Basic Wavelength Physics Question
Nov 6, 2008 at 2:54 AM Thread Starter Post #1 of 6

texashorn91

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Hopefully someone can answer this question easily, it just does not make sense to me.
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I was reading here that a 16.4 Hz wave is the lowest frequency we can hear, if we have good ears. It also says that a 16.4 Hz sound wave has a wavelength of 69 feet.

Doesn't sound have to its entire wavelength for us to be able to recognize it and set it apart from other sound waves? By this reasoning we can only hear sounds over 1khz in headphones, so I know I am wrong. I just don't understand it, and I would really appreciate it someone could help me out! Thanks!
 
Nov 6, 2008 at 6:03 AM Post #2 of 6

myinitialsaredac

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|---69 ft---| can simply be |-1 inch-| 828 times. Or |-2inch-| 414 times or |-3inch-| 276 times. The speed of sound is about 1059.7 ft per second so we can see that 69 feet can bounce back and fourth against our eardrum in .065 seconds to realize the full wavelength.
This is my guess =D.
Dave
 
Nov 7, 2008 at 3:28 AM Post #3 of 6

P_A_W

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myinitialsaredac is right. It isn't really useful to think about the wavelength of sounds in this context, only the frequency. Your ear doesn't measure wavelength so much as frequency.

The only time that the wavelength of a sound wave would be important is to determine what the resonant frequencies of a room/speaker box/instrument are. For instance, if you were in a room that was 10 ft x 10 ft x 10 ft, the lowest frequency standing wave could be computed by setting half the wavelength equal to the width of the room. It turns out you need to do this for each dimension of the room and the frequency is

nu = c/ ((20ft)^2+(20ft)^2+(20ft)^2)^.5 ~ 30 Hz

where c is the speed of sound. Now... this doesn't mean that you can't hear lower frequency sounds in this room... it just means they won't resonate.

"What about the piano?" you might ask. How can a piano resonate for the low C? Your table suggests that the lowest C on the piano is 32.7 Hz which has a wavelength of 34 feet 6 inches! Well something in the piano is resonating at 32.7 Hz, but it isn't the air, but the piano strings. Again, the string length sets the lowest resonant frequency of the string, but it is the mass density of the string and its tension that determine the speed of the wave and therefore its frequency... Again, when this wave couples into the air to form the sound we hear, it is the frequency--not the wavelength--that conserved... that is why the piano doesn't need to be 34 ft long!
 
Nov 7, 2008 at 4:35 AM Post #4 of 6

monolith

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...Wavelength and frequency are equivalent.

The string of a piano causes the air to vibrate at the same frequency, and thus with that wavelength. The string doesn't have to be 34.5 feet long in order for it to vibrate at that frequecy/wavelength.
 
Nov 12, 2008 at 11:43 PM Post #5 of 6

Mark Ovchain

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The wave is travelling past you. You hear (or not) the whole wave as a time function as it passes you by, so saying "hearing the whole wave" is a bit of a misnomer.

At very low frequencies in small spaces, under the frequency where the space acts like its pressure-driven the issue changes, but the whole time waveform is still presented to the ear.

And 16.4 seems somewhat arbitrary to me, my understanding is that low frequency sensation is primarily not via hearing, and that separating out hearing from other effects (chest, gut, etc) is going to be very hard.

And we can sense, but not hear, frequencies well below 15Hz, but not particularly by hearing...
 
Dec 3, 2008 at 4:52 AM Post #6 of 6

myinitialsaredac

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Sorry all I feel we are all incorrect thus far except I believe Mark got close to my understanding. I got down to some critical thinking recently and I believe I have the answer to this question.

So lets say we have a 20hz wave. 20hz simply means that wave will have 20 cycles per second. It will have a wavelength of 56.5 feet in air. So a 20hz wave for 2 seconds will be double that distance, so 113 ft. Now, what about if we broke it down from there, what is the length of a 20hz wave for .5 seconds? 28.25 ft. How about for a ms? .0565 ft. Now lets move the time to 0, we will see the wavelength also move to zero. After due consideration it dawned on me that at every time there is a corresponding point relevant to the frequency of the wave. So if we listened to a 20hz wave for a full second we would here all 20cycles and have 56.5 ft of wave moving through our ears. But, at the instantaneous times there would be an immeasurable instantaneous point that adds up with all the other times to equal the entire wave or 56.5ft. There is likely a limit on how short of a time period relevant to frequency and intensity that we can hear (which is where we develop our hearing limits) when the wave is too long at the smallest amount of time necessary for the ear to respond or too short at the necessary time.
So what the issue that presents itself to me is how you have to specify with hz. One must say x seconds of a x hz wave or x wavelengths of a x hertz wave.

This is what I believe the answer to be.
Great question man!

Dave
 

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