Doppler Effect

Whenever a train waiting on the station, it blows its whistle, but listeners nearby notice nothing unusual. Although here what happens is that there’s an increase in the degree of intensity—between the sound heard by someone on the platform, and the sound of the train as heard by someone standing behind the main engine. Why does this happen? This happens because of Doppler Effect. What is it? Let us study more about it in-depth to ensure that you have a better clarity on the subject.

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We are surrounded by scientific events that occur every minute, every second. Do you actually try to put a question in your mind after hearing different sounds in your vicinity? Ever noticed when sounds transform their pitch while travelling close by? Supposedly, you are sitting near a stoplight, managing your work and suddenly you hear the sound of an ambulance.

At this moment, the siren screams a high pitch almost half a mile from the nearby road. Now, you wait for the approaching vehicle as the ambulance rushes through the crossing. As it passes, one can note that the siren sound is now different. Here, it has a lower pitch as compared to what it was before. The question is, why did the siren sound change?

In order to decode this mystery, one must get familiar with the concept of Doppler Effect. Through this, we can gain an explanation on how people observe variations in sound when the prime sound source is moving. Although the ambulance siren didn’t change pitch, it does transform as the vehicle rushes past us.

Apparent Vs Actual Frequency

When we discuss details about how a spectator recognizes waves, it is crucial to learn about apparent and actual frequencies.

• Talking about actual frequency, it is the true frequency, irrespective of any external factor. Under this, the position of the observer doesn’t disturb the actual wave frequency.
• Apparent frequency is termed as that frequency which is processed by an external observer. There are chances that it might or might not be similar to the actual frequency.

Based on this concept, we can say that the apparent downward or upward change in frequency as a result of movement of wave source is called as Doppler Effect. 

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Calculation of Doppler Effect in Sound

Let us try to understand the proper formulation and terms to logically define Doppler Effect. Let us assume the motion is leaning in a line lying between source S and listener L. Here the track from the listener towards the source is taken as the positive direction. Further, velocities v_S and v_L are the velocities concerned with the source and listener relative to air or wave medium. Also, the speed of the sound wave (v), is at all times measured positive.

Once we apply these motions (leaving aside all the chaotic derivations), we receive the frequency which is heard by f_L or listener, in the form of f_S or frequency of the source:

f_L = [(v + v_L)/(v + v_S)] f_S

In case, the listener stays stationery, then v_L = 0. In case, the source stays stationery, then v_S = 0.

• Hence, if neither the listener nor the source is moving, in this situation f_L = f_S.
• Suppose the listener starts to walk toward the source, here v_L > 0, however, if it starts to move different from the source, at that point v_L < 0.
• Consecutively, if the movement of the source is towards the listener and motion is measured in the negative direction, then v_S < 0. However, if the source travels away from the listener, here v_S > 0.

Doppler Effect Types

There are two basic Doppler Effect versions. So, let us now learn about these two basic Doppler Effect versions which are also necessary to be understood by you.

Symmetrical

Under this, the Doppler shift stays similar when the light source travels towards or away from a resting observer. In the other case, the spectator travels with the same velocity either towards or away from the resting stationary.

Asymmetrical

It is believed that apparent shift in frequency is altered when the sound source travels towards or away from the resting observer. This effect can be further observed when the observer travels with similar speed towards or away from the resting source.

Solved Example For You

Question: Suppose a bus is heading towards Sean at 1.5 × 108 m/s. If the bus flashes the headlight on Sean at a frequency of 4200 Hz. What is the frequency of light Sean with receive?

Solution: Given that, the observer velocity (v) = c, source velocity (v_s) = 1.5 × 108 m/s; that is 0.5 c, & the frequency (ν) = 4200 Hz

The light frequency received by Sean is:

ν’ = ν/(1 ± v_s/v)

ν’ = 4200/1 – 0.5 c/ c; ν’ = 2100 Hz. (Answer)

Hence, the light frequency that Sean obtains is 2100 Hz.