Question

Equal volumes of water are added to three cylindrical jars A, B and C of the same height and radii \(r_A\), \(r_B\) and \(r_C\) respectively with \(r_A<r_B<r_C\). If you blow across the mouth of these jars, which tube will produce the shrillest note?

• A. A
• B. B
• C. C
• D. All will produce the notes of same shrillness

Hint:

For resonance in air columns, remember: Short air column = High frequency = Shrill sound. Long air column = Low frequency = Grave sound.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Shrillness is another term for high pitch or high frequency. For an air column in a pipe, the frequency is inversely proportional to the length of the air column (\( f \propto 1/L \)).
Step 2: Detailed Explanation:
Volume of water \( V \) is constant. \( V = \pi r^2 h \), where \( h \) is the height of water.
Since \( r_A \) is the smallest, the height of water \( h_A \) will be the greatest (\( h = V / \pi r^2 \)).
Length of the air column \( L = \text{Height of Jar} - \text{Height of Water} \).
Jar A, having the most water, will have the shortest air column.
Since Jar A has the shortest air column, it produces the highest frequency (shrillest note).
Step 3: Final Answer:
Jar A produces the shrillest note.