Finding time difference between two arriving wave fronts

In summary, the conversation discusses the formula AB=2Rsin30° and its derivation. It is shown that this formula is derived from drawing a perpendicular line from the center to the base AB and splitting it into two equal parts. The conversation also touches upon the dimensionality of angles and the concept of assigning a dimension to them, with some resources provided for further reading.
  • #1
ChiralSuperfields
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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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  • #2
##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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  • #3
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!
 
  • #4
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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  • #5
Thanks @kuruman ! But isn't degrees have no dimensions too?

Many thanks!
 
  • #7
Ok thank you @haruspex ! - I will check that out.

Many thanks!
 

Related to Finding time difference between two arriving wave fronts

What is the concept of finding time difference between two arriving wave fronts?

The concept of finding time difference between two arriving wave fronts involves measuring the difference in time it takes for two wave fronts to reach a given point. This can be used to determine the distance between the two wave sources or to calculate the speed of the wave.

What is the importance of finding time difference between two arriving wave fronts?

Finding time difference between two arriving wave fronts is important in a variety of fields, including physics, engineering, and astronomy. It can help us understand the behavior of waves and their sources, and can also be used to make precise measurements and calculations.

What factors can affect the accuracy of finding time difference between two arriving wave fronts?

There are several factors that can affect the accuracy of finding time difference between two arriving wave fronts. These include the precision of the measuring instruments, the distance between the wave sources, and any external factors that may influence the speed of the waves, such as temperature or interference.

What methods can be used to find the time difference between two arriving wave fronts?

There are several methods that can be used to find the time difference between two arriving wave fronts. These include using a stopwatch or timer, using specialized equipment such as oscilloscopes or interferometers, and using mathematical calculations based on the known speed of the wave.

How can the concept of finding time difference between two arriving wave fronts be applied in real-world situations?

The concept of finding time difference between two arriving wave fronts has many practical applications. It can be used in navigation systems, such as GPS, to determine location and calculate travel time. It can also be used in seismology to study earthquakes and in sonar technology for underwater mapping and communication.

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