Equal volumes of water are added to three cylindrical jars A, B and C of same height and radii rA, rB and rC respectively with rB < rA < rC. If you blow air into 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
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B
Reason — When air is blown across the mouth of a jar, the pitch of the sound depends on the length of the air column above the water. A shorter air column produces a higher-pitched (shriller) sound, while a longer air column produces a lower pitch.
As, volume of a cylindrical jar is given by,
Volume = πr2h
Where r is the radius and h is the height of the jar and since equal volumes of water are poured into jars with radii rB < rA < rC, the jar with the smallest radius (B) will have the greatest height of water, leaving the shortest air column.
Therefore, jar B produces the shrillest note.