Question

Evaluate the solution:
A friend proposes a solution for the folowing problem.
A violin A string is 0.33 m long and has mass 0.30 x 10^-3 kg. It vibrates a fundamental frequency of 440 Hz (concert A). What is the tension in the string?
Proposed solution: Speed depends on the tension and string mass (v = [T/m]^1/2). Thus:
T = v^2 m = (340 m/s)^2 (0.30g) = 34.680 N.
a. Evaluate the solution and identify any errors.
b. Provide a corrected solution if you find errors.

Answer 1

Answer:

Tension, T = 105.09 N

Explanation:

Given that,

Length of the string, l = 0.33 m

Mass of the string, $m=0.3\times 10^{-3}\ kg$

Fundamental frequency, f = 440 Hz

The expression for the speed in terms of tension is given by :

$v=\sqrt{\dfrac{T}{(m/l)}}$

$v^2=\dfrac{Tl}{m}\\\\T=\dfrac{v^2m}{l}\\\\T=\dfrac{(340)^2\times 0.3\times 10^{-3}}{0.33}\\\\T=105.09\ N$

So, the tension in the string is 105.09 N.