Answer:
(a) 12.9m/s
(b) 193Hz
Step-by-step explanation:
The principle and concept of this question is based on Doppler's effect.
Doppler's effect is a change in the observed frequency of a wave when the source or the observer move relative to the transmitting medium. Doppler's effect can be expressed mathematically as;

Where,
f is given in terms of the sound frequency f₀
U is the speed of sound in the medium
U₀ is the speed of the observer
is the speed of the source
When applying Doppler's equation, the signs U₀ and
depend on the direction and velocity of of the observer and the source.
+ Positive sign, for U₀ and
if the velocity one is moving towards the other.
- Negative sign, for U₀ and
if the velocity one is moving away from the other.
Now, let's applying this information to the question given.
Given:
Frequency of the train's horn, f₀ = 200Hz
Speed of sound , U = 335m/s
Frequency of the approaching train's horn the observer received, f = 208Hz
Since the observer is waiting at the crossing, he/she is at a stationary position.
So, the speed of the observer, U₀ = 0
(a) The train approaches the observer. Following the sign rule, the speed of the source
is + positive. Applying this to the equation,


Solving for
,
= (\frac{U}{U - U_{s}})[/tex]









(b) The speed train approaches the observer. Following the sign rule, the speed of the source
is - negative. Applying this to the equation,





f = 193Hz