Question

A 5.01-m, 0.735-kg wire is used to support two uniform 230-Nposts of equal length (the figure (Figure 1)). Assume that the wire is essentially horizontal and that the speed of sound is 344 m/s. A strong wind is blowing, causing the wire to vibrate in its 5th overtone.

What is the wavelength of the sound this wire produces?

Answer 1

First find the Tension in the wire by summing moments about the right pivot
Assume pole length is L, positive moment is CCW and replace wire with tension T
0 = TLsin57 - 230(L/2)cos57
T = 230(L/2)cos57 / Lsin57
T = (230/2)cos57 / sin57
T = 74.681 N

From resonance studies
f = (n (T / (m/L))^0.5) / 2L
for the fifth resonant
f = (5 (74.681 / (0.735/5.01))^0.5) / 2(5.01)
f = 11.258 Hz

wavelength is 344 / 11.258 = 30.55 m

Hope it will help you.

Please rate the answer.