What is the equation for finding the maximum frequency in a towed-array sonar?

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The discussion focuses on determining the maximum frequency for a towed-array sonar system with 100 transducers spaced 3 meters apart, to be used while scanning from -90 to 90 degrees. The key equation presented is dsin(theta) + delta x wavelength/2pi = n x wavelength, where d is the transducer spacing, delta represents phase delay, and n indicates the diffraction order. The user seeks clarification on the origin and meaning of this equation, as well as its application in calculating frequency. Understanding this equation is crucial for ensuring only one diffraction order is present during beam steering. The conversation highlights the need for a more accessible explanation of the underlying principles.
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Homework Statement


A towed - array sonar comprises 100 transducers equally spaced at every 3m and towed behind a ship so the array stays just below the surface of the water (effectively horizontal). An adjustable phase delay can be introduced for each transducer, allowing the sonar beam to be steered. Speed of sound in water = approx 1500 ms^-1

Find the maximum frequency that may be used if only one diffraction order is ever to present as the beam is scanned from -90 to 90 degrees.


Homework Equations





The Attempt at a Solution


i have this equation but don't know where it comes from:

dsin(theta) + delta x wavelength/2pi = n x wavelength (1)

where d = spacing between transducers, delta = phase and n is the order

I can use this to find the frequency but don't understand what this equation means or is saying and where it comes from?
 
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I've looked online but didn't find a simple introductory explanation. Does the text for your course not cover this?
 
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