1. What is the Doppler Effect Equation?

The Doppler Effect equation calculates the observed frequency of a wave when there is relative motion between the source and the observer. It's commonly used in acoustics, astronomy, and radar technology to determine frequency shifts.

2. How Does the Calculator Work?

The calculator uses the Doppler Effect equation:

Where:

• \( f_{obs} \) — Observed frequency (Hz)
• \( f_{source} \) — Source frequency (Hz)
• \( c \) — Speed of sound (m/s)
• \( v_{observer} \) — Observer velocity (m/s)
• \( v_{source} \) — Source velocity (m/s)

Explanation: The ± signs depend on the direction of motion. When observer moves toward source, use + in numerator. When source moves toward observer, use - in denominator.

3. Importance of Frequency Calculation

Details: Accurate frequency calculation is crucial for applications like medical ultrasound, speed detection radar, astronomical redshift measurements, and sound engineering.

4. Using the Calculator

Tips: Enter source frequency in Hz, speed of sound in m/s, velocities in m/s. Select appropriate directions for observer and source. All values must be valid (f_source > 0, c > 0).

5. Frequently Asked Questions (FAQ)

Q1: What is the standard speed of sound in air?
A: Approximately 343 m/s at 20°C, but it varies with temperature, humidity, and altitude.

Q2: How do I determine the correct signs in the equation?
A: Use + when observer moves toward source, - when away. Use - when source moves toward observer, + when away.

Q3: Can this calculator be used for light waves?
A: The relativistic Doppler effect should be used for light, as it accounts for effects at speeds approaching light speed.

Q4: What happens if both source and observer are stationary?
A: The observed frequency equals the source frequency (no Doppler shift).

Q5: Are there limitations to this equation?
A: This classical formula works well for sound waves at speeds much slower than light. For electromagnetic waves or high velocities, relativistic corrections are needed.