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.

Answer 1

Because the trombone is a half open tube, the fundamental frequency of the sound wave produced corresponds to half a wavelength.

Therefore, the wavelength of the fundamental frequency is equal to the length of the half open tube:
λ = 3 m

We know that the speed of sound in air is approximately 343 m/s.
Since the fundamental frequency is the lowest frequency produced by the trombone, it is equal to the speed of sound divided by the wavelength:
f = v / λ
f = 343 m/s / 3 m
f ≈ 114.33 Hz

Therefore, the fundamental frequency of the trombone when played at the end zone of the football field is approximately 114.33 Hz.