Final answer:
The lowest two frequencies that produce a maximum sound intensity at the positions of Moe and Curly can be found by considering the interference of sound waves. Using the equation mΛ = d sin(θ), where m is an integer, Λ is the wavelength, d is the distance between the speakers, and θ is the angle at which the maximum intensity occurs, we can solve for the frequencies that produce the maximum sound intensity.
Step-by-step explanation:
The lowest two frequencies that produce a maximum sound intensity at the positions of Moe and Curly can be found by considering the interference of sound waves. When two waves interfere constructively, they produce maximum intensity. In this case, the interference occurs between two speakers that are a distance of d apart. The maximum intensity occurs at positions where the path difference between the waves is an integer multiple of the wavelength. This can be represented by the equation: mΛ = d sin(θ), where m is an integer representing the number of nodes (maxima), Λ is the wavelength, d is the distance between the speakers, and θ is the angle at which the maximum intensity occurs.
To find the lowest two frequencies, we can use the equation v = fΛ, where v is the speed of sound and f is the frequency. Rearranging the equation to solve for Λ, we have Λ = v/f. Plugging this into the previous equation, we get m(v/f) = d sin(θ). We can solve for θ by taking the inverse sine of both sides: θ = sin^(-1)(mfv/d).
Since we are looking for the lowest two frequencies that produce maximum intensity, we can start by considering the first two nodes (m=1 and m=2). For m=1, θ = sin^(-1)(vf/d) and for m=2, θ = sin^(-1)(2vf/d). To find the frequencies, we can substitute the given values for v and d into the equations and solve for f, which gives us the lowest two frequencies.