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  • A wire stretched between two rigid supports vibrates in its fundamental mode with a frequency of 45 Hz. (a) What is the speed of a transverse wave on the string?

Q.15.14  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\times 10^{-2}\: kg and its linear mass density is 4.0\times 10^{-2}\: kg\: m^{-1}. What is   (a) the speed of a transverse wave on the string?

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Length of the string is l given by

\\l=\frac{M}{\mu }\\ l=\frac{3.5\times 10^{-2}}{4\times 10^{-2}}\\ l=0.875m

Since the wire is vibrating in the fundamental mode

\\l=\frac{\lambda }{2}\\ \lambda =2l\\ \lambda =2\times 0.875\\ \lambda =1.75m

Speed of the string (v) is

\\v=\nu l\\ v=45\times 1.75\\ v=78.75\ ms^{-1}

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