Doppler Frequency Calculation

Doppler Frequency Shift Equation:

\[ f_d = \frac{2 \times v \times f}{c} \times \cos \theta \]

Velocity (v):

m/s

Frequency (f):

Speed (c):

m/s

Angle (θ):

degrees

Doppler Frequency Shift (f_d):

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1. What is Doppler Frequency Shift?

The Doppler frequency shift is the change in frequency of a wave in relation to an observer who is moving relative to the wave source. It is commonly observed in sound waves, light waves, and radar systems.

2. How Does the Calculator Work?

The calculator uses the Doppler frequency shift equation:

\[ f_d = \frac{2 \times v \times f}{c} \times \cos \theta \]

Where:

\( f_d \) — Doppler frequency shift (Hz)
\( v \) — Velocity of the object (m/s)
\( f \) — Original frequency (Hz)
\( c \) — Speed of wave propagation (m/s)
\( \theta \) — Angle between direction of motion and wave propagation (degrees)

Explanation: The equation calculates the frequency shift caused by the relative motion between the source and observer, taking into account the angle of approach.

3. Importance of Doppler Frequency Calculation

Details: Doppler frequency calculations are crucial in various applications including radar systems, medical ultrasound, astronomy, speed measurement, and weather forecasting.

4. Using the Calculator

Tips: Enter velocity in m/s, frequency in Hz, wave speed in m/s, and angle in degrees. All values must be valid positive numbers with angle between 0-180 degrees.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the factor 2 in the equation?
A: The factor 2 accounts for the two-way path in radar and sonar systems where the wave travels to the target and back.

Q2: How does the angle affect the Doppler shift?
A: The maximum shift occurs when θ = 0° (direct approach) and minimum when θ = 90° (perpendicular motion). No shift occurs at θ = 90°.

Q3: What values should be used for speed of light/sound?
A: For electromagnetic waves use c = 3×10⁸ m/s, for sound in air use c = 343 m/s (at 20°C), adjust for different media.

Q4: Can this calculator be used for both approaching and receding objects?
A: Yes, the sign of the velocity (positive/negative) or the angle calculation will determine if it's a positive (approaching) or negative (receding) shift.

Q5: What are typical applications of Doppler frequency shift?
A: Radar speed guns, medical ultrasound blood flow measurement, weather radar, astronomical redshift measurements, and police speed detection.