Answer:
68.6 m/s
Explanation:
v = Speed of sound in air = 343 m/s
u = Speed of train
[tex]f_1[/tex] = Actual frequency
From the Doppler effect we have the observed frequency as
When the train is approaching
[tex]f=f_1\frac{v+u}{v}[/tex]
When the train is receeding
[tex]\frac{2f}{3}=f_1\frac{v-u}{v}[/tex]
Dividing the above equations we have
[tex]\frac{f}{\frac{2f}{3}}=\frac{f_1\frac{v+u}{v}}{f_1\frac{v-u}{v}}\\\Rightarrow \frac{3}{2}=\frac{v+u}{v-u}\\\Rightarrow 3v-3u=2v+2u\\\Rightarrow v=5u\\\Rightarrow u=\frac{v}{5}\\\Rightarrow u=\frac{343}{5}\\\Rightarrow u=68.6\ m/s[/tex]
The speed of the train is 68.6 m/s
