Sound waves produced by two vibrators have the same wavelength in two different gases. The speed of the waves in the two gases are 420 m/s and 400 m/s. The vibrators, when sounded together produce 8 beats/second. The wavelength in the two gases will be

Options

A. 1.25 cm
B. 2 m
C. 2.5 m
D. 3m

Answer

C

Explanation

`(v_(1))/(v_(2)) = (n_(1)lamda)/(n_(2) lamda) :. (420)/(400) = (21)/(20) = (n_(1))/(n_(2))`
`:. n_(1) = (21)/(20) n_(2) and n_(1) - n_(2) = 8`
`:. (21)/(20) n_(2) = 8 " " :. n_(2) = 160Hz`
`:. lamda = (v_(2))/(n_(2)) = (400)/(160) = 2.5 m`