Question

A travelling wave on a string is given by \[ y = 3\sin\left(100t + 0.018x + \frac{\pi}{6}\right) \] Find the minimum distance (in m) between two crests.

• A. \(349.06\)
• B. \(625.75\)
• C. \(475.56\)
• D. \(175.75\)

Answer 1

The Correct Option is A

Concept: \includegraphics[width=0.5\linewidth]{4p ans.png} The general equation of a travelling wave is \[ y = A\sin(\omega t + kx + \phi) \] where \[ k = \frac{2\pi}{\lambda} \] Distance between two consecutive crests equals the wavelength \(\lambda\). Step 1: Identify wave number \[ k = 0.018 \] Step 2: Find wavelength \[ \lambda = \frac{2\pi}{k} \] \[ \lambda = \frac{2\pi}{0.018} \] \[ \lambda = 349.06\ \text{m} \] Thus the minimum distance between two crests is \[ \boxed{349.06\ \text{m}} \]