Question

There is an inextensible string of linear density µ. If it is given that ω = \(k\sqrt{\frac{T}{μ}}\), then what is the group velocity of the string?

(a) \(\sqrt{\frac{T}{μ}}\)

(b) ħ\(\sqrt{\frac{T}{μ}}\)

(c) \(\frac{\hbar}{2}\sqrt{\frac{T}{μ}}\)

(d) \(\frac{1}{\hbar}\sqrt{\frac{T}{μ}}\)

This question was posed to me in an international level competition.

This intriguing question originated from Quantum Nature of Elastic Waves topic in division Quantum Physics of Engineering Physics I

Answer 1

The correct answer is (a) \(\sqrt{\frac{T}{μ}}\)

To elaborate: As we know, vg = dω/dk

Therefore, vg = d( k\(\sqrt{\frac{T}{μ}}\))/dk

= \(\sqrt{\frac{T}{μ}}\).