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 3m long.
How much would the trombone player have to move the slider in cm to play 25 Hz?
To calculate how much the trombone player would have to move the slider in order to play a specific frequency, we can use the formula for the fundamental frequency of a half open tube:
f = v / (2L)
Where:
f = fundamental frequency in Hz
v = speed of sound in air (approximately 343 m/s)
L = length of the tube in meters
In this case, the player wants to play a frequency of 25 Hz. So we can rearrange the formula to solve for L:
L = v / (2f)
Plugging in the values, we get:
L = 343 m/s / (2 * 25 Hz)
L = 343 m/s / 50 Hz
L = 6.86 m
Since the trombone is only 3m long, the trombone player would have to move the slider to increase the length of the tube to 6.86m. The difference between the initial length (3m) and the required length (6.86m) is 6.86m - 3m = 3.86m. Converting this to centimeters, we get:
3.86m * 100 cm/m = 386 cm
Therefore, the trombone player would have to move the slider 386 cm in order to play a frequency of 25 Hz.