## Question

A wire has a mass 30 g and linear density 4 × 10^{ –2} kg m^{–1}. It is stretched between two rigid supports and vibrates in its fundamental mode with a frequency of 50 Hz. What is the speed of transverse waves on the wire?

### Solution

Mass of the wire (*M*) = 30 *g* = 30 × 10^{ –3} kg. Mass per unit length of the wire (*m*) = 4 × 10^{ –2} kg m^{–1}.

Therefore, length of the wire is

Now, for the fundamental mode, Therefore,

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