A 2.50-m-long wire having a mass of 0.100 kg is fixed at both ends. The tension

Question

A 2.50-m-long wire having a mass of 0.100 kg is fixed at both ends. The tension in the wire is maintained at 15.0 N.

(a) What are the frequencies of the first three allowed modes of vibration?
f1 =   Hz
f2 =  Hz
f3 =  Hz

(b) If a node is observed at a point 0.500 m from one end, in what mode and with what frequency is it vibrating? (Select all that apply.)

The frequency is the second state at 7.7 Hz

The frequency is the fifth state at 19.4 Hz

The frequency is the tenth state at 7.7 Hz

The frequency is the twentieth state at 77.5 Hz

The frequency is the fifth state at 9.7 Hz

The frequency is the tenth state at 38.7 Hz

Explanation / Answer

u = m/L = 0.1/2.5 = 0.04 kg /m

V = sqrt(T/u) = 19.36 m/s

f1 = V/2L = 3.872 Hz

f2 = 2f1 = 7.744 Hz

f3 = 3f1 = 3.872 Hz

b) l = lamda/2 = 0.5 m

nl = L

n = L/l = 5

f = nV/2L = 19.4 Hz

The frequency is the fifth state at 19.4 Hz

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