# How can the amplitude of the same acoustic wave be different in a interferometer?

I came up with an exercise on Halliday Resnick Krane that asked a question which consfuses me. I premit that I do not look for a solution of the exercise but for suggestions only regarding the highlighted part.

Consider the acoustic interferometer in the picture. The lenght SAD is fixed, while SBD can be changed. A sound is produced in S and detected in D. We know that for a certain position of B a minimum of intensity of $10\mu W/cm^2$ is detected in D, and if we move B of a quantity $\Delta s=1.65m$ a maximum on intensity of $90\mu W/cm^2$ is detected in D. Find the amplitudes of the waves that arrives in D. How can you explain that these aplitudes are different even if the waves were generated by the same source?

Indeed I find that $\frac{A_1}{A_2}=2$.

Is it correct to say that the differce in amplitude of the two single waves generated by the same source is due to the fact that the wave-fronts are (even if it is not specified in the text) spherical, hence $A\propto \frac{1}{r}$? Therefore a longer path covered implies a smaller amplitude?