Three equal-amplitude sound sources start in phase and have frequencies f-Δf, f and f+Δf. Which expression correctly gives the resultant displacement?
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Question

Three equal-amplitude sound sources start in phase and have frequencies f−Δf, f and f+Δf. Which expression correctly gives the resultant displacement?

G1 Physics · Accepted Answer

Write the three waves as Acos[2π(f−Δf)t], Acos(2πft), Acos[2π(f+Δf)t]. Add the first and third waves: cos[2π(f−Δf)t] + cos[2π(f+Δf)t] = 2cos(2πΔf t)cos(2πft). Now add the middle wave: y = A[1+2cos(2πΔf t)]cos(2πft). Correct option: A.