A transverse wave with an amplitude of 0.50 mm and a frequency of 100 Hz is generated on a wire stretched under a tension of 100 N . Given that the wave speed is 100 m s ⁻¹ , determine the average power transmitted to the wire by the source.

Step-by-step solution

The average power transmitted by a transverse wave on a stretched string is given by: P_ avg = 1 2 ^2 A^2 v The wave speed is related to tension and linear mass density by v = T , which gives = T v^2 . Substituting into the power equation: P_ avg = 1 2 ( T v^2 ) ^2 A^2 v = T ^2 A^2 2v Given values are: T = 100 N v = 100 m s ⁻¹ f = 100 Hz = 2 f = 200 rad s ⁻¹ A = 0.50 mm = 0.5 10⁻³ m Substituting these values: P_ avg = 100 (200 )^2 (0.5 10⁻³)^2 2 100 P_ avg = 1 2 40000 ^2 0.25 10⁻⁶ P_ avg = 5000 ^2 10⁻⁶ W P_ avg = 5