Question

A wave travelling in the positive \(x\)-direction having displacement along \(y\)-direction as \(1\) m, wavelength \(2\pi\) m and frequency \(\frac{1}{\pi }\) Hz is represented by

• A. \(y=\sin (x-2t)\)
• B. \(y=\sin (2\pi x-2\pi t)\)
• C. \(y=\sin (10\pi x-20\pi t)\)
• D. \(y=\sin (2\pi x+2\pi t)\)

Hint:

Use \(y=A\sin(kx-\omega t)\) with \(k=2\pi/\lambda\) and \(\omega=2\pi f\).

Answer 1

The Correct Option is A

Step 1: Understanding the Concept
A wave moving in the positive x-direction is \(y=A\sin(kx-\omega t)\).

Step 2: Find k and omega
\(k=\dfrac{2\pi}{\lambda}=\dfrac{2\pi}{2\pi}=1\text{ m}^{-1}\)
\(\omega=2\pi f=2\pi\times\dfrac{1}{\pi}=2\text{ rad/s}\)

Step 3: Write the Equation
With \(A=1\) m, \(y=\sin(x-2t)\).

Step 4: Compare the options
This matches option (A).

Final Answer:
The wave is \(y=\sin(x-2t)\). \[ \boxed{\text{(A) }y=\sin(x-2t)} \]