Question

Sinusoidal waves 5.00 cm in amplitude are to be transmitted along a string that has a linear mass density of 4.00 10-2 kg/m. The source can deliver a maximum power of 275 W, and the string is under a tension of 121 N. What is the highest frequency f at which the source can operate?

Answer 1

50.4 Hz

Step-by-step explanation:

A = amplitude of the wave = 5 cm = 0.05 m

μ = linear mass density = 0.04 kg/m

P = maximum power delivered by source = 275 Watt

T = tension force in the string = 121 N

Speed of the wave is given as

`v=\sqrt{(T)/(\mu )}`

`v=\sqrt{(121)/(0.04 )}`

`v` = 55 m/s

maximum power is given as

`P = (\mu (2\pi f)^(2) A^(2)v)/(2)`

`275 = ((0.04) (2(3.14) f)^(2) (0.05)^(2)(55))/(2)`

`f` = 50.4 Hz