Question

A vibrating tuning fork of frequency $\upsilon$ is placed near the open end of a long cylindrical tube. The tube has a side opening and is also fitted with a movable reflecting piston. As the piston is moved through $8.75 \,cm$, the intensity of sound changes from a maximum to minimum. If the speed of sound is $350 \,m \,s^{-1}$, then $\upsilon$ is

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

Answer 1

Answer: (B)

$1000 \, Hz$

Answer 2

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