Question

An open organ pipe of length l is sounded together with another open organ pipe of length l + x in their fundamental tones. Speed of sound in air is v. The beat frequency heard will be (x ≪ l)

• A. $\frac{vx}{4l^2}$
• B. $\frac{v{l}^1}{2x}$
• C. $\frac{vx}{2l^2}$
• D. $\frac{v{x}^2}{2l}$

Answer 1

The correct option is C

$\frac{vx}{2l^2}$

Beat frequency =$f_1-f_2$

$=\frac{v}{2l}-\frac{v}{1(l+x)}=\frac{v}{21}[1-{(1+\frac{x}{1})}^{-1}]$

$=\frac{v}{2l}[1-1+\frac{x}{1}]=\frac{vx}{2l^2}$