Period of the observer, we find that it will be equal to the wavelength of the source, divided by the speed of the wave, plus the speed of the observer. We can now pull out aĬommon factor of TOBS. If we add up the distance that we ran plus the distance that the next wave crest traveled to meet us, they have to equal one Not the observed wavelength but the actual source wavelength emitted by the speaker at rest. Now what do we do? We know that the distanceīetween crests is the actual wavelength of the wave, The speed of the wave VW times that same amount of time, which is the period you are observing. Next wave crest will travel in meeting you, will be We'll write the time as TOBSįor period of the observer. This time is just going toīe the period you observe since it'll be the time youĮxperience between wave crests. Travel in order to reach the next crest will be your speed times the time requiredįor you to get there. Let's say you're movingĪt a constant speed that we'll call VOBS, for If you can figure out how long it takes for the next crest to hit you, that would be the period that The speaker, or wave source, you don't have to waitĪs long since you'll meet the next wave crest somewhere in between. Would be the actual period of the wave emitted by the speaker. You'll just have to wait until another wave crest The time it takes untilĪnother wave crest hits you will be the period that you'll observe since that will be the time you observed between wave crests. What frequency you'll hear? To find out, let's zoom If you run away from the speaker, you'll hear a lower frequency because less wave crests You run toward the speaker? You'll hear a higher frequencyīecause more wave crests will strike you per second. If the speaker moves away from you, you'll hear a lower frequency. If the speaker moves toward you, you'll hear a higher frequency. Rate at which wave crests strike your location. That you'll observe when standing next to a speaker is determined by the Notice that both equations decrease the period or increase the frequency when he distance between the source and observer becomes less, however, the first does it by making the speed of sound "faster" and the other does it by making the speed of sound "slower". So Basically, The first equation can be interpreted as how much faster the sound emitted from the source reaches the observer compared to what the speed of sound allows whereas the second equation can be interpreted as how much the source has caught up with the speed of sound. When the source moves toward you it is still emitting a wave every 5 seconds but because the speed of sound is relatively constant and the moving source can not increase the speed of sound it causes an increase in frequency when moving toward you by "chasing" the previous wave emitted, effectively reducing the distance between each wave (wavelength) in front of it. Now think of the opposite for the equation | T-observed = T-source[(V-wave - V-source/V-wave) | where the source is moving toward you and you are standing still. Notice what this equation is saying: It is saying that you have allowed the sound (each wave) to reach you faster than what the speed (velocity) of sound would normally allow [the faster you move toward the source-larger denominator-you experience an increasingly smaller period (observed) of the original period (Source, 5). This will give you the equation | T-observed = T-source[V-wave/(V-wave + V-observer) |. the period Lets say you hear a constant tone for which the time between each wave is 5 seconds (5 seconds/Wave), now as you are moving toward the source you are effectively reducing the time with which you perceive each wave even though the source is still emitting a wave every 5 seconds. Now lets think in terms of time per wave (sec/Wave) I.E. Now if you are standing still the F(0) = F(S) (O = observed frequency S = source Frequency). The source emits a frequency of X or a period of 1/X. The best way to visualize what is happening is by doing the following:
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