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It is only when a string is perfectly flexible that the phase velocity of a wave on a string is given by sqrt(T/n). The dispersion relations for the real piano wire can be written as w^2/k^2=T/n + ak^2 where d is a small positive quantity which depends on the stiffness of the string. For perfectly flexible string, d = 0. Obtain expressions for phase velocity (vp ) and group velocity vg and show that vp increases as wavelength decreases. |
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