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pkc111
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A friend of mine says they can tell which 2 notes are being played together on a piano keyboard. How can this be if the 2 notes combine to form a single wave (sum of the 2) ?
Vanadium 50 said:The ear doesn't. The brain does.
pkc111 said:Thank you for your comments.
Im still confused how an ear can make out the two component waves shown in (row A) from the wave received (rowA) ?
pkc111 said:OK I can accept that the brain may be a giant computer that can do a Fourier analysis on waves to analyse their components.
I asked a Science teacher today and they gave me another possibility that I wanted to put out there ie:
"There are hairs in the Cochlea which resonate at different frequencies (like antennae). The components of the summed wave are able to effect each antenna separately according to which frequencies match which hair."
This sort of made sense because I imagine radio receivers face the same problem as ears and brains. They would receive a "wave sum" of all the radio waves in the area and would therefore only have to be able to resonate at the frequency of one of the component waves .
Is this a correct analogy?
Thanks for your ideas.
chrisbaird said:Yes, an antenna picks up waves at many frequencies, but it has a natural resonance depending on its length and picks up waves best near its resonant frequency. So you still need electronics to isolate your frequency of interest, but designing the antenna with the frequency in mind boosts performance.
Yes, the hairs in the Cochlea are like antennas in this way. One hair can pick up vibrations at many frequencies, but picks up best near its resonance frequencies. With hairs of different lengths, and thus different resonant frequencies, we literally hear many frequencies at once using different parts of our ear. The brain gets sound in frequency representation, not in time representation. The original question is similar to the question, "Can our eyes see the colors blue and red at the same time?" Yes, because there are different parts of the eye that are tuned to these wavelengths. There are red cone cells, blue cone cells, and green cone cells.
pkc111 said:"Why does any object resonate at its resonance frequency when the wave sum that arrives is not at the resonant frequency of the object, but is rather only the result of the resonant frequency wave added to many others to create the odd sort of shape wave eg shown at the end of row A above. ?"
RedX said:An infinitismal antenna should pick up EM waves of any frequency. If you have an antenna longer than the wavelength of the wave hitting it, then I think you would have to worry if the wave hits it obliquely, i.e., the wave number has a component in the direction of the antenna, since this would cause destructive interference since different parts of the antenna would differ in phase.
I think where resonance comes in would be where the transmission line connects the antenna to the receiver. So if your antenna has a length of half the wavelength of the chosen frequency, then the impedance is set at around 73 Ohms, which would require the transmission line to have the same impedance. So a wave of a different frequency hitting the antenna would have a different impedance, while the line was set to 73 Ohms, so you get reflection of the power by the receiver (where does this power go, back out the antenna?).
Would a hair be like a quarter-wave antenna, since there is only one follicle sticking out? What would be the grounding plane?
Born2bwire said:This also means that our rope can be excited by multiple frequencies... This means that he can only excite waves that have wavelengths that are integer multiples of twice the length of the rope. .
pkc111 said:OK, so does that mean when C and F are played together on a keyboard, the wave sum has a wavelength that is some simple multiple of both C and F so that detectors (resonating elements tuned to C and F) preferentially vibrate when the wave sum reaches them ?
atyy said:The sum is simply the sum, so both frequencies are still present - in the Fourier (sinusoidal) sense.
Born2bwire said:A Hertzian dipole may work at all frequencies but it is absurdly inefficient because it isn't resonant. What you want is an antenna that is half-wavelength in size because then the excited currents satisfy a resonant mode on the antenna. That is, the excited currents naturally satisfy the boundary conditions imposed by the physical structure of the antenna. However, this only strictly applies to wire dipole antennas. A wire dipole antenna of orders greater than a half-wavelength are undesirable because some versions try to force infinite output impedance and they all suffer from poorer performance in the transmitted power because some sections of the antenna will be out of phase from others causing cancellation (though the obliqueness of the receiving/transmitted wave is not a factor in this).
pkc111 said:This is what I don't understand :the sum is differnt to the components: just as both 2 and 3 are different to five.
How does something as simple as a hair do a Fourier decomposition on a wave sum to respond to one of the components that went into the wave summation ?
Dadface said:For sounds to exist and be detected the pressure must vary with time and it is variations such as this that the ear responds to.We can analyse this as a resultant effect but when we do so and by reference to the OPs question we find that the resultant is due to the two separate sets of waves.