The Effect of Sound Speed on Fundamental Frequency

How does the speed of sound in different mediums affect the fundamental frequency of an open-closed tube?

Given that the speed of sound in room temperature air is 343 m/s and in room temperature helium is 1010 m/s, and the fundamental frequency of an open-closed tube is 315 Hz when filled with air, what happens to the fundamental frequency if the air is replaced with helium?

Answer

The fundamental frequency of an open-closed tube increases from 315 Hz to approximately 930 Hz when the air in the tube is replaced with helium. This is due to the higher speed of sound in helium.

Explanation: The fundamental frequency of a gas in an open-closed tube is determined by the speed of sound in that gas divided by four times the length of the tube. In the case where the fundamental frequency is 315 Hz with air in the tube and the speed of sound in air is 343 m/s, the length of the tube would be approximately 0.272 m.

If the tube is filled with helium, where the speed of sound is 1010 m/s, and the length of the tube remains at 0.272 m, the fundamental frequency in helium would be around 930 Hz. This increase is a result of the higher speed of sound in helium compared to air.

By understanding the relationship between speed of sound and fundamental frequency, we can see how changes in the medium within the tube affect the frequency of sound waves. This phenomenon showcases the importance of medium properties in determining acoustic behavior.

For further insights into fundamental frequency and its relation to sound speed, you can explore additional resources on the topic.