A wire stretched between two rigid supports vibrates in its fundamental mode with a frequency of 45

Question

A wire stretched between two rigid supports vibrates in its fundamental mode with a frequency of 45 Hz. The mass of the wire is $3.5 	imes 10^{-2}$ kg and its linear mass density is $4.0 	imes 10^{-2}$ kg/m. What is the speed of a transverse wave on the string?

Professor PC Thomas Classes · Answer

Length of the string $L = m/\mu = 3.5 	imes 10^{-2} / 4.0 	imes 10^{-2} = 0.875$ m. For the fundamental mode, $\lambda = 2L = 1.75$ m. Wave speed $v = f\lambda = 45 	imes 1.75 = 78.75$ m/s.