In a large room, a person receives direct sound waves from a source 120 metres away from him. He also receives waves from the same source which reach him, being reflected from the 25 metre high ceiling at a point halfway between them. The two waves interfere constructively for wavelength of

Let S be source of sound and P the person or listner.The waves from S reach point P directly following the path SMP and being reflected from the ceiling at point A following the path  SAP.  M is mid-point of  SP (i.e. SM = MP) and ∠ SMA=90o Path difference between waves Δx=SAP−SMP We have  SAP=SA+AP=2(SA) =2[(SM)2+(MA)2]=2(602+252)=130m∴Path difference = SAP – SMP = 130 -120 = 10 mPath difference due to reflection from ceiling = λ2∴Effective path difference Δx=10+λ2For constructive interference Δx=10+λ2=nλ⇒(2n−1)λ2=10(n=1,  2,  3....)∴Wavelength λ=2×10(2n−1)=202n−1. The possible wavelength are λ=20,  203,  205 ,  207 ,  209 ,  …..= 20 m, 6.67 m, 4 m, 2.85 m, 2.22 m, …..