Question

A sound wave travels with a velocity of 300 m `s^(-1)` through a gas. 9 beats are produced in 3 s when two waves pass through it simultaneously. lf one of the waves has 2 m wavelength, the wavelength of the other wave is
A. 1.98 m
B. 2.04 m
C. 2.06 m
D. 1.99 m

Answer 1

Correct Answer - B
No. of beats per second=`9/3=3s^(-1)`
No. of beats per second=`upsilon_(1)-upsilon_(2)`
`3=v/(lamda_(1))-v/(lamda_2)=v[1/lamda_(1)-1/lamda_(2)]`
`3/300=1/2-1/lamda_(2)`
`1/lamda_(2)=1/2-1/lamda_(2)`
`1/lamda_(2)=1/2-1/100=(50-1)/100=49/100`
`lamda_(2)=100/49=2.04m`