An engineer in an acoustics lab is setting up a high-precision calibration rig containing a tensioned alloy wire.
Explain how a stationary wave is established on the tensioned calibration wire when its vibrating section is excited into resonance.
In the initial setup of the calibration rig:
- The vibrating length of the wire between the rigid supports is 0.50 m.
- Under an initial tension of 90 N, the wire resonates at a first-harmonic frequency of 120 Hz.
Calculate the mass of a 1.0 m length of this wire.
Determine the speed of the transverse waves traveling along the wire when it vibrates at this frequency.
The tension in the wire is directly proportional to its extension, with a stiffness (tension increase per unit extension) of 5.0 N mm-1. The wire is further tensioned by rotating a circular tuning axle of diameter 12.0 mm through an angle of 60∘60^\circ60∘, as shown in the diagram. Determine the new first-harmonic resonance frequency of the wire, assuming its mass per unit length remains constant.