Question

A 1.95m long wire having a mass of 0.100kg is at both ends.The tension in the wire is maintained at 21.0N.

(a).What are the frequencies of the first three allowed modes of vibration?

Answer 1

The fundamental frequency:

$$f_1=\frac{1}{2L}\sqrt{\frac T{m/L}}=2.66\text{ Hz}.$$

Other two frequencies:

$$f_2=2f_1=5.32\text{ Hz},\\ f_3=3f_1=7.98\text{ Hz}.$$