MHTCET 11 Apr 2026 Shift 2 Paper

Concept:A progressive wave equation is compared with the standard form to identify its amplitude, wavelength, frequency, and velocity.Explanation:The given wave equation is:$$Y = 3 \sin \left[\pi\left(\frac{t}{3}-\frac{x}{5}\right)+\frac{\pi}{4}\right]$$This can be rewritten as:$$Y = 3 \sin \left(\frac{\pi}{3}t - \frac{\pi}{5}x + \frac{\pi}{4}\right)$$Compare it with the standard equation:$$Y = A \sin(\omega t - kx + \phi)$$Here, amplitude is $A = 3\ \text{m} = 300\ \text{cm}$.So, option B (Amplitude $= 30\ \text{cm}$) is incorrect.Angular frequency, $\omega = \frac{\pi}{3}$.Wave number, $k = \frac{\pi}{5}$.Wavelength is given by $k = \frac{2\pi}{\lambda}$.So, $\frac{\pi}{5} = \frac{2\pi}{\lambda}$, which gives $\lambda = 10\ \text{m}$.Thus, option C is correct.Frequency, $f = \frac{\omega}{2\pi} = \frac{\pi/3}{2\pi} = \frac{1}{6}\ \text{Hz}$, so option D is incorrect.Velocity, $v = f\lambda = \frac{1}{6} \times 10 = \frac{5}{3}\ \text{m/s}$, so option A is incorrect.Answer:Option C: Wavelength $= 10\ \text{m}$