A band playing music at a frequency n is moving towards a wall at a speed vb . 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

The motorist receives two sounds : direct one and that reflected from the wall'  For direct sound,n′=v+vmv+vbn For reflected sound, the reflected frequency of sound will be n′′=VV−vbn This frequency is received by the moving motorist. The apparent frequency received by him is given by n′′′=v+vmvn′′ =v+vmvvv−vbn=v+vmv−vbn ∴  Beat frequency =n"′−n′ =v+vmv−vbn−v+vmv+vbn =v+vm2vbv2−vb2n