Finding time difference between two arriving wave fronts

AI Thread Summary
The discussion focuses on deriving the formula AB=2R*sin(30°) for the time difference between two wave fronts. Participants clarify that drawing a perpendicular from the center to the base AB helps in understanding the formula's origin. The conversation shifts to the use of radians versus degrees in the arc length formula, emphasizing that radians represent a ratio of length, while degrees are dimensionless but have different units. The distinction between radians and degrees is acknowledged, with a suggestion to explore the concept of assigning dimensions to angles. Overall, the thread highlights the mathematical reasoning behind the formula and the dimensionality of angles.
member 731016
Homework Statement
Please see below
Relevant Equations
S = Rθ
For part(b),
1670377033527.png

The solution is,
1670377172104.png

However, where did they get the formula shown in red from?

Many thanks!
 

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##AB=2R\sin30^o.## Do you see why? Hint: Draw a perpendicular from the center to the base AB. It splits AB into two equal parts. What is the length of each part?
 
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kuruman said:
##AB=2R\sin30^o.## Do you see why? Hint: Draw a perpendicular from the center to the base AB. It splits AB into two equal parts. What is the length of each part?
Thanks I see it now @kuruman ! Is the reason why they used radians instead of degrees in the arc length formula is because radians is a ratio of the length while degrees is not.

Many thanks!
 
What you call the arc length formula is actually the definition of the angle as the ratio of the arc length to the radius. As such it has no dimensions.
 
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Thanks @kuruman ! But isn't degrees have no dimensions too?

Many thanks!
 
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Ok thank you @haruspex ! - I will check that out.

Many thanks!
 
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