You want to make an open-ended flute, open at both ends, with fundamental frequency (lowest pitch sound it produces) of 680 Hz. Assume speed of sound in air is 340 m/s. a) What should the length of the flute be?
0.2
To determine the length of an open-ended flute that produces a specific fundamental frequency, we can use the formula for the fundamental frequency of a tube that is open at both ends:
f = (v / 2L)
where:
- f is the fundamental frequency in hertz (Hz)
- v is the speed of sound in the medium, which is 340 m/s in this case
- L is the length of the flute in meters
Rearranging the formula, we can solve for the length L:
L = v / (2f)
Now, we can substitute the given values into the formula:
L = 340 m/s / (2 * 680 Hz)
Simplifying the equation:
L = 340 m/s / 1360 Hz
L = 0.25 m
Therefore, the length of the open-ended flute that produces a fundamental frequency of 680 Hz should be 0.25 meters.