The Doppler effect explains the change in sound frequency as a result of the relative motion between a sound source and an observer. Here’s how it works:

Principle

The Doppler effect describes how sound waves are compressed or stretched depending on the movement of the source or the observer:

• Compressed Waves: When the source and observer are moving closer together, the sound waves get compressed, increasing the frequency (higher pitch).
• Stretched Waves: When the source and observer are moving apart, the sound waves stretch out, decreasing the frequency (lower pitch).

Key Scenarios

1. Source Moving Toward Observer:
   • The wavelength of the sound decreases.
   • Frequency increases, resulting in a higher-pitched sound.
   • Example: An ambulance siren sounds higher-pitched as it approaches.
2. Source Moving Away from Observer:
   • The wavelength of the sound increases.
   • Frequency decreases, resulting in a lower-pitched sound.
   • Example: The same ambulance siren sounds lower-pitched as it moves away.
3. Stationary Source and Moving Observer:
   • If the observer moves toward the stationary source, they encounter sound waves more frequently, increasing the perceived frequency.
   • If the observer moves away, they encounter sound waves less frequently, decreasing the perceived frequency.
4. Relative Motion in General:
   • The effect depends only on the relative velocity between the source and observer.

Mathematical Representation

The observed frequency $f^{\prime }f’$ is given by:

$f^{\prime }=f\times \frac{v+v_o}{v-v_{\mathrm{s<span\; style="font-size:\; 16px"><span><span></span></span></span><span\; style="font-size:\; 16px">\; </span>}}}$Where:

• $ff$: Frequency of the sound source.
• $vv$: Speed of sound in the medium.
• $v_{o}v\_o$: Speed of the observer (positive if moving toward the source, negative if moving away).
• $v_{s}v\_s$​: Speed of the source (positive if moving toward the observer, negative if moving away).

Real-Life Applications

• Astronomy: Explains the redshift (stretching of light waves) and blueshift (compression of light waves) of stars and galaxies.
• Radar and Sonar: Measures speed (e.g., vehicles, oceanic objects) using sound or electromagnetic waves.
• Medical Imaging: Doppler ultrasound measures blood flow by detecting frequency changes in reflected sound waves.

The Doppler effect explains how motion alters the perceived sound frequency due to the compression or stretching of sound waves. This phenomenon is not only a fundamental concept in wave physics but also a practical tool in various fields.

Vaccines work by training the immune system to recognize and fight specific pathogens (such as viruses or bacteria) without causing the disease itself. Here’s how vaccines typically work:

1. Introduction of Antigen: A vaccine contains a harmless part of a pathogen, known as an antigen, which could be a dead or weakened form of the pathogen, a piece of the pathogen (like a protein), or a blueprint for making that piece (such as messenger RNA in some vaccines). This antigen stimulates the immune system.

2. Immune Response Activation: When the vaccine is administered (usually by injection), the immune system recognizes the antigen as foreign and activates an immune response. This includes the production of antibodies (proteins that can specifically bind to the pathogen) and the activation of T-cells (cells that help destroy infected cells or assist other immune cells).

3. Memory Formation: After the immune response is triggered, the body generates memory cells (memory B-cells and memory T-cells). These cells “remember” the specific antigen and remain in the body long after the vaccination.

4. Protection Upon Exposure: If the person is later exposed to the actual pathogen (e.g., a virus or bacterium), their immune system recognizes it quickly because of the memory cells. The immune system can then mount a rapid and effective response, producing antibodies to neutralize the pathogen and activate immune cells to destroy infected cells, thus preventing illness or reducing the severity of the disease.

In summary, vaccines prime the immune system by exposing it to an antigen without causing illness, helping the body “learn” how to defend itself if it encounters the real pathogen in the future.