To calculate how much the trombone player would have to move the slider to play at a frequency of 25 hertz, we first need to determine the wavelength of the fundamental tone.
The wavelength of the fundamental tone in a half-open tube is equal to four times the length of the tube. Therefore, the wavelength (λ) is:
λ = 4 * length = 4 * 3 m = 12 m
The formula for the frequency of a wave is:
frequency = speed of sound / wavelength
The speed of sound in air at room temperature is approximately 343 m/s. Therefore, the frequency of the fundamental tone is:
25 Hz = 343 m/s / λ
Rearranging the formula to solve for λ:
λ = 343 m/s / 25 Hz = 13.72 m
Since the trombone player needs to adjust the length of the tube to match the wavelength of 25 Hz, the new length (L') is:
L' = λ / 4 = 13.72 m / 4 = 3.43 m
The trombone player would have to move the slider by the difference between the new length and the original length:
ΔL = L' - 3 m = 3.43 m - 3 m = 0.43 m = 43 cm
Therefore, the trombone player would have to move the slider by 43 cm to play the fundamental tone at a frequency of 25 hertz.
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 hertz?
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