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

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SUMMARY

In the wave interference problem involving two loudspeakers producing circular waves of 7m wavelength, a person located on the sixth nodal line at a fixed distance of 50m from one source can indeed have varying distances from the second source. This variation occurs due to the geometric arrangement and the angles involved in the wave interference pattern. The concept of nodal lines and the trigonometric relationships governing wave propagation explain the multiple possible distances to the second source, despite the person's fixed position relative to the first source.

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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
 
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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)
 

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