Question

Two open organ pipes of length $25\, cm$ and $25.5\, cm$ produce $0.1$ beat/sec. The velocity of sound will be :

• A. 255 m/s
• B. 250 m/s
• C. 350 m/s
• D. none of these

Answer 1

Answer: (A)

255 m/s

Answer 2

Here : Length of first pipe $l_{1}=25\, cm$ Length of second pipe $l_{2}=25.5\, cm$ Frequency $f$ beat $=0.1$ beat/sec Frequence of first pipe $f_{1}$ is given by, $\frac{v}{2 l_{1}}=\frac{v}{2 \times 25}=\frac{v}{50} Hz$ Frequency of second pipe $f_{2}$ is given by, $\frac{v}{2 l_{2}}=\frac{v}{2 \times 25.5}=\frac{v}{51} Hz$ (where $v$ is velocity of sound) Hence, the frequency $f =f_{1}-f_{2}$ $0.1 =\frac{v}{50}-\frac{v}{51}=\frac{v}{50 \times 51}$ or $v =0.1 \times 50 \times 51$ $v =255\, m / s$