ω$ and $k$ :

v = \frac{200 π rad/s}{\frac{π}{150} rad/cm} = 200 \times 150 cm/s

v = 30000 cm/s

Step 3: Convert Units to m/s○ Expand

The question asks for the velocity in m/s. Since $1 m = 100 cm$ , we convert the velocity from cm/s to m/s:

v = 30000 cm/s \times \frac{1 m}{100 cm}

v = 300 m/s

💡 Teacher's Secret Hint

Always double-check the required units for the final answer and perform necessary conversions.

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Physics Question 35 – JEE-MAIN 2026

Clue 1 of 3: Standard Wave Equation

🧠 Full Solution Path