(i) The transverse displacement of a string (clamped at its two ends ) is given by `y(x,t)=0.06 sin[ (2pi)/(3)x] cos 120pit,`
where x, y are in m and t is in s.
Do all the points on the string oscillate with the same (a) frequency, (b) phase, (c) amplitude ? Explain your answers.

Explanation

To solve the problem, we need to analyze the given wave function for the transverse displacement of a string clamped at both ends, which is given by:

\[ y(x,t) = 0.06 \sin\left(\frac{2\pi}{3} x\right) \cos(120\pi t) \]

This equation represents a standing wave, and we will examine whether all points on the string oscillate with the same frequency, phase, and amplitude.

### Step 1: Determine the Frequency
The frequency of the wave can be determined from the cosine term in the equation. The term \( \cos(120\pi t) \) indicates the frequency of oscillation.
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