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?
To determine how much the trombone player would have to move the slider to play a specific frequency, we need to understand the relationship between the length of the tube and the fundamental frequency it produces.
Instruments like trombones, which are open on one end and closed on the other, produce a fundamental frequency determined by the length of the vibrating air column. The equation that relates the length of the tube to the fundamental frequency is given by:
f = (v/2L),
where f is the fundamental frequency, v is the speed of sound (which is approximately 343 m/s at room temperature), and L is the length of the air column.
In this case, we want to find the length L required to produce a frequency of 25 Hz. Rearranging the equation, we have:
L = v / (2f).
Substituting the given values:
L = 343 m/s / (2 * 25 Hz) = 6.86 m.
However, we are asked to provide the answer in centimeters. So, we need to convert the length to centimeters by multiplying by 100:
L_cm = 6.86 m * 100 cm/m = 686 cm.
Therefore, the trombone player would need to move the slider by 686 cm to play a frequency of 25 Hz.