Question

A hollow pipe of length $0.8m$ is closed at one end. At its open end, a $0.5m$ long uniform string is vibrating in its second harmonic and it resonates with the fundamental frequency of the pipe. If the tension in the wire is $50N$ and the speed of sound is $320m{s}^{-1}$, the mass of the string is

• A. $5grams$
• B. $10grams$
• C. $20grams$
• D. $40grams$

Answer 1

Answer: (B)

$10grams$

Velocity of sound $=c$

$\frac{c}{4L}=\frac{2v}{l}$

$\Rightarrow \frac{320}{4\times 0.8}=\frac{1}{5}\sqrt{\frac{T}{\mu }}$

$\Rightarrow \mu =0.02kg{m}^{-1}$

$\Rightarrow m=\mu l=10g$