Introduction to Wind Instruments

[sphouxay]

Homework Statement

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.


What is the frequency of the first possible harmonic after the fundamental frequency in the open-closed pipe described in Part E?

Part E was 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.

Part A was 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? frequency 214 Hz

Homework Equations

The Attempt at a Solution

What is the frequency of the first possible harmonic after the fundamental frequency in the open-closed pipe described in Part E?

 

[Mark44]

Your text or notes should define the first possible harmonic after the fundamental frequency.

 

[Mene]

The first possible harmonic after the fundamental frequency in an open-closed pipe can be calculated using the equation f = n(v/4L), where f is the frequency, n is the harmonic number, v is the speed of sound, and L is the length of the pipe. Since the length of the open-closed pipe is half of the open-open pipe, the frequency of the first possible harmonic would be twice that of the fundamental frequency.

Therefore, the frequency of the first possible harmonic would be 428 Hz (214 Hz x 2). This is because the open-closed pipe has only half the length of the open-open pipe, meaning that the standing wave produced would have twice the frequency. This is known as the first overtone or second harmonic.