Why Can the Distance to the Second Source Vary in a Wave Interference Problem?

[preet]

Two loudspeakers are producing circular waves of 7m wavelength in phase. A person on the sixth nodal line is 50m from one source. What are the possible distances of the person from the other source?

I know how to do this question but I don't understand how there can be two different distances. The question states the person is 50m from one source and is on the sixth nodal line. So he shouldn't be able to move at all. If he is fixed 50m from one source, how can the distance to the other source vary? I even roughly drew it out but I can't see it. TiA

Preet

 

[Hootenanny]

The distance from the other speaker can vary depending in theangle at which the 50m difference is taken. As this is a trig function I would expect there to be limits as in theory there could be an infinite number of nodes (ignoring work done against resistive forces)

 

[quicknote]

i, it is understandable that you may be confused by this question. However, it is important to remember that wave interference is a dynamic phenomenon and the position of the nodal lines can change depending on the relative positions of the two sources.

In this specific scenario, the person is 50m from one source and on the sixth nodal line. This means that at that specific moment, the distance between the person and the first source is equal to 50m. However, as the person moves along the sixth nodal line, the distance between them and the first source will remain constant, but the distance between them and the second source will change, resulting in different possible distances.

To fully understand this, it may be helpful to visualize the situation in three dimensions. The two sources are producing circular waves, and the person is located on a nodal line, which is essentially a line where the two waves intersect and cancel each other out. As the person moves along this nodal line, they are essentially changing their position in relation to the two sources, resulting in different distances between them and the second source.

In summary, the possible distances of the person from the other source will vary as they move along the sixth nodal line, while remaining a fixed distance of 50m from the first source. This is a fundamental principle of wave interference and is important to understand in order to accurately analyze and solve problems involving it. I hope this explanation helps clarify any confusion.