A tuning fork of frequency 546 Hz isplaced near the top of the pipe. The water l

Question

A tuning fork of frequency 546 Hz isplaced near the top of the pipe. The water level is lowered so thatthe length L slowly increases from an initial value of20.0 cm. Determine the next two values of L thatcorrespond to resonant modes. (Assume that the speed ofsound in air is 343 m/s.)
-------m (shorter length)
-------- m (longer length) A tuning fork of frequency 546 Hz isplaced near the top of the pipe. The water level is lowered so thatthe length L slowly increases from an initial value of20.0 cm. Determine the next two values of L thatcorrespond to resonant modes. (Assume that the speed ofsound in air is 343 m/s.)
-------m (shorter length)
-------- m (longer length)

Explanation / Answer

A tuning fork of frequency 546 Hz isplaced near the top of the pipe. The water level is lowered so thatthe length L slowly increases from an initial value of20.0 cm. Determine the next two values of L thatcorrespond to resonant modes. (Assume that the speed ofsound in air is 343 m/s.)
-------m (shorter length)
-------- m (longer length)
in closed pipe n=V/4l
so l=V/4n=343/4*546=0.1570=15.70cm
this is the first length at which the first resonance occurs.
as we started from 20 cm the next length will be 3l and 5l so
3l=3*15.7=47.11cm
5l=78.5cm
hence next two values are 47.11cm and 78.5cm.

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