A source of sound produces wave of 60 cm wavelength. This source is moving towards north with a speed one-fifth the sound speed. Find the apparent wavelength of the waves in the north and south directions.

Options

A. 72 cm and 48 cm
B. 48 cm and 72 cm
C. 82 cm and 52 cm
D. none of these

Answer

B

Explanation

When the source moves towards the north, the observer in the north will observe higher frequency i.e. lower wavelength.
`lambda . = lambda ((v_("sound") - v_("source") )) /( v_("sound") ) `
`rArr lambda. = (60 xx (4)/(5) v_("sound") ) /( v_("sound") ) ("Given" v_("source") = (1)/(5) v_("sound") )`
`rArr lambda . = 48" cm"`
The observer situated in the south will observe
`lambda_("south") = lambda((v_("sound") + v_("source") ))/( v_("sound" ) )= lambda (6/5 v_("sound") )/( v_("sound") ) = (60 xx 6)/(5)`
`rArr lambda_("south") = 72` cm
The wavelengths observed in the north and south are 48 cm and 72 cm.