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3.1 WAVES

P31 010

When an organ pipe is blown gently, it excites the fundamental frequency of the pipe which is 192 Hz. If the pipe is blown more strongly, the note produced has a frequency of 384 Hz.

(A)

Show that the pipe must be open at both ends.

(B)

Calculate the length of the pipe if the speed of sound in air is 340 m.s^-1.

View solution below only after you have completed answering the question. The solution is not in a form that you would answer in an examination. The answers are often in more detail to help improve your appreciation and understanding of the physics.

Solution

Knowledge standing waves in pipes

The first natural frequency of vibration is the fundamental

The next natural frequency that was excited is 394 Hz, which must be the second harmonic since .

For an organ pipe which is open at both ends, all the harmonics can be excited:

For an organ pipe closed at one end and open at the other, only the odd harmonics can be excited:

Therefore, the pipe must be open at both ends.

For fundamental mode of vibration of a pipe open at both ends, the length of the pipe L is equal to ½ wavelength

speed of sound in air

Fundamental (1^st harmonic)

2^nd harmonic (1^st overtone)