A trombone player stands at the end zone (x=0) of a football field and begins to play its fundamental tone. Assume the trombone is a half open tube that is 3 m long.
What is the frequency of the note in Hz?
To find the frequency of the fundamental tone of the trombone, we can use the formula:
f = v / λ
Where:
- f is the frequency of the wave
- v is the velocity of the wave
- λ is the wavelength of the wave
In this case, we know that the trombone is a half open tube that is 3 m long. A half open tube has one end open and another end closed. The fundamental mode of vibration in a half open tube has a wavelength that is four times the length of the tube.
Therefore, the wavelength (λ) of the wave produced by the trombone is 4 times the length of the tube (3 m), which is equal to 12 m.
Now, we need to determine the velocity of the wave. The velocity of a wave depends on the medium through which it travels. In air, the speed of sound is approximately 343 m/s at room temperature.
Using the formula, we can calculate the frequency:
f = v / λ
f = 343 m/s / 12 m
f ≈ 28.58 Hz
Therefore, the frequency of the fundamental tone produced by the trombone is approximately 28.58 Hz.