Question

A couple in love, after a long time apart, finally are able to meet for a weekend. They each arrive at the train station riding on different trains. Both trains approach the station coming from opposite directions, and at different speeds. Not able to contain their excitment, they both stick their heads out of their windows and the man starts singing loudly "their song", as the train continues to approach each other. at the moment when he is singing a 440Hz note, what frequency does she hear?

Answer 1

The question deals with the Doppler effect, which affects the frequency observed by a stationary person as a sound source moves towards or away from them. For the stationary person, the observed frequency will be higher when the source approaches and lower when it recedes. The moving observer, such as the train's engineer, hears the actual frequency as they are moving with the sound source.

Step-by-step explanation:

The question at hand pertains to the Doppler effect, which describes the change in frequency or wavelength of a wave in relation to an observer who is moving relative to the wave source. The frequency heard by one train passenger when the other is singing at 440Hz involves understanding this principle.

(a) A stationary person at the side of the tracks would observe a higher frequency as the train approaches due to the compression of sound waves, and a lower frequency as the train recedes because of the stretching out of these waves. (b) The train's engineer, who is moving with the source of the sound (the horn), would hear the actual frequency of the sound, which is not affected by the Doppler effect in this scenario.

For example, regarding the question about the frequency heard by someone as a horn being blown at 200Hz approaches, we can calculate the train's speed if a stationary observer hears 208Hz: the speed of sound is given at 335 m/s, and applying the Doppler effect formula helps us determine the speed of the train.