Back to Directory
NEET PHYSICSEasy

A wave travelling in the positive x-direction having maximum displacement along y-direction as 1 m1 \text{ m}, wavelength 2π m2\pi \text{ m} and frequency of 1/π Hz1/\pi \text{ Hz} is represented by

A

y=sin⁡(x−2t)y=\sin(x-2t)

B

y=sin⁡(2πx−2πt)y=\sin(2\pi x-2\pi t)

C

y=sin⁡(10πx−20πt)y=\sin(10\pi x-20\pi t)

D

y=sin⁡(2πx+2πt)y=\sin(2\pi x+2\pi t)

Step-by-Step Solution

  1. Identify the given parameters: Maximum displacement (Amplitude), A=1 mA = 1 \text{ m}; Wavelength, λ=2π m\lambda = 2\pi \text{ m}; Frequency, f=1π Hzf = \frac{1}{\pi} \text{ Hz}.
  2. Calculate wave number (kk): The wave number is given by k=2πλk = \frac{2\pi}{\lambda}. k=2π2π=1 m−1k = \frac{2\pi}{2\pi} = 1 \text{ m}^{-1}
  3. Calculate angular frequency (ω\omega): The angular frequency is given by ω=2πf\omega = 2\pi f. ω=2π×1π=2 rad/s\omega = 2\pi \times \frac{1}{\pi} = 2 \text{ rad/s}
  4. Formulate the wave equation: The general equation for a progressive wave travelling in the positive x-direction is y=Asin⁡(kx−ωt)y = A \sin(kx - \omega t) or y=Asin⁡(ωt−kx)y = A \sin(\omega t - kx) . Substituting the calculated values into the first form: y=1⋅sin⁡(1⋅x−2⋅t)=sin⁡(x−2t)y = 1 \cdot \sin(1 \cdot x - 2 \cdot t) = \sin(x - 2t)
Practice Mode Available

Master this Topic on Sushrut

Join thousands of students and practice with AI-generated mock tests.

Get Started