Basic Wavelength Physics Question
Nov 6, 2008 at 2:54 AM Thread Starter

#### texashorn91

Hopefully someone can answer this question easily, it just does not make sense to me.

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

#### myinitialsaredac

|---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

#### P_A_W

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

#### monolith

...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

#### Mark Ovchain

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