Question

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

पर्याय

• A

• B

• C

• All will produce the notes of same shrillness.

Answer 1

B

Explanation:

The pitch of the sound produced when air is blown across the mouth of a jar depends upon the length of the air column above the water. A shorter air column produces a higher-pitched sound, whereas a longer air column produces a lower pitch.

The volume of a cylindrical jar is given by:

V = πr²h

Let r represent the radius, and h denote the height of the jar. Given that equal volumes of water are introduced into jars with radii r_B < r_A < r_C, the jar with the smallest radius (B) will exhibit the greatest height of water, resulting in the shortest air column.

Therefore, jar B produces the shrillest note.