A transverse wave on a string is described by \(y = 3\sin(36t + 0.018x + \pi/4)\), where \(x, y\) are in cm and \(t\) in seconds. The least distance between the two successive crests in the wave is _____ cm. (Nearest integer)
(\(\pi = 3.14\))

The standard equation of a transverse wave is given by \(y = A\sin(\omega t + kx + \phi)\)

Comparing this with the given equation \(y = 3\sin(36t + 0.018x + \pi/4)\), we get the wave number \(k = 0.018 \text{ cm}^{-1}\).

The least distance between two successive crests is the wavelength \(\lambda\) of the wave.

We know that \(k = \dfrac{2\pi}{\lambda}\)

\(\lambda = \dfrac{2\pi}{k} = \dfrac{2 \times 3.14}{0.018}\)

\(\lambda = \dfrac{6.28}{0.018} = \dfrac{6280}{18} = 348.88 \text{ cm}\)

Rounding to the nearest integer, we get \(349 \text{ cm}\).

Answer: \(349\)