The fundamental frequency of vibration of a string stretched between two rigid supports is 50 Hz. The mass of the string is 18 g and its linear mass density is 20 g/m. The speed of the transverse waves so produced in the string is ______ .

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Solution

Q.
The fundamental frequency of vibration of a string stretched between two rigid supports is 50 Hz. The mass of the string is 18 g and its linear mass density is 20 g/m. The speed of the transverse waves so produced in the string is ______ ${m s}^{- 1}$ . [2023]

Ans.
(90)

$Fundamental frequency = 50 Hz$

$\frac{mass}{length} = 20 g/m$

$mass = 18 g$

$length of string = \frac{18}{20} m = \frac{9}{10} m$

$From diagram \frac{λ}{2} = ℓ$

$\Rightarrow λ = 2 ℓ = \frac{9}{5} m$

$Again, speed v = f λ = 50 \times \frac{9}{5} = 90 m/s$

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