# Doppler Effect Calculator

Created by Krishna Nelaturu
Last updated: Jun 28, 2022

If you need to calculate the Doppler shift in the observed frequency (also called the apparent frequency), use our Doppler effect calculator! Here you shall learn what is the Doppler effect and how to calculate the Doppler shift frequency using the Doppler shift formula.

## How to use this Doppler effect calcualtor

This Doppler effect calculator is a simple tool to determine the apparent frequency or observed frequency of a wave when its source or the receiver is in motion:

• Enter the emitted frequency value.
• Provide the value for the wave velocity in the medium. We've set it to 343.2 \text{ m/s} by default, the speed of sound, but feel free to enter a custom value. To calculate the speed of sound precisely, use our speed of sound calculator.
• Enter the values for the source velocity and the receiver velocity in their corresponding fields. The calculator will automatically determine the observed frequency using the Doppler effect equation.
• This Doppler effect calculator can work backward! If you have one unknown in the Doppler effect equation, enter the remaining values and find your solution easily!

While calculating the Doppler effect on sound in air, keep in mind that the speed of sound in air depends on many factors, including the humidity and . In the following sections, we shall explore the Doppler effect and how to calculate the Doppler shift frequency.

## What is Doppler effect?

Have you ever heard an ambulance speeding past you with its siren blaring? You must've noticed how the siren's pitch changed as the ambulance approached and went past you. The frequency of the sound you receive changes as the ambulance speeds past you.

When the source of the sound approaches you, every successive sound wave's crest is closer to you than the previous wave, thus changing the frequency and wavelength of the sound wave at your end. Similarly, when the sound source is moving away from you, each successive sound wave's crest is farther away from you than the previous wave. This phenomenon of a change (or shift) in the observed frequency is called the Doppler effect.

Doppler shift is not unique to sound waves; it affects all waves, depending on the motion of the source and receiver. We can calculate the change in the observed frequency using the Doppler effect equation.

## Doppler shift formula

The Doppler shift formula is given by:

$f = f_0 \frac{(v+v_r)}{(v+v_s)}$

Where:

• $f$ is the observed frequency or the apparent frequency;
• $f_0$ is the emitted wave frequency;
• $v$ is the velocity of the wave in the medium;
• $v_r$ is the velocity of the receiver relative to the medium, positive if it is moving towards the source; and
• $v_s$ is the velocity of the source relative to the medium, positive if it is moving away from the receiver.

If you must calculate the velocity of the source or receiver, use our velocity calculator.

## Example of how to calculate doppler shift frequency

Say you're waiting at a level crossing as a train approaches you blaring its horn. Let's calculate the Doppler effect on the observed frequency in this case:

• Assume the train is moving at $100 \text{ km/h}$ while you're at rest. Since the train is moving towards you, we shall consider its velocity negative. $v_s = -100 \text{ km/h} = -27.78 \text{ m/s}$.
• The sound frequency in the medium (air) is $440 \text{ Hz}$.

Combining this information with the speed of sound $v = 343.2 \text{ km/h}$, we can calculate the Doppler shift as:

\begin{align*} f &= 440 \times \frac{343.2}{(343.2- 27.78)}\\ f &= 478.75 \text{ Hz} \end{align*}

Now suppose the train is moving away from you at the same speed. In this case, we should take its velocity as positive. $v_s = 27.78 \text{ m/s}$:

\begin{align*} f &= 440 \times \frac{343.2}{(343.2+ 27.78)}\\ f &= 407.05 \text{ Hz} \end{align*}

This change in frequency is why the horn sounds different as the train speeds away from you.

To calculate how much the Doppler shift affects the wavelength, use our wavelength calculator.

Krishna Nelaturu
f = f₀(v + vr)/(v + vs)
Emitted frequency (f₀)
Hz
Wave velocity (v)
ft/s
ft/s
Source velocity (vs)
ft/s
Observed frequency (f)
Hz
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