The range of human hearing is roughly from twenty hertz to twenty kilohertz. Based on these limits and a value of 350 m/s for the speed of sound, what are the lengths of the longest and shortest pipes (open at both ends and producing sound at their fundamental frequencies) that you expect to find in a pipe organ?
m (shortest pipe)
m (longest pipe)
Compute the shortest and the longest wavelengths, using the standard formula
(wavelength) = (sound speed)/(frequency)
The length of a double-open-ended organ pipe is half of the wavelength.
ref:
http://www.glenbrook.k12.il.us/GBSSCI/PHYS/Class/sound/u11l5c.htm
Well, since the range of human hearing is from twenty hertz to twenty kilohertz, let's use those limits to calculate the lengths of the longest and shortest pipes you could expect to find in a pipe organ.
For the shortest pipe, we'll use a frequency of 20 Hz:
wavelength = speed of sound / frequency
wavelength = 350 m/s / 20 Hz
wavelength ≈ 17.5 meters
Since the length of a double-open-ended organ pipe is half of the wavelength, the shortest pipe would be around 8.75 meters long.
Now, for the longest pipe, we'll use a frequency of 20,000 Hz (or 20 kHz):
wavelength = speed of sound / frequency
wavelength = 350 m/s / 20,000 Hz
wavelength ≈ 0.0175 meters
So, the longest pipe would be around 0.00875 meters long.
Now, I'm no organ player, but I imagine finding a pipe organ with a pipe as long as 8.75 meters would be quite a challenge, and one as short as 0.00875 meters might just be too tiny to even see! But hey, stranger things have happened in the world of music.
To find the lengths of the longest and shortest pipes in a pipe organ, we can use the formula:
wavelength = (sound speed) / (frequency)
Given that the range of human hearing is from 20 Hz to 20,000 Hz, and the speed of sound is 350 m/s, we can calculate the shortest and longest wavelengths.
Calculating the shortest wavelength:
frequency = 20 Hz
wavelength = 350 m/s / 20 Hz
wavelength = 17.5 m
Since the length of a double-open-ended organ pipe is half of the wavelength, the length of the shortest pipe would be half of 17.5 m.
Therefore, the shortest pipe length (m) = 8.75 m
Calculating the longest wavelength:
frequency = 20,000 Hz
wavelength = 350 m/s / 20,000 Hz
wavelength = 0.0175 m
Again, the length of a double-open-ended organ pipe is half of the wavelength, so the length of the longest pipe would be half of 0.0175 m.
Therefore, the longest pipe length (m) = 0.00875 m
To find the lengths of the longest and shortest pipes in a pipe organ, we can use the formula:
wavelength = sound speed / frequency,
where the sound speed is given as 350 m/s.
For the shortest pipe, we need to find the wavelength corresponding to the lowest frequency audible to humans, which is 20 Hz. Plugging these values into the formula, we get:
wavelength(shortest) = 350 m/s / 20 Hz = 17.5 m.
Since the length of a double-open-ended organ pipe is half the wavelength, we have:
length(shortest pipe) = 17.5 m / 2 = 8.75 m.
Therefore, the length of the shortest pipe would be approximately 8.75 meters.
For the longest pipe, we need to find the wavelength corresponding to the highest frequency audible to humans, which is 20 kHz (20,000 Hz). Plugging these values into the formula, we get:
wavelength(longest) = 350 m/s / 20,000 Hz = 0.0175 m.
Again, since the length of a double-open-ended organ pipe is half the wavelength, we have:
length(longest pipe) = 0.0175 m / 2 = 0.00875 m.
Therefore, the length of the longest pipe would be approximately 0.00875 meters (or 8.75 millimeters).
Note: These calculations assume idealized pipe lengths and may not reflect exact lengths found in practical pipe organs.