1. What is the Doppler Effect?

The Doppler Effect is the change in frequency or wavelength of a wave in relation to an observer who is moving relative to the wave source. It's commonly experienced with sound waves (like a passing ambulance siren) or light waves (redshift/blueshift in astronomy).

2. How Does the Calculator Work?

The calculator uses the Doppler Effect equation:

Where:

• \( f_o \) — Observed frequency (Hz)
• \( f_s \) — Source frequency (Hz)
• \( c \) — Speed of waves in the medium (m/s)
• \( v \) — Velocity of the source relative to the medium (m/s)

Explanation: This equation calculates the frequency heard by a stationary observer when the source is moving toward the observer. For movement away from the observer, the denominator becomes (c + v).

3. Importance of Doppler Effect

Details: The Doppler Effect has applications in radar, medical imaging (Doppler ultrasound), astronomy (measuring star velocities), and meteorology (weather radar).

4. Using the Calculator

Tips: Enter the source frequency in Hz, wave speed in m/s (343 m/s for sound in air at 20°C), and source velocity in m/s. Positive velocity means source is moving toward observer.

5. Frequently Asked Questions (FAQ)

Q1: What if the source is moving away?
A: Use a negative velocity value for movement away from the observer.

Q2: What's the speed of sound in air?
A: Approximately 343 m/s at 20°C, but varies with temperature (331 m/s at 0°C).

Q3: Does this work for light waves?
A: For light, relativistic equations must be used as the speed of light is constant in all reference frames.

Q4: What if the observer is moving too?
A: The general equation becomes \( f_o = f_s \frac{c + v_o}{c - v_s} \), where \( v_o \) is observer velocity.

Q5: Why does the pitch change as an ambulance passes?
A: As it approaches, the sound waves are compressed (higher pitch). As it moves away, they're stretched (lower pitch).