Least Distance Between Two Successive Crests in Wave

A transverse wave on a string is described by the equation: $y = 3\sin\left(36t + 0.018x + \frac{\pi}{4}\right)$

Comparing this with the standard wave equation $y = A\sin(\omega t + kx + \phi)$, we get the wave number $k$ as: $k = 0.018 \text{ cm}^{-1}$

The least distance between two successive crests of a wave represents its wavelength ($\lambda$). The relation between the wavelength $\lambda$ and the wave number $k$ is given by: $k = \frac{2\pi}{\lambda}$

Rearranging for $\lambda$: $\lambda = \frac{2\pi}{k}$

Given $\pi = 3.14$, substituting the values into the formula gives: $\lambda = \frac{2 \times 3.14}{0.018} = \frac{6.28}{0.018} = \frac{6280}{18} = \frac{3140}{9} \approx 348.89 \text{ cm}$

Rounding off to the nearest integer, we get: $\lambda \approx 349 \text{ cm}$