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.
How much would the trombone player have to move the slider in cm to play 25 Hz? Be sure you know how a trombone works!
To calculate the required movement of the slider, we need to determine the wavelength of the fundamental frequency (25 Hz) of the sound produced by the trombone.
The fundamental frequency (f) of a half open tube can be found using the formula:
f = v / (2L)
Where:
- f is the frequency (25 Hz)
- v is the velocity of sound in air (approximately 343 m/s)
- L is the length of the tube (3 m)
By rearranging the formula, we can solve for the wavelength (λ):
λ = v / f = 343 m/s / 25 Hz
λ ≈ 13.72 m
Since the trombone is a half open tube, the wavelength is twice the length of the tube. Therefore, the trombone player needs to adjust the slide such that the effective length of the trombone tube is half the wavelength:
Slide movement in meters = λ / 2 = 13.72 m / 2
Slide movement in centimeters = Slide movement in meters * 100 = (13.72 m / 2) * 100 ≈ 686 cm
Thus, the trombone player would need to move the slider approximately 686 cm to play a fundamental frequency of 25 Hz.