The fundamental frequency of vibration of a string between two rigid support is $$50$$ Hz. The mass of the string is $$18$$ g and its linear mass density is $$20$$ g m$$^{-1}$$. The speed of the transverse waves so produced in the string is _____ m s$$^{-1}$$.

Given: fundamental frequency $$f = 50$$ Hz, mass $$m = 18$$ g, linear mass density $$\mu = 20$$ g/m.

Length of string: $$L = \frac{m}{\mu} = \frac{18}{20} = 0.9$$ m

For fundamental frequency: $$f = \frac{v}{2L}$$

$$v = 2Lf = 2 \times 0.9 \times 50 = 90$$ m/s

The speed of transverse waves is $$\mathbf{90}$$ m/s.