Find the first three harmonics of a string of linear mass density 2.00 g/m and length 0.600 m when it is subjected to tension of 50.0 N.
A) 264 Hz, 528 Hz, 792 Hz
B) 66 Hz, 132 Hz, 198 Hz
C) 132 Hz, 264 Hz, 396 Hz
D) none of the above

Question

Quizplus · Accepted Answer

The fundamental frequency (first harmonic) is calculated using the formula $ f_1 = \frac{1}{2L} \sqrt{\frac{T}{\mu}} $, where $ L = 0.600 \, \text{m} $, $ T = 50.0 \, \text{N} $, and $ \mu = 2.00 \, \text{g/m} = 0.002 \, \text{kg/m} $. This gives $ f_1 = 132 \, \text{Hz} $. The second harmonic is $ 2 \times 132 = 264 \, \text{Hz} $, and the third harmonic is $ 3 \times 132 = 396 \, \text{Hz} $.

Find the First Three Harmonics of a String of Linear