Question

The diagram he below shows two tubes partially filled with water: A students holds a 1024 Hz tuning fork above the tube in two different cases. In one case, the air tube is measured by the student to be 7.0 cm , as pictured.
By pouring out some water, the air column is longer and is the measured by the student to be 23.0 cm, as pictured. At both of these lengths and at no lengths between these two, the air tube resonates with the tuning fork, in effect amplifying tuning fork's sound.
What is the calculated speed of the sound that causes this to happen?

• A. 328 m/s
• B. 236 m/s
• C. 471 m/s
• D. 164 m/s
• E. 6400 m/s

Answer 1

The correct option is A 328 m/s

At resonance frequency of the air column inside the tube will be equal to the frequency of tuning fork .

We can see fro the diagram that ,

difference in height of air column , $23-7=$ $3\lambda /4-\lambda /4$ ,

or $16=\lambda /2$ ,

or $\lambda =32cm=0.32m$ ,

now we have $v_s=f\lambda =1024\times 0.32=328m/s$ ,(given $f=1024Hz$)