A band playing music at a frequency f is moving towards a wall at a speed v b . A motorist is following the band with a speed v m . If v is the speed of sound, the expression for the beat frequency heard by the motorist is

Step-by-step solution

The motorist receives two sound waves, direct one from the band and that reflected from the wall, figure. For direct sound waves, apparent frequency f ′ = ( v + v m ) f v + v b For reflected sound waves. Frequency of sound wave reflected from the wall f ′ ′ = v × f v - v b Frequency of reflected waves as received by the moving motorist, f ′ = v + v m f ′ ′ v = ( v + v m ) f v - v b ∴ Beat frequency = f ′ ′ - f ′ = ( v + v m ) f v - v b - ( v + v m ) f v + v b = 2 v b ( v + v m ) f v 2 - v b 2