A cylindrical metal tube has a length of 50 cm and is open at both end

1.	A cylindrical metal tube has a length of 50 cm and is open at both ends. Find the frequencies between 1000 Hz and 2000 Hz at which the air column in the tube can resonate. The speed of sound in air is 340 m/s.
Answer» The resonant frequencies in an open organ pipe is given as ν = nV/2L. Where n = 1, 2, 3, ... Given V = 340 m/s and L = 50 cm =0.50 m. Hence, ν = n(340/20.50) =340 n. The resonant frequencies between 1000 Hz to 2000 Hz can be found by putting n = 3, 4 and 5 in it. For n = 3, ν₃ = 3403 = 1020 Hz, for n = 4, ν₄ = 3404 = 1360 Hz,* for n = 5, ν₅ = 3405 = 1700 Hz.*

A cylindrical metal tube has a length of 50 cm and is open at both ends. Find the frequencies between 1000 Hz and 2000 Hz at which the air column in the tube can resonate. The speed of sound in air is 340 m/s.

Answer»

The resonant frequencies in an open organ pipe is given as ν = nV/2L. Where n = 1, 2, 3, ...

Given V = 340 m/s and L = 50 cm =0.50 m.

Hence,

ν = n(340/2*0.50) =340 n.

The resonant frequencies between 1000 Hz to 2000 Hz can be found by putting n = 3, 4 and 5 in it.

For n = 3, ν₃ = 340*3 = 1020 Hz,

for n = 4, ν₄ = 340*4 = 1360 Hz,

for n = 5, ν₅ = 340*5 = 1700 Hz.

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A cylindrical metal tube has a length of 50 cm and is open at both ends. Find the frequencies between 1000 Hz and 2000 Hz at which the air column in the tube can resonate. The speed of sound in air is 340 m/s.

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