Introduction to Wind Instruments

(See attached file for full problem description)

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Introduction to Wind Instruments

The physics of wind instruments is based on the concept of standing waves. When the player blows into the mouthpiece, the column of air inside the instrument vibrates, and standing waves are produced. Although the acoustics of wind instruments is complicated, a simple description in terms of open and closed tubes can help in understanding the physical phenomena related to these instruments. For example, a flute can be described as an open-open pipe because a flutist covers the mouthpiece of the flute only partially. Meanwhile, a clarinet can be described as an open-closed pipe because the mouthpiece of the clarinet is almost completely closed by the reed.

Throughout the problem, take the speed of sound in air to be 343 .

Part A
Consider a pipe of length 80.0 open at both ends. What is the lowest frequency of the sound wave produced when you blow into the pipe?
Express your answer in hertz.
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Part B
A hole is now drilled through the side of the pipe and air is blown again into the pipe through the same opening. The fundamental frequency of the sound wave generated in the pipe is now

the same as before.

lower than before.

higher than before.

Part C
If you drill a hole at a position half the length of the pipe, what is the fundamental frequency of the sound that can be produced in the pipe?
Express your answer in hertz.
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Part D
What frequencies can you create when blowing air into the pipe that has a hole halfway down its length?

Only the odd multiples of

Only the even multiples of

All integer multiples of

Part E
What length of open-closed pipe would you need to achieve the same fundamental frequency as the open-open pipe discussed in Part A?

Half the length of the open-open pipe

Twice the length of the open-open pipe

One-fourth the length of the open-open pipe

Four times the length of the open-open pipe

The same as the length of the open-open pipe

Part F
What is the frequency of the first possible harmonic in the open-closed pipe described in?
Express your answer in hertz.
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