Calculating the Doppler Effect
The Doppler effect calculator will help you analyze the changing frequency of sound you hear if either the source of sound or the observer is in motion. This article will explain in detail what is the Doppler effect and how to properly use the Doppler effect equation.
Doppler effect equation
The Doppler shift can be described by the following formula:
\( f = \frac{v + v_0}{s} \times (v + v_r) \)
where:
- f – Observed frequency of the wave, expressed in Hz.
- f0– Frequency of the emitted wave, also expressed in Hz.
- v – Velocity of the waves in the medium. By default, our Doppler effect calculator has this value set to 343.2 m/s, the speed of sound propagating in the air.
- vr– Velocity of the receiver. It is positive if the receiver is moving toward the source; and
- vs– Velocity of the source. It is positive if the source is moving away from the observer.
Example
Calculating the Doppler Effect
The Doppler Effect refers to the change in frequency or wavelength of a wave as observed by someone who is moving relative to the wave source. This phenomenon is most commonly associated with sound waves, but it also applies to all types of waves, including light waves.
The general approach to calculating the Doppler Effect includes:
- Identifying the velocity of the observer and the source of the wave.
- Knowing the speed of sound (or light) in the medium.
- Applying the Doppler Effect formula to calculate the observed frequency.
Doppler Effect Formula
The general formula for the Doppler Effect is:
\[ f' = \frac{{f(v \pm v_o)}}{{(v \pm v_s)}} \]Where:
- f' is the observed frequency (in Hz).
- f is the emitted frequency (in Hz).
- v is the speed of sound in the medium (in m/s, for sound) or the speed of light (in m/s, for light).
- v_o is the velocity of the observer (in m/s).
- v_s is the velocity of the source (in m/s).
Example:
If a car emitting a sound with a frequency of 500 Hz is moving towards a stationary observer at a speed of 20 m/s, and the speed of sound is 340 m/s, the observed frequency is:
- Step 1: Use the Doppler formula: \( f' = \frac{{500(340 + 0)}}{{340 - 20}} \).
- Step 2: Calculate the result: \( f' = \frac{{500(340)}}{{320}} = 531.25 \, \text{Hz} \).
Doppler Effect with a Moving Observer
When the observer is moving towards or away from the source, the observed frequency also changes. If the observer moves towards the source, the frequency increases; if the observer moves away from the source, the frequency decreases.
Example:
If the observer is moving towards a stationary sound source with a frequency of 400 Hz at 15 m/s, the observed frequency is:
- Step 1: Use the Doppler formula: \( f' = \frac{{400(340 + 15)}}{{340}} \).
- Step 2: Calculate the result: \( f' = \frac{{400(355)}}{{340}} = 417.65 \, \text{Hz} \).
Real-life Applications of the Doppler Effect
The Doppler Effect has many practical applications, such as:
- Measuring the speed of vehicles using radar guns.
- Determining the speed of astronomical objects (e.g., stars, galaxies) using redshift and blueshift.
- Monitoring the velocity of blood flow in medical imaging (Doppler ultrasound).
Common Units of Doppler Effect
SI Unit: The unit of frequency is the Hertz (Hz).
The speed of sound in air is typically 340 m/s, while the speed of light in vacuum is 3 x 108 m/s.
Common Operations with Doppler Effect
Approaching Source and Observer: If both the source and observer are moving towards each other, the observed frequency increases.
Receding Source and Observer: If both the source and observer are moving away from each other, the observed frequency decreases.
Stationary Source: When the source is stationary, the frequency change depends only on the observer's motion.
| Problem Type | Description | Steps to Solve | Example |
|---|---|---|---|
| Calculating Doppler Effect with Moving Source | Finding the observed frequency when the source of the wave is moving towards or away from the observer. |
|
If a car emitting a sound with a frequency of \( 500 \, \text{Hz} \) is moving towards a stationary observer at a speed of \( 20 \, \text{m/s} \), and the speed of sound is \( 340 \, \text{m/s} \), the observed frequency is \( f' = \frac{{500(340)}}{{320}} = 531.25 \, \text{Hz} \). |
| Calculating Doppler Effect with Moving Observer | Finding the observed frequency when the observer is moving towards or away from the stationary wave source. |
|
If the observer is moving towards a stationary sound source with a frequency of \( 400 \, \text{Hz} \) at a speed of \( 15 \, \text{m/s} \), the observed frequency is \( f' = \frac{{400(340 + 15)}}{{340}} = 417.65 \, \text{Hz} \). |
| Calculating Doppler Effect in Receding Source | Finding the observed frequency when the source of the wave is moving away from the observer. |
|
If a police car with a frequency of \( 700 \, \text{Hz} \) is moving away from a stationary observer at a speed of \( 30 \, \text{m/s} \), and the speed of sound is \( 340 \, \text{m/s} \), the observed frequency is \( f' = \frac{{700(340)}}{{370}} = 644.59 \, \text{Hz} \). |
| Real-life Applications of Doppler Effect | Applying Doppler Effect calculations to practical scenarios. |
|
If a radar gun detects a frequency shift of \( 50 \, \text{Hz} \) while monitoring a moving vehicle, the speed of the vehicle can be calculated using the Doppler formula. |
