Geometric Attenuation and Doppler Effect
This page delves into more advanced topics in acoustics, specifically geometric attenuation and the Doppler effect. It provides formulas and explanations for these phenomena, which are essential in understanding how sound behaves in different scenarios.
The section on geometric attenuation begins with the formula:
Formula: A = L_proche - L_éloigné
Where:
- A is the attenuation
- L_proche is the sound level near the source
- L_éloigné is the sound level at a distance
This is followed by a more detailed formula:
Formula: A = 10 × log(4πd₁² / 4πd₂²) = 20 × log(d₂ / d₁)
This formula demonstrates how sound intensity decreases with distance due to the spreading of sound waves over a larger area.
Highlight: Geometric attenuation is a crucial concept in understanding how sound levels change with distance from the source.
The page then introduces attenuation by absorption:
Formula: A = L_incident - L_transmit
Where:
- L_incident is the sound level of the incident sound
- L_transmit is the sound level of the transmitted sound
This concept is important for understanding how sound is affected when passing through different materials.
The final section of the page covers the Doppler effect, a phenomenon where the observed frequency of a sound changes when the source and observer are in relative motion. The formula for the Doppler effect is presented:
Formula: Δf = f_r - f_e = (v ± v_r / c ± v_s) × f_e - f_e
Where:
- Δf is the change in frequency
- f_r is the received frequency
- f_e is the emitted frequency
- v is the speed of sound
- v_r is the speed of the receiver
- v_s is the speed of the source
Example: The Doppler effect explains why the pitch of a siren changes as an ambulance passes by an observer.
The page concludes with a reminder of basic wave equations:
Formula: c = λf and T = 1/f
Where:
- c is the speed of sound
- λ is the wavelength
- f is the frequency
- T is the period
These equations are fundamental in understanding wave propagation and are essential for calculations involving the Doppler effect.
Highlight: The Doppler effect has numerous practical applications, including radar systems, medical ultrasound, and the study of astronomical objects.
