JEE Main · 2023 · 15 Apr 2023 · Shift 1 · Waves & Sound

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The fundamental frequency of vibration of a string stretched between two rigid support 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 ______

ms^{- 1}

Answer: 90

Solution

The string length follows from

ℓ = \frac{mass}{linear mass density} = \frac{18}{20} = 0.9 m

. In the fundamental mode the string carries a single loop, so

λ = 2 ℓ = 1.8 m

. The wave speed is

v = f λ = 50 \times 1.8 = 90 m s^{- 1}

JEE Main · 2023 · 15 Apr 2023 · Shift 1 · Integer answer

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