Most people know that what makes sounds different is that they have different frequencies. \u00a0Moreover, a high pitched sound has a higher frequency than a low pitched one. \u00a0Likely, that’s whence the idea of “high note” vs “low note” originates.<\/p>\n
Every wave has not only a frequency, but also a wavelength. \u00a0The two go hand in hand according to the formula<\/p>\n
v=fλ<\/p>\n
where
\nv means velocity (which, for this purpose, can be reduced to speed),
\nf means frequency
\n\u03bb means wavelength<\/p>\n
Dividing both sides by f, we arrive at a formula for the wavelength, λ:<\/p>\n
v\/f=λ<\/p>\n
As I mentioned in my January 13<\/a> post, the speed of sound s is given by <\/p>\n s=(332 + 0.6T)m\/s<\/p>\n where T is the temperature in degrees Celsius.<\/p>\n Let’s imagine, for temperature, a pleasant 20C. We have, for the speed of sound,<\/p>\n s=(332+0.6(20))m\/s=344m\/s<\/p>\n Since speed and velocity are, for this purpose, the same, we can say that v=344.<\/p>\n Next, we need f, the frequency. Specifically, in this case, we want the frequency of “middle” F, which is meant to be the F just three keys above middle C. The physics dept at Michigan Tech provides this handy page<\/a>, informing us that the F above middle C has frequency 349.23Hz.<\/p>\n With v=344 and f=349.23, we are ready to find the wavelength of middle F:<\/p>\n v\/f=344\/349.23=0.985m=λ<\/p>\n Therefore, the wavelength of middle F, at 20\u00b0C, is 0.985m or 98.5cm.<\/p>\n HTH:)<\/p>\n