A road passes at some distance from a standing man. A truck is coming on the road with some acceleration. The truck driver blows a whistle of frequency 500 Hz when the line joining the truck and the man makes an angle θ with the road. The man hears a note having a frequency of 600 Hz when the truck is closest to him. Also the speed of truck has got doubled during this time. Find the value of 'θ'.
Text Solution
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(θ = 60º)
Let the truck velocity be v S
then, 600 = 
500...(i)
As 2v S = v S + at
v S = at ...(ii)
where 'a' is acceleration.
As vt = 
where v is velocity of sound.
Also, λ cot θ = v S t + 
at 2
= 
at 2 (from eqn (ii))
= 
a 
= 
...(iii)
∴ from (i)
= 
= 
Put 
from (iii)
∴ θ = 60º
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