Physics Sound Frequency

Question

The trunk of a elephant may extend up to 2.4 m. It acts much like an organ pipe only open at one end when the elephant blows air through it.

1) Calculate the fundamental frequency of the sound the elephant can create with its trunk. (Express your answer to two significant figures.)

2) If the elephant blows even harder, the next harmonic may be sounded. What is the frequency of the first overtone? (Express your answer to two significant figures.)

Answer 1

Hi Annie C.,

You probably have your answer already, but if not, I can help. What are the physics conditions here? The trunk is a tube, (driven and) closed at one end, and open at the other. At the closed end, there can be no longitudinal movement of air (zero wave amplitude)**; at the open end, the air movement must be maximal (crest of the wave), since nothing is holding it in (or out!). That describes exactly 1/4 of a full wavelength of a sinusoidal wave. You already know speed of sound in air, and speed = .frequency. * .wavelength. .

For the first overtone, you still have these conditions at the ends, except now you have exactly one additional node (zero amplitude point) between. So you can draw the wave, and figure out how long it must be in all.

** Qualifier: you probably know that you must buzz some air out to make the tube sound at all. But that's just the requirement for exciting the air column into movement. There are really two complementary ways of thinking about what the wave is: the first way is to think about the pressure, over time, at a particular spot, and the second way is to think about how the air is moving longitudinally at that particular spot, over time. Above I have described the longitudinal movements of the air. The way of describing the pressures is the exact opposite. For pressures, you (the elephant) are pulsing the pressure at your trunk base (that's called an "anti-node"), but the pressures at the tip must be "zero" at all times (a "node"), because the air is free to leave or enter. You definitely need to think about those two ways of describing a wave, so that you don't try to mix and match the two ways and get confused. Either way is OK to think about a wave,as long as you keep to that way throughout a single problem.

That wind you "buzzed" out? After it's done its thing exciting the air column, it's "de nada". Except that it tends to condense some water out into the tube -- a problem for brass players, but not for elephants!

--- Cheers, Mr. d.