A C note (f = 256 Hz)is sounded on a piano.If the length of the piano wire is 2 m and its mass density is 2.2 g/m,what is the tension in the wire?

Question

Quizplus · Accepted Answer

The wave velocity of the transverse wave on the stretched wire is given by the following formula, where T is the tension in the wire and μ is the mass density of the wire:

v = √(T/μ)

For the wave to produce the frequency of 256 Hz, the wavelength of the wave must be twice the length of the wire, or 4 m. The speed of the wave can also be expressed as v = fλ, where λ is the wavelength and f is the frequency.

Therefore, T = μv^2 = μ(fλ)^2 = 2.2 g/m x (256 Hz x 4 m)^2 = 2,307 N (to three significant figures). Thus, the correct answer is C).

A C Note (F = 256 Hz)is Sounded on a Piano.If