Question

Vibrating tuning fork of frequency $n$ is placed near the open end of a long cylindrical tube. The tube has a side opening and is fitted with a movable reflecting piston. As the piston is moved through $8.75cm$, the intensity of sound changes from a maximum to minimum. If the speed of sound is $350m/s$. Then $n$ is

• A. $500Hz$
• B. $1000Hz$
• C. $2000Hz$
• D. $4000Hz$

Answer 1

Answer: (B)

When the piston is moved through a distance of $8.75cm$, the path difference produced is $2\times 8.75cm=17.5cm$. This must be equal to $\frac{\lambda }{2}$ for maximum to change to minimum.
$\therefore \frac{\lambda }{2}=17.5cm$
$\Rightarrow \lambda =35cm=0.35m$
So, $v=n\lambda \Rightarrow n=\frac{v}{\lambda }$
$=\frac{350}{0.35}=1000Hz$