More Doppler Effect problems... please help!!!?

Question

1.) Two automobiles are equipped with the same single-frequency horn. When one is at rest and the other is moving toward an observer at 15 m/s, a beat frequency of 5.0 Hz is heard. What is the frequency the horns emit? Assume T = 20°C.

2.) Two trains emit whistles of the same frequency, 275 Hz. If one train is at rest and the other is traveling at 45 km/h away from an observer at rest, what beat frequency will the observer detect?

I have been trying to do these problems for quite a long time already, but I just can't seem to get it. Can someone please help?! Thanks.

Answer 1

(1)
f '=[V/(V +/- Vs)]f

f- Transmitted frequency
V - Speed of waves in the medium (in air at T degrees Celsius, this is 332 + 0.59T m/s)
Vs - Velocity of the source (the thing emitting the sound)

V=V(speed of sound in air) = 331.3 sqrt(1 + t/273.15)

t- temperature in deg. C.
so at 20C V=331.3 sqrt(1 + 20/273.15)= 343.2 m/s

f(emitted)=f(heard)[V + Vs]/V (+ is used since the sound travels in the same direction as the source.

f(emitted)=5 [343.2 + 15.0]/ 343.2]= 5.22 Hz

(2)
Train at rest no observed change in frequency
Train at in motion away from the observer the frequency heard is

f '=[V/(V - Vs)]f=
f’=[343.2/(343.2 – 45 x 3600/1000)] 275 = 520.9 Hz

I hope it helps