# Doppler Effect

The Doppler Effect is when a wave, like sound or light, has a specific wavelength and frequency that are related. The energy that a wave carries is related to its frequency, with higher frequencies carrying more energy. If the wave source or the receiver is moving, the frequency/wavelength can change. This is known as the Doppler Effect.

## Doppler effect definition

The Doppler effect is the change in frequency of a wave when the source moves relative to the observer. However, the wave itself does not change its wavelength when measured in its own frame of reference. In sound, the Doppler effect causes a change in pitch, while in light it can cause a change in perceived color. We can experience the Doppler effect in everyday life with ambulance sirens. As an ambulance approaches, the pitch of the siren will increase because the waves are being compressed. Once it passes you, the pitch will decrease as the waves are stretched out. This effect can be explained by the movement of the ambulance towards, and then away from, the observer.

This apparent change only occurs in your frame of reference with respect to the moving ambulance.

## Doppler effect equation

To calculate the frequency of waves due to the Doppler effect, we need to know the frequency of the wave in its frame of reference (fs), the speed of the wave (v), the speed of the observer (vo), and the speed of the object emitting the waves (vs). The equation is:

f' = fs(v +/- vo) / (v +/- vs)

The frequency is measured in Hertz (Hz) and the speed in meters per second (m/s). The signs of the speeds depend on their relative orientation with respect to the wave.

For example, if an observer is moving towards an emitter, their speed will be positive. If the emitter moves towards the observer, their speed will be negative. In the case of an observer with a speed of 8000m/s moving towards an emitter with a speed of 500m/s and a frequency of 900Hz, what is the perceived frequency of the wave for the observer moving closer to the source?

We can use the Doppler effect equation to find out:

f' = 900(343 + 8000) / (343 - 500)

f' = 10,234.4 Hz

Therefore, the perceived frequency of the wave for the observer moving closer to the source is 10,234.4 Hz.

## What is the relativistic Doppler effect?

When moving at speeds close to the speed of light in a vacuum, two important effects will occur: length contraction and time dilation. These effects are a consequence of the theory of relativity, which states that physical laws apply equally to all inertial frames of reference, regardless of their relative motion.

In the case of length contraction, objects observed by a moving observer will appear shorter in the direction of motion than they would if the observer were at rest. This effect becomes more pronounced as the speed of the observer approaches the speed of light.

Time dilation, on the other hand, means that time appears to move slower for a moving observer than for one at rest. This effect has been observed in experiments with high-speed particles and has been confirmed to be accurate.

When an object is moving at relativistic speeds, the frequency of any wave it emits or receives will be different from what would be expected using classical formulas. To account for this, the Lorentz transformations can be used. These equations map coordinates and time of one system system moving at relative the.

The Lorentz transformations take into account the effects of length contraction and time dilation and are essential for accurately predicting the behavior of objects moving at high speeds.

In relativity, the coordinates of an object moving at a velocity v will change as time t increases. At speeds close to the speed of light, this change happens at the speed of light, and time also dilates. To account for these effects, the Lorentz transformations can be used to calculate the lengths and time as seen from one frame when knowing the values as seen from the other.

When an observer or emitter moves at speeds close to relativistic speeds, any wave emitted will present an extra deformation of its frequency due to the change in length and time. To calculate this effect, we use the relativistic Doppler effect equation:

fobs = fs / (1 ± v/c)

Here, fobs is the observed frequency, fs is the source frequency, c is the speed of light in a vacuum, and v is the observed speed. The sign in the equation depends on whether the observer is moving towards or away from the source.

These equations are essential for accurately predicting the behavior of waves emitted or received by objects moving at high speeds, and they have been confirmed by numerous experiments in particle physics and astrophysics.

## Doppler effect in light

Sure, I can that we can calculate the observed frequency as:

fobs = fs * (c ± v) / c

where fs is the source frequency (2.06 PHz), c is the speed of light (3 x 10^8 m/s) and v is the observer's velocity (0.8c).

Converting the velocity to meters per second, we get:

v = 0.8c = 0.8 * 3 x 10^8 = 2.4 x 10^8 m/s

Plugging in the values, we get:

fobs = 2.06 x 10^15 * (3 x 10^8 + 2.4 x 10^8) / 3 x 10^8 = 2.57 x 10^15 Hz

Using the relativistic Doppler effect equation, we get:

fobs = fs / (γ(1 ± v/c))

where γ is the Lorentz factor given by γ = 1 / sqrt(1 - v^2/c^2).

Calculating γ, we get:

γ = 1 / sqrt(1 - v^2/c^2) = 1.67

Plugging in the values, we get:

fobs = 2.06 x 10^15 / (1.67(1 ± 0.8)) = 1.93 x 10^15 Hz

The observed frequency using the classical equation is 2.57 x 10^15 Hz, while the observed frequency using the relativistic equation is 1.93 x 10^15 Hz. The difference between the two is about 25%.

It's important to note that the relativistic approach is necessary for accurate predictions when dealing with objects moving at high speeds, as the classical approach fails to account for the effects of length contraction and time dilation.

### Hubble findings

The Doppler effect is a key phenomenon in understanding the redshift observed Edwin Hubble. The Doppler effect creates an apparent shift (Doppler shift) in the observed frequency of a wave. When the source and observer approach, there is a shift towards higher frequencies (shorter wavelengths), and when they move away, the opposite effect occurs.

When objects move at relativistic speeds (close to the speed of light), the frequency shift still exists, but it acquires a different mathematical form. This is because of the contraction of length and dilatation of time that appears when traveling at relativistic speeds.

Edwin Hubble's observations of the redshift in faraway galaxies revealed that galaxies are moving away from each other, and the universe is expanding. This was a significant discovery that helped us to understand the history and evolution of the universe.

## Doppler Effect

**What is the Doppler effect? **

The Doppler effect is the perceived change in frequency of a wave due to therelative movement of the emitter and the observer. **How do you calculate the Doppler effect? **

To calculate the Doppler effect, you can use the formula: f=fs(v+ vo)/(v+vs)and use the appropriate signs depending on the relative orientation of thespeeds. **When does the Doppler effect occur? **

The Doppler effect occurs when there is a relative movement between theobserver and the emitter of waves. **How does the Doppler effect work? **

When a wave is emitted, like a sound wave or a light wave, it has an associatedwavelength and frequency, which are inversely related. The frequency (or thewavelength) is related to the energy a wave carries. The higher the frequency(the shorter the wavelength), the higher the energy. If the source of the waveor whoever is receiving the wave is moving, the measured frequency/wavelengthwill change. This is known as the Doppler effect. The Doppler effect is themeasured change in the frequency of a wave when the source that emits the wavemoves relative to the observer.