Question

A hollow string with inside cross-sectional area 5 × 10^-4 m² is used to generate travelling transverse waves of speed 10 m/s keeping it under a tension of 2.0 × 10² N. If string is completely filled with water (density of water = 100 kg/m³) and is kept under same tension then new wave speed is most near to

• A. 8.9 m/s
• B. 9.3 m/s
• C. 10 m/s
• D. 7.6 m/s

Answer 1

Answer: (A)

8.9 m/s

Answer 2

Using v = $\sqrt{\frac{T}{\mu}}$ for initial condition

10 = $\sqrt{\frac{200}{\mu}}$

μ = 2 kg/m Mass of water in 1 m of string = A × l × = 5 × 10^-4 × 1 × 1000

= 0.5 kg

Now new μ = 2.0 +0.5 = 2.5 kg/m

v' = $\sqrt{\frac{200}{2.5}}$= 8.9 m/s