Answer:
(a) Speed of train is 7.66 m/s and it is traveling away from the bicycle.
(b) Frequency heard by the stationary observer is 821.50 Hz.
Explanation:
Doppler effect is defines as the change in the frequency of the wave as the observer and/or source are moving away or towards each other.
(a) According to the problem,
Speed of the observer, v₀ = 18 m/s
Speed of sound in air, v = 340 m/s
Original frequency emitted by train, f = 840 Hz
Apparent frequency heard by the observer, f₀ = 778 Hz
Let v₁ be the speed of the train.
Since, apparent frequency is less than original frequency i.e. f₀ > f . Hence, train are travelling away from the bicycle.
Thus, the Doppler effect equation is :
[tex]f_{0} = (\frac{v - v_{0} }{v+v_{1} } )f[/tex]
Substitute the suitable values in the above equation.
[tex]778 = (\frac{340 -18 }{340+v_{1} } )840[/tex]
340 + v₁ = 347.66
v₁ = 7.66 m/s
(b) In this case, speed of observer, v₀ = 0 m/s
Apparent frequency, [tex]f_{0} = (\frac{v }{v+v_{1} } )f[/tex]
Substitute the suitable values in the above equation.
[tex]f_{0} = (\frac{340 }{340+7.66 } )840[/tex]
f₀ = 821.50 Hz
