Doppler shift formula – Electricity

Explore the Doppler Shift formula, its physics, applications, and an example calculation for sound waves in motion.

Doppler Shift Formula: Exploring the Physics of Moving Sound and Light

The Doppler Shift formula is a fundamental equation in the realm of physics that explains the change in frequency and wavelength of a wave as observed by an observer moving relative to the source of the wave. This phenomenon is commonly experienced with sound waves, such as the change in pitch of a moving vehicle’s siren, but also applies to light waves, which leads to the concepts of redshift and blueshift in astronomy.

Understanding the Doppler Shift

The Doppler Shift occurs when a source of waves (either sound or light) and an observer are in relative motion. The observed frequency (f_obs) differs from the emitted frequency (f_source) due to the relative motion between the observer and the source. The Doppler Shift formula enables us to calculate this observed frequency.

Deriving the Doppler Shift Formula

Two main Doppler Shift equations exist, one for sound waves and another for electromagnetic waves, such as light. However, the principles behind both formulas are similar, as they describe the relationship between the source and observer’s relative velocities, the speed of the waves in their respective media, and the observed and emitted frequencies.

Sound Waves

For sound waves, the Doppler Shift formula is given by:

f_obs = f_source * (v_sound ± v_observer) / (v_sound ± v_source)

Here, f_obs is the observed frequency, f_source is the emitted frequency, v_sound is the speed of sound in the medium, v_observer is the observer’s velocity relative to the medium, and v_source is the source’s velocity relative to the medium. The choice of the plus or minus signs depends on the direction of motion of the observer and source.

Light Waves

For light waves, the Doppler Shift formula is expressed in terms of wavelengths and is given by:

λ_obs = λ_source * (1 + (v_relative / c))

Where λ_obs is the observed wavelength, λ_source is the emitted wavelength, v_relative is the relative velocity between the observer and the source, and c is the speed of light. In this case, a positive v_relative signifies the source is moving away from the observer (redshift), while a negative value indicates that the source is moving towards the observer (blueshift).

Applications of the Doppler Shift Formula

Measuring the speed of a moving vehicle using radar guns.
Determining the flow of blood through arteries and veins using Doppler ultrasound.
Estimating the velocities of stars and galaxies in astronomy.
Weather forecasting using Doppler radar to measure wind speeds and precipitation.

In conclusion, the Doppler Shift formula offers valuable insights into the behavior of waves when there is relative motion between the source and the observer.

Example of Doppler Shift Calculation

Let’s consider an example of Doppler Shift using sound waves. Suppose an ambulance is approaching an observer with a siren emitting a frequency of 700 Hz. The ambulance is moving at a speed of 20 m/s towards the observer, and the observer is stationary. The speed of sound in the air is approximately 340 m/s. We will use the Doppler Shift formula for sound waves to calculate the observed frequency:

f_obs = f_source * (v_sound ± v_observer) / (v_sound ± v_source)

Since the observer is stationary, v_observer = 0, and since the source is moving towards the observer, we will use the minus sign in the denominator:

f_obs = (700 Hz) * (340 m/s) / (340 m/s – 20 m/s)

By calculating, we find:

f_obs ≈ 786.5 Hz

So, the frequency observed by the stationary observer as the ambulance approaches is approximately 786.5 Hz, which is higher than the emitted frequency of 700 Hz. This increase in frequency is consistent with the Doppler Shift phenomenon, as the source and observer are moving closer together.