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The transverse displacement of a string ...

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 theh same
(a) frequency (b) phase (c) amplitude
Explain your answer.

Text Solution

Verified by Experts

In the given equation, terms containing x and t are independent. Therefore, the equation t are independent. Therefore, the equation represents a stationary wave. Hence,
(i) All the points on the string do not oscillate with the same frequency. For example, frequency at nodes is zero.
(ii) Phase diff. between particle in between successive pair of nodes is `180^(@)`.
(iii) The amplitude of vibration of different points on the string is different. At nodes, the amplitude of vibration is zero.
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