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Francis is standing at a railway crossing. A train sounds its horn as it moves toward him at a speed of 45 km/hr. If the train conductor hears the horn at 287 Hz, what frequency (in Hz) does Francis hear?

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onyebuchinnaji

The frequency observed by Francis when the train approaches is 297.4 Hz.

Doppler effect

The frequency observed by Francis is determined by applying the principle of Doppler effect.

The frequency observed by Francis is calculated as follows;

[tex]f = f_o(\frac{V}{V \pm V_s} )[/tex]

where;

  • f is the source frequency
  • fâ‚€ is the observed frequency
  • Vs velocity of the source when it is moving towards the observer
  • V is velocity of sound

45 km/h = 12.5 m/s

Speed of sound in air = 343 m/s

Since the train is moving towards the observer, the frequency heard by the observer will be greater than the source frequency, thus we will choose positive sign for the source velocity.

[tex]f = f_o(\frac{V}{V + V_s} )\\\\287 = f_0 (\frac{343}{343+ 12.5)} )\\\\287 = 0.965f_0\\\\f_0 = \frac{287}{0.965} \\\\f_0 = 297.4 \ Hz[/tex]

Thus, the frequency observed by Francis when the train approaches is 297.4 Hz.

Learn more about Doppler effect here: https://brainly.com/question/3841958