B Why don't we use arc length formula to calculate wavelength?

[LLT71]

can you please explain me why don't we use arc length formula to calculate wavelength? seems a bit confusing...

 

[DrClaude]

Could you please be more specific?

 

[LLT71]

Wavelength of a sine wave, λ, can be measured between any two points with the same phase, such as between crests, or troughs, or corresponding zero crossings as shown.
Why don't we treat that as length of sine function between that two points instead, cause that would give us full length of that function in that interval? This way it seems to me like "length of a line" between two points (crests etc.)=wavelength.

 

[boneh3ad]

Well for one, that measurement wouldn't be useful. Wavelength as it is currently defined has a lot of physical meaning. Some sort of length along the curve does not.

 

[Dale]

Why don't we treat that as length of sine function between that two points instead, cause that would give us full length of that function in that interval?

If you have a sin function usually the vertical axis is something like E field strength or pressure, not distance. So it usually wouldn't make sense unit-wise to use the arc length formula.

 

[PeroK]

Wavelength of a sine wave, λ, can be measured between any two points with the same phase, such as between crests, or troughs, or corresponding zero crossings as shown.
Why don't we treat that as length of sine function between that two points instead, cause that would give us full length of that function in that interval? This way it seems to me like "length of a line" between two points (crests etc.)=wavelength.

It's an interesting idea. That would actually be a combination of the wavelength and the amplitude. If you think about music, and notes on a stringed instrument, you can see why the traditional definitions of wavelength and amplitude are important.

 

[LLT71]

thank you all! I think seeing a wave just in a way of math function and not understanding what that function actually represents led me to misinterpret wavelength.

 

[Dale]

thank you all! I think seeing a wave just in a way of math function and not understanding what that function actually represents led me to misinterpret wavelength.

You are welcome! It is a pretty common misunderstanding for electromagnetic waves just because of the way books draw EM waves.

 

[LLT71]

You are welcome! It is a pretty common misunderstanding for electromagnetic waves just because of the way books draw EM waves.

you are totally right! for ex. one can easily conclude from the way pictures represent them (particulary, basic wave function) that T[period]=lambda[wavelength], which at first seems very obvious and unit-wise not.