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Question
The transverse displacement of a string (clamped at its both ends) is given by y(x, t) = 0.06 sin (2πx/3) cos (120 πt). All the points on the string between two consecutive nodes vibrate with ______.
- same frequency
- same phase
- same energy
- different amplitude.
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Solution
a, b and d
Explanation:
Given equation is `y(x, t) = 0.06 sin ((2pi)/3 x) cos (120 pit)`
Comparing with standard equation of stationary wave `y(x, t) = a sin(kx) cos(ωt)`
It is represented by the diagram,
Where N denotes nodes and A denotes antinodes.
a. Clearly, frequency is common for all the points.
b. Consider all the particles between two nodes they are having the same phase of (120 πt) at a given time.
c. and d. But are having different amplitudes of `0.06 sin ((2pi)/3 x)` and because of different amplitudes, they are having different energies.
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