A 4.0 g string,0.39 m long,is under tension.The string produces a 600 Hz tone when it vibrates in the third harmonic.The speed of sound in air is 344 m/s.The tension in the string,in SI units,is closest to:
A)250
B)200
C)160
D)290
E)340

Question

Quizplus · Accepted Answer

The frequency of the third harmonic is given by $ f = \frac{3v}{2L} $. Solving for $ v $ gives $ v = \frac{2Lf}{3} $. Substituting $ L = 0.39 $ m and $ f = 600 $ Hz, we find $ v \approx 156 $ m/s. The mass per unit length $ \mu = \frac{4.0 \times 10^{-3}}{0.39} $ kg/m. The tension $ T = \mu v^2 \approx 250 $ N.

A 40 G String,0