Question:
$y = 3 \sin \pi(\frac{t}{2} - \frac{x}{4})$ represents an equation of a progressive wave, where t is in second and x is in metre. The distance travelled by the wave in 5 s is
$y = 3 \sin \pi(\frac{t}{2} - \frac{x}{4})$ represents an equation of a progressive wave, where t is in second and x is in metre. The distance travelled by the wave in 5 s is
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Distance = (Wavelength / Time Period) $\times$ Time.
Updated On: Apr 10, 2026
- 8 m
- 10 m
- 5 m
- 32 m
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The Correct Option is B
Solution and Explanation
Step 1: Compare Equations
Standard wave equation: $y = A \sin 2\pi(\frac{t}{T} - \frac{x}{\lambda})$. The given equation is $y = 3 \sin 2\pi(\frac{t}{4} - \frac{x}{8})$.
Step 2: Find Velocity
From comparison, $T = 4~\text{s}$ and $\lambda = 8~\text{m}$. Wave velocity $v = \frac{\lambda}{T} = \frac{8}{4} = 2~\text{ms}^{-1}$.
Step 3: Distance
Distance $s = v \times t = 2 \times 5 = 10~\text{m}$.
Final Answer: (b)
Standard wave equation: $y = A \sin 2\pi(\frac{t}{T} - \frac{x}{\lambda})$. The given equation is $y = 3 \sin 2\pi(\frac{t}{4} - \frac{x}{8})$.
Step 2: Find Velocity
From comparison, $T = 4~\text{s}$ and $\lambda = 8~\text{m}$. Wave velocity $v = \frac{\lambda}{T} = \frac{8}{4} = 2~\text{ms}^{-1}$.
Step 3: Distance
Distance $s = v \times t = 2 \times 5 = 10~\text{m}$.
Final Answer: (b)
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