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J. Perelman
"Entertaining physics". Book 2.
Chapter 10. Sound. Wave motion

THE PROBLEM OF LOCOMOTIVE WHISTLES

If you have developed a musical ear, I noticed, probably, the change of tone (not the volume, namely tone, height) of a locomotive whistle, when oncoming train comes past your. While both trains were closer together, the tone was markedly higher than that which can hear you when trains are removed from each other. If trains go from a speed of 50 km per hour, the difference in pitch is almost a whole tone.

Why is this happening?

It shouldn't be hard to guess about the cause, if you will remember that pitch depends on the number of vibrations per second; compare it with what you learned in the discussion of the previous task. The whistle of an oncoming locomotive all the time emits the same sound with a specific frequency. But your ear perceives a different number of oscillations depending on whether you go forward, whether you stand in place or removed from the vibration source.

And like on the way to Moscow you read a daily newspaper more than once a day, and here, closer to the sound source, you catch fluctuations more often than they come from the whistle of the locomotive. But here you won't talk your ear gets increased the number of oscillations, and you immediately hear a higher tone. Away, you get fewer vibrations and hear a lower tone.

If this explanation is not entirely convinced you, you can try to directly trace (of course, mentally) how are propagated sound wave from the whistle of the locomotive. Consider first the stationary steam engine.


The problem of locomotive whistles. Above, the sound waves emitted by a stationary steam engine at the bottom moving.

Whistle produces air waves, and we will consider for simplicity only four waves (see upper wavy line): from a stationary locomotive they have time to spread some period of time for the same distance in all directions. Wave # 0 will reach the observer And the same time, as well as to the observer; then to both observers at the same time get to wave No. 1, No. 2, then No. 3, and so on, the Ears of the two observers per second have the same number of shocks, and therefore both will hear the same tone.

Another thing, if whistling locomotive moves from b to A (lower wavy line). Let at some point the whistle is at point C', and for the time when he gave up four waves, he managed to reach point D.

Now compare how you will spread the sound waves. Wave No. 0 issued from point C', comes simultaneously to both observers And' and'. But the fourth wave generated at the point D, will reach them are not simultaneously; the path of DA' less DB path', and hence As' it will come earlier than In'. Intermediate wave - No. 1 and No. 2 will also come in' later than', but the delay will be less. What would it be? The observer at point a' will be more likely to perceive sound waves, rather than the observer at point b': first you will hear a higher pitch than the second. However, it can easily be seen from the drawing, the length of the waves traveling in the direction of the point a'will be correspondingly shorter waves coming In' *.

* It must be borne in mind that the wavy lines in the picture does not depict the form of sound waves: the oscillation of particles in the air occurs along the direction of the sound, not across. Waves cross pictured here only for the sake of clarity, and the hump of this wavelength corresponds to the highest compression in a longitudinal sound wave.

Entertaining physics J. Perelman

 




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