Doppler Effect: Comprehensive NEET Physics Notes

1. Doppler Effect

The Doppler Effect is a crucial concept for NEET Physics that describes the change in observed frequency of a wave when there is relative motion between the source of the wave and the observer. This effect is widely applicable to both sound and light waves.

1.1 Introduction to Doppler Effect

The Doppler Effect occurs when there is a relative motion between a wave source and an observer. The observed frequency differs from the actual emitted frequency:

When the source and observer are moving towards each other, the observed frequency increases.
When moving apart, the observed frequency decreases.

The Doppler Effect is observed in all wave types, such as sound and electromagnetic waves (light).

NEET Tip:

Doppler Effect questions in NEET often involve moving sources or observers, so practice applying the formulas under different conditions.

1.2 Mathematical Derivation

Case 1: Source in Motion, Observer Stationary

When the source is moving towards or away from a stationary observer, the observed frequency, $f_{o}$ , changes.

For a source moving towards the observer: $f_{o} = \frac{v}{v - v _{s}} f_{s}$

For a source moving away from the observer: $f_{o} = \frac{v}{v + v _{s}} f_{s}$

where:

$f_{s}$ is the actual frequency emitted by the source
$v$ is the speed of sound in the medium
$v_{s}$ is the velocity of the moving source

Case 2: Observer in Motion, Source Stationary

If the observer is moving towards or away from a stationary source:

When moving towards the source: $f_{o} = (\frac{v + v _{o}}{v}) f_{s}$
When moving away: $f_{o} = (\frac{v - v _{o}}{v}) f_{s}$

Case 3: Both Source and Observer in Motion

For both source and observer moving: $f_{o} = (\frac{v + v _{o}}{v - v _{s}}) f_{s}$

1.3 Applications of Doppler Effect

1.3.1 Astronomy

Redshift: Light from stars moving away from Earth shifts towards the red end of the spectrum.
Blueshift: Stars moving towards Earth shift towards the blue end.

1.3.2 Medical Imaging

The Doppler Effect is used in ultrasound imaging to measure blood flow in arteries and veins.

1.3.3 Weather Radar

Doppler radars measure the speed and direction of weather patterns, like thunderstorms, helping in weather forecasting.

Real-life Application:

Ambulance sirens sound different as they approach and then pass by due to the Doppler Effect.

Mnemonic:

"Towards = Tighter waves (higher frequency), Away = Apart waves (lower frequency)."

Quick Recap

The Doppler Effect causes a shift in observed frequency due to the relative motion of source and observer.
Frequency increases when the source and observer move towards each other; it decreases when moving apart.
Applicable to both sound and light waves.

1.4 NEET Problem-Solving Strategy

Identify whether the source, observer, or both are moving.
Choose the appropriate Doppler Effect formula.
Pay attention to the direction (towards or away) to determine the sign in the equation.

Common Misconception:

Students often mix up the effect of the source and observer's motion. Remember, when the observer moves, the observed frequency directly depends on their speed, while a moving source affects the wavelength.

Practice Questions

Q1. A train moving at 30 m/s approaches a stationary observer. The train emits a whistle at a frequency of 600 Hz. What frequency does the observer hear if the speed of sound is 340 m/s?

Solution: Given:

$f_{s} = 600 Hz$
$v_{s} = 30 m/s$
$v = 340 m/s$

Using the formula: $f_{o} = \frac{v}{v - v _{s}} f_{s}$ $f_{o} = \frac{340}{340 - 30} \times 600$ $f_{o} \approx 654.55 Hz$

Q2. An ambulance moves away from you at 20 m/s, emitting a siren sound at a frequency of 500 Hz. What frequency will you hear if the speed of sound is 340 m/s?

Solution: $f_{o} = \frac{v}{v + v _{s}} f_{s}$ $f_{o} = \frac{340}{340 + 20} \times 500$ $f_{o} \approx 472.22 Hz$

Concept Connection

Physics and Biology: The Doppler Effect's application in medical ultrasound imaging connects Physics with Biology. It helps in visualizing blood flow in veins and arteries, crucial for diagnosing cardiovascular conditions.

Visual Aids

Diagram 1: Doppler Effect with Moving Source and Observer

Include a diagram showing a source emitting sound waves while moving towards and away from an observer, depicting wave compression and rarefaction.

Diagram 2: Redshift and Blueshift

Create a visual representation of how light shifts towards red or blue, depending on whether a celestial body moves away or towards the observer.

Supplementary Features

Glossary

Frequency: Number of wave cycles per second (Hz).
Wavelength: Distance between consecutive wave crests.
Redshift: Increase in wavelength when a source moves away.
Blueshift: Decrease in wavelength when a source moves towards.

Summary Table

Parameter	Formula	Moving Towards	Moving Away
Source moving	$f_{o} = \frac{v}{v \pm v _{s}} f_{s}$	Minus (-)	Plus (+)
Observer moving	$f_{o} = (\frac{v \pm v _{o}}{v}) f_{s}$	Plus (+)	Minus (-)

Engagement and Memorability

Use mnemonic techniques like "Tighter towards, Apart away" to remember how frequency changes. Relate the Doppler Effect to everyday experiences, like hearing an ambulance passing by, to make the concept more relatable.

Practice Questions with Detailed Solutions

Q3. Two cars are moving towards each other. Car A emits a sound at a frequency of 400 Hz, and Car B moves at 15 m/s. If the speed of sound is 340 m/s, what frequency will Car B hear as Car A approaches it?

Solution: Using the combined Doppler formula: $f_{o} = (v - v _{s}$