## Question

A steel rod of length 1.0 *m* is clamped rigidly at its middle. What is the frequency of the fundamental mode for the longitudinal vibrations of the rod? The speed of sound in steel = 5 × 10^{3} ms^{ –1}. ^{ }

### Solution

2.5 kHz

Since the rod is clamped rigidly in the middle, the middle point of the rod is a node. In the fundamental mode, the end-points of the rod are antinodes. Therefore, the distance between two consecutive antinodes = *L*= 1.0 m. But, the distance between two consecutive antinodes is λ/2.

The frequency of the fundamental mode is

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