Question

A wave travelling in the +ve x-direction having displacement along y-direction as 1 m, wavelength 2π in and frequency of $\frac1{π}$Hz is represented by

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

Answer 1

The Correct Option is A

To represent a wave traveling in the positive x-direction with a given displacement, wavelength, and frequency, we can use the standard wave equation:

y(x, t) = A \sin(kx - \omega t + \phi)

where:

• A is the amplitude of the wave.
• k is the wave number, which is given by k = \frac{2\pi}{\lambda}, with \lambda being the wavelength.
• \omega is the angular frequency, given by \omega = 2\pi f, where f is the frequency.
• \phi is the phase constant, which we assume to be zero if not given.

Given in the problem:

• Amplitude, A = 1 \, \text{m}
• Wavelength, \lambda = 2\pi
• Frequency, f = \frac{1}{\pi} \, \text{Hz}

Calculate the wave number, k, and angular frequency, \omega:

• k = \frac{2\pi}{\lambda} = \frac{2\pi}{2\pi} = 1
• \omega = 2\pi f = 2\pi \times \frac{1}{\pi} = 2

Substituting these values into the wave equation:

• y(x, t) = \sin(x - 2t)

Thus, the correct representation of the wave is y(x, t) = \sin(x - 2t), which matches the given option: y = sin(x - 2t).

Conclusion: The correct answer is y = sin(x - 2t), as it accurately represents the given wave parameters. The other options either have incorrect wave numbers or angular frequencies that do not match the given data.