Doppler Effect Calculator

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When you stand at a train platform while a train speeds by, have you ever noticed how the sound of the train changes as it passes? It seems as if the pitch of the train’s sound changes as it moves closer to you and then changes once more as it moves further away. This is the called the Doppler effect. It’s a physics concept that applies to sound, light, or other waves. However, more often than not, it is easier to perceive the Doppler effect through sound.

Understanding Wavelengths

Sounds carry a frequency and wavelength that we perceive through its pitch. Certain sounds like that of a whistle have a high pitch while sounds from foghorns have a low pitch. With the Doppler effect, you can perceive a change in the pitch of a sound when its source moves. As an object making a sound approaches you (like a train), its pitch rises as the volume of the sound it makes increases. However, as the train moves further away from you, the pitch of the sound lowers as the volume of its sound decreases. You can easily perceive this change in frequency.

Doppler’s hypothesis states that if a source of sound waves moves relative to the one perceiving it, the frequency of the waves it emits changes along with its wavelength.

The next time you find yourself on a busy street, try to perceive the changes in pitch and frequency of loud objects that pass you by. This is one of the easiest ways to experience the Doppler effect.

Calculating the Doppler Effect

You can calculate the Doppler effect through the use of the Doppler Effect Calculator. This calculator helps you determine the difference between the frequency emitted by an object and what the perceiver observes. The Doppler Effect Calculator uses the following formula:

Observed Frequency = Frequency of the Emitted Wave * (Velocity of the Waves in the Medium + Velocity of the Receiver) / (Velocity of the Waves in the Medium + Velocity of the Source)

For the calculator, the Velocity of the Waves in the Medium is set to 343.2 m/s as a default. This is the speed of sound propagating in the air. For the Velocity of the Receiver, the value is positive if the receiver is moving towards the source. Likewise, for the Velocity of the Source, the value is positive if the source is moving away from the receiver.

Sample Problem for Calculating the Doppler Effect

Let’s say you are standing stationary in a park. A biker speeds closer to you at a velocity of 2 m/s as he rings his bell at a frequency of 60 Hz. This is how we can compute for the Doppler effect:

Observed Frequency = 60 Hz * (343.2 m/s + 0 m/s) / (343.2 m/s + 2 m/s)
                                         = 60 Hz * (343.2 m/s / 345.2 m/s)
                                         = 60 Hz * 0.9942 m/s
                                         = 59.6524 Hz

This indicates that the true frequency of the biker’s bell is 60 Hz, but as he speeds towards you, you only perceive the frequency to be 59.6524 Hz.

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