Question

Two Train Whistles from trains A and B have the same frequency of 180hz......

at rent standing nearby. between thea when the On the station ble apeeda ons that the .oving train ean take relative to you? E) 2 No stand

Answers should be 3.79m/s and 3.88m/s

Thanks in advance

Answer 1

The beat frequency equals the absolute value of the difference between the two source frequency, or :

f(b) = |f₂ - f₁|

This allows for two different frequencies, one for approach and one for recession. The approach frequency is :

2.00Hz = |180Hz - f₁|
2.00Hz = f₁- 180Hz
f₁= 182Hz

The recession frequency is :

2.00Hz = |180Hz - f₁|
2.00Hz = 180Hz - f₁
f₁= 178Hz

Now, from the Doppler shift equation, the approach velocity is :

f₀ = f(s)[v / v + v(s)]
v(s) = v[f₀ - f(s)] / f₀
= 345m/s[178Hz – 180Hz] / 180Hz
= 3.79m/s

The velocity of recession is (from the same equation) :

v(s) = 345m/s[178Hz - 180Hz] / 178Hz
= -3.88m/s