Question

A wave is travelling in the negative x direction having displacement 3 cm along Y direction, wavelength \(2 \pi \mathrm{~m}\) and frequency \(\left(\frac{1}{2 \pi}\right) \mathrm{Hz}\) is represented as ( \(t=\) time)

• A. \(3\mathrm{sin}(\mathrm{x}+\mathrm{t})\mathrm{m}\)
• B. \(3\times 10^{-2}\mathrm{sin}(x+t)m\)
• C. \(3\mathrm{sin}(x+2t)m\)
• D. \(3\times 10^{-3}\mathrm{sin}(x+2t)\mathrm{m}\)

Hint:

Find k and omega from the wavelength and frequency and convert the amplitude to metres.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
A wave travelling in the negative x direction has the form \(y=A\sin(kx+\omega t)\).

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

Step 3: Amplitude
\(A=3\ \text{cm}=3\times10^{-2}\ \text{m}\).

Step 4: Write the equation
\(y=3\times10^{-2}\sin(x+t)\ \text{m}\).

Final Answer:
The wave is \(y=3\times10^{-2}\sin(x+t)\) metres. \[ \boxed{\text{(B) }3\times 10^{-2}\sin(x+t)\,\text{m}} \]