Question

Musical notes have names (A,B,C, etc). The lowest A on a piano is called A0. If you go up an octave, the next A would be called A1. An octave higher, A2. The A near the middle of the keyboard is A4 (also called "concert A"). A similar pattern is true for all the notes. In a certain set of organ pipes, the speaking length (that's an effective physical length) for the pipe that makes the note E5 (f=660 Hz) is 26.06 cm. How long a pipe do you expect for E2? Compute your answer in meters, but do not enter units. (If the answer is 850 cm = 8.5 m, enter the number 8.5) For you to think about: What is the wavelength of sound produced by the E5 pipe described in this problem? It's not the same as the length of the pipe, it should be different by a factor of 2 (that's not an accident, we'll discuss why later). The longest organ pipe in the world (according to my quick web search) is 64 feet long. Based on the numbers in this problem, could you actually hear the sound produced by this pipe? Why or why not? What might be the effect of such a pipe? What would you need to do (lengthen? shorten? by how much?) to this pipe to get a sound with a wavelength twice as long?

Answer 1

The frequency for E2 note is around 82.41 Hz. The effective physical length for an organ can be calculated as

L = c/2f where c is speed of sound in air at room temperature which is approximately equal to 346 m/s

Therefore, L = 346 / 2*82.41

L = 2.099 meters.

Wavelength is related to frequency through speed of sound

lambda*f = c

lambda = c/f = 346 / 660 = 0.5242 meters. As we can see effective length for a given frequency f is almost equal to half of a wavelength that is wavelength is 2(effective length)

From web search, I found out that humans can hear between frequency range of 20 Hz to 20,000 Hz. However, the best we can hear is 1000 Hz to 5000 Hz.

Now, for L = 64 feet or 19.5072 meters, the frequency is 346 / 2*19.5072 = 8.868 Hz which is very less than lowest range value of what we can hear (20 Hz). We will not be able to hear any sound from this organ.