According to my physics book, ar my memory of what it says, the speed of sound is not dependent on frequency.
However, I have noticed what at first seemed to be a counter-example. When lighning strikes nearby, you hear the instant blast of thunder. When it is not so nearby, sometimes the thunder lasts several seconds, first starting with some high-pitched crackling folowed by some mid-pitched crackling and ending with the bass thud and roar.
What is the cause of the diffent phases of thunder, and why don’t you hear it when the lightning strikes nearby?
You don’t hear the different phases when lightning strikes nearby because there isn’t enough time. Take two pulses – one traveling at v1, the second at v2, both starting at a distance d. The first will reach you at t1 = d/v1, the second at t2 = d/v2. The time difference will be [symbol]D[/symbol]t = d(1/v1 - 1/v2). So the greater the distance, the greater the time difference.
High frequencies get damped out over shorter distances than lower frequencies. Since lightning bolts are nearly instantaneous, the sound you here after the initial crack is coming from further away, and has more of the high frequencies damped by the time it gets to you.
As an aside, the ‘crackling’ sound you hear is the air actually clipping into distortion. At a certain point, the air cannot handle the sound waves, and ‘clips’ just like an amplifier will clip if you try to drive the transistor amps past their maximum signal level.
I’m thinking on the same lines as you. I assume that the drawn-out thunder comes from the situation in which a bolt extends from high in the atmosphere to the ground. The listener is closer to the portion of the bolt hitting the ground than the portion in the clouds, and if the bolt is “tall” enough, that would account for the drawn-outness of the thunderclap.
So, you hear the lighning near the ground first, then the portion from higher. But according to what you say, the high frequencies have expired by the time the loud bass portion from the upper atmosphere arrive. I can buy that, but it doesn’t seem to explain the lack of bass with the initial crackling.
And Sam, do you know why the “cliping” of the air arrives before the rest of the thunder?
The volume of the sound will get louder and softer depending on the orientation of different parts of the lightning bolt. If a segment of the bolt is directed straight at the listener, the volume will be minimized because the sound arrives sequentially from different parts of the bolt. If the bolt travels on a path that is always the same distance from the listener, all the sound will arrive at the same time and be relatively loud. I think that this effect combined with the attenuation of high frequencies with distance can account for the apparent increase in base over the duration of the thunder. Not only are the high frequencies diminishing with time, but the overall volume is changing erratically as the sound reaches you from the parts of the bolt at increasing distances from the ear.
Also, whenever sound travels horizontally over a long distance it will be refracted upwards because of the atmosphere’s density gradient. I would expect that different frequencies will bend differently because of diffraction (1KHz “crack” is one ft wavelength, 10 Hz “thud” is 100ft wavelength.)
And speaking of"atmospheric clipping, another word for this is “shock wave.” When a supersonic plane flys close by, you hear a loud “snap.” That’s a shock wave. Because of nonlinear response of air, the shock wave compresses into a pulse just a few millimeters thick. But the shock wave also heats the air as it travels, so it loses energy and quickly converts into normal sound. And when a supersonic plane flys by in the distance, you hear a “thud” rather than a “snap” sound.