Question

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

• A. 20, $\frac{20}{3}$, $\frac{20}{5}$, etc
• B. 10, 5, 2.5, etc
• C. 10, 20, 30, etc
• D. 15, 25, 35, etc

Answer 1

Answer: (A)

20, $\frac{20}{3}$, $\frac{20}{5}$, etc

Answer 2

Path difference between the waves

Dx = 130 – 120 = 10 m

As phase between the two waves in p, because reflection takes place from the rigid end, so for constructive

interference.

Dx = (2n + 1) $\frac { \lambda } { 2 }$

10 = (2n + 1) $\frac { \lambda } { 2 }$

\ l = $\frac { 20 } { 2 n + 1 }$ , n = 0, l₁ = 20m

n = 1, l₂ = $\frac { 20 } { 3 }$ m

n = 2, l₃ = $\frac { 20 } { 5 }$m