Question

A vibrating tuning fork of frequency $\upsilon$ is placed near the open end of a long cylindrical tube. The tube has side opening and is also 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 $350m{s}^{-1}$, then, $\upsilon$ is

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

Answer 1

The correct option is B $1000Hz$

Additional path difference introduced when the piston is moved through $8.75cm=2\times 8.75=17.50cm$ since, the intensity changes from maximum to a minimum additional path $=\lambda /2$
$\therefore \left(\lambda /2\right)=17.50or\lambda =35.0cm$
Velocity, $v=350m{s}^{-1}=35000cm{s}^{-1}$
$\therefore Frequency,\nu =\frac{v}{\lambda }=\frac{35000}{35}=1000Hz$