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LLT71
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can you please explain me why don't we use arc length formula to calculate wavelength? seems a bit confusing...
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.LLT71 said: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?
LLT71 said: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.
You are welcome! It is a pretty common misunderstanding for electromagnetic waves just because of the way books draw EM waves.LLT71 said: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 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.Dale said:You are welcome! It is a pretty common misunderstanding for electromagnetic waves just because of the way books draw EM waves.
The arc length formula, s = rθ, is used to calculate the length of a circular arc. However, the wavelength of a wave is not a circular arc and does not have a defined radius or central angle. Therefore, this formula is not applicable to calculate wavelength.
Wavelength is calculated using the formula λ = v/f, where λ represents wavelength, v represents wave velocity, and f represents frequency. This formula is derived from the relationship between wavelength, frequency, and wave velocity in the wave equation, c = fλ, where c is the speed of light.
No, the arc length formula cannot be used to calculate the wavelength of a circular wave because the formula calculates the length of a circular arc, not the distance between two points on the circumference of the circle.
Yes, the arc length formula is commonly used in geometry and trigonometry to calculate the length of a circular arc, as well as in physics to determine the displacement of an object moving in a circular motion. However, it is not applicable to calculate the wavelength of a wave.
Using the correct formula to calculate wavelength is important because it ensures accurate and precise measurements. The arc length formula is not applicable to calculate wavelength, and using it would result in incorrect values. By using the correct formula, scientists can obtain reliable data and make accurate conclusions in their research.