Question

The shortest pipe in a particular organ is 1.37 m.

(a)

Determine the frequency (in Hz) of the seventh harmonic (at 0°C) if the pipe is closed at one end.

Hz

(b)

Determine the frequency (in Hz) of the seventh harmonic (at 0°C) if the pipe is open at both ends.

(c)

Determine these frequencies (in Hz) at 20.0°C.

pipe	frequency (Hz)
closed
open

Answer 1

given

L = 1.37 m

a) at 0 degrees Celsius speed of sound, v = 331 m/s

for a closed pipe,

7th harmonic, f7 = 7*v/((4*L)

= 7*331/(4*1.37)

= 423 Hz   <<<<<<------------------Answer

b)

for an open pipe,

7th harmonic, f7 = 7*v/((2*L)

= 7*331/(2*1.37)

= 846 Hz   <<<<<<------------------Answer

c) at 20 degrees celius, v = 331 + 0.6*20 = 343 m/s

for a closed pipe,

7th harmonic, f7 = 7*v/((4*L)

= 7*343/(4*1.37)

= 438 Hz   <<<<<<------------------Answer

for an open pipe,

7th harmonic, f7 = 7*v/((2*L)

= 7*343/(2*1.37)

= 876 Hz <<<<<<------------------Answer