How long is an open organ pipe with a fundamental frequency of 493.88 Hz?
To determine the length of an open organ pipe with a fundamental frequency of 493.88 Hz, you can use the formula for the fundamental frequency of an open organ pipe, which is given by:
f = (v/2L) * n
where:
- f is the fundamental frequency (in Hz)
- v is the speed of sound in air (approximately 343 m/s at room temperature)
- L is the length of the pipe (in meters)
- n is a positive integer representing the harmonic number (1 for the fundamental frequency)
In this case, we are given the fundamental frequency (f) as 493.88 Hz. We can substitute the known values into the formula and solve for L:
493.88 = (343/2L) * 1
To isolate L, we rearrange the equation:
L = (343/2) / 493.88
L = 0.3478 meters
Therefore, an open organ pipe with a fundamental frequency of 493.88 Hz has a length of approximately 0.3478 meters.
The length of an open organ pipe can be determined using the formula:
Length = (Speed of Sound) / (4 * frequency)
The speed of sound in air is approximately 343 meters per second.
So, plugging in the values:
Length = 343 m/s / (4 * 493.88 Hz)
Length = 0.1736 meters (or 173.6 mm)
Therefore, an open organ pipe with a fundamental frequency of 493.88 Hz would have a length of approximately 0.1736 meters or 173.6 mm.