The frequency heard by the traveller waiting at the station is 0 Hz. The frequency heard by the traveller at the station when the second train is approaching is -127 Hz. The dominant frequency heard by the traveller when both trains blare their horns simultaneously is -127 Hz.
Step-by-step explanation:
To solve this problem, we need to use the formula for the Doppler effect. The formula for the observed frequency of a moving source is given by:
fobs = fs * (vt + vs) / (vt - vs)
where fobs is the observed frequency, fs is the source frequency, vt is the speed of the traveller, and vs is the speed of sound.
(a) For the first part of the question, the observer is at rest, so vt is 0. Plugging in the values, we get:
fobs = 278 * 0 / (0-327) = 0
Therefore, the frequency heard by the traveller waiting at the station is 0.
(b) For the second part of the question, the observer is stationary and the second train is moving towards the station, so the speed of the second train is negative. Plugging in the values, we get:
fobs = 278 * (38+0) / (38-327) = -127 Hz
Therefore, the frequency heard by the traveller at the station when the second train is approaching is -127 Hz.
(c) For the last part of the question, if both trains blare their horns simultaneously, the dominant frequency heard by the traveller will be the sum of the frequencies, which is 0 + (-127) = -127 Hz.