Question

Two open organ pipes of length $25cm$ and $25.5cm$ 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)

Here : Length of first pipe $l_1=25cm$
Length of second pipe $l_2=25.5cm$
Frequency $f$ beat $=0.1$ beat/sec
Frequence of first pipe $f_1$ is given by,
$\frac{v}{2l_1}=\frac{v}{2\times 25}=\frac{v}{50}Hz$
Frequency of second pipe $f_2$ is given by,
$\frac{v}{2l_2}=\frac{v}{2\times 25.5}=\frac{v}{51}Hz$
(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 $v=0.1\times 50\times 51$
$v=255m/s$