Question

A tuning fork vibrates with frequency $256\, Hz$ and gives one beat per second with the third normal mode of vibration of an open pipe. What is the length of the pipe ? (Speed of sound in air is $340\, ms^{-1}$)

• A. 220 cm
• B. 190 cm
• C. 180 cm
• D. 200 cm

Answer 1

Answer: (D)

200 cm

Answer 2

Given: Frequency of tuning fork $=256 Hz$.
It gives one beat per second with the third normal mode of vibration of an open pipe.
Therefore, frequency of open pipe $=(256+1) Hz$
Speed of sound in air is $340 m / s$.
Now we know, frequency of third normal mode of vibration of an open pipe is given as
$f=\frac{3 v_{\text {sound }}}{2 l}$
$\Rightarrow \frac{3 \times 340}{2 l}=255$
$\Rightarrow l=\frac{3 \times 340}{2 \times 255}=2\, m =200\, cm$