Basic - Acoustic Formulas
For those seeking notes on Basic Acoustic Formulas and Properties, the following provides such information. Furthermore, by using the navigational menu to the left, one can obtain information on Acoustic Equations, Unit Conversions, Acoustic Definitions, References, and Decibels.
| Electro-Acoustic Properties |
| Name | Symbol | Unit | Quick Formula | Explanation | Frequency | fkHz | kHz | - | Frequency is cycles per time unit | Input Voltage | Vin | Volt-rms | - | Input voltage at the transducer terminals in rms-value while transmitting | Output Voltage | OCV | Volt-rms | - | Open Circuit Voltage. Output voltage at the transducer terminals in rms-value while receiving when no current passes its terminals | Electric Impedance | Z | Ohm | Z=V/I=|Z|∠φ |Z|2=R2+X2 | The transducer’s impedance, which is the ratio between voltage V and current I. Z is a complex number Z=R+j·X with modulus |Z| and phase φ | Electric Phase | φ | deg | tan(φ)=X/R | The transducer’s phase. The phase angle between the current and the voltage | Electric Resistance | R | Ohm | R=|Z|cos(φ) | Equivalent series resistance. Real part of Z, | Electric Reactance | X | Ohm | X=|Z|sin(φ) | Equivalent series reactance. Imaginary part of Z, | Conductance | GP | Ohm-1 | R/(R2+X2) | Equivalent parallel conductance. GP=R/|Z|2=cos(φ)/|Z| | Electric Power | Pe | Watt | Pe,in=V2in· GP | Electrical power at the transducer terminals | Speed of Sound | c | m/s | - | About ~1500m/s for water | Density | ρ | kg/m3 | - | About ~1000kg/m3 for water | Pressure | P | Pa | - | The rms-amplitude of a sound wave. For plane waves in compress-ible medias p=ρ·c ·u where u is the particle velocity. | Acoustic Intensity | Ia | Watt/m3 | Ia=p2/(ρc) | Acoustic power per area. Loudness of sound. | Acoustic Power | Pa | Watt | Pa=Ia ·Aa | Acoustic power | Acoustic Area | Aa | m2 | Square: L2 Circle: πr2 Sphere: 4πr2 Cylinder: 2πrh | Any area, through which acoustic energy is transferred. Often used to describe the size of the active sound-emitting parts of a transducer | Efficiency | ηea | - | ηea=Pa,out /Pe,in | Electric to acoustic efficiency | Directivity Index | DI | dB | - | The directivity index is the ratio (in dB) of the maximum intensity produced by the transducer compared to a point source, which is putting out the same acoustic power. | Source Level | SL | dB re 1μPa@1m | SL=TRV+20log(Vin) | The source level is the ratio (in dB) of the maximum intensity pro-duced by the transducer at 1m distance compared to the intensity of a plane wave with rms-amplitude 1μPa (0.667·10-18w/m2). | Transmitting Response to Voltage | TRV | dB re 1μPa/V@1m | - | Transmit response with respect to voltage taken at the reference distance 1m | Transmitting Response to Current | TRC | dB re 1μPa/Amp@1m | - | Transmit response with respect to current taken at the reference distance 1m | Receiving Response | RR | dB re 1V/μPa | RR=20log(OCV)-IL | Open circuit voltage response with respect to 1μPa. Also called receiving sensitivity. | Intensity Level | IL | dB re 1μPa | IL=20log(p/1μPa) | The intensity level is the ratio (in dB) of an intensity compared to the reference intensity of a plane wave with rms-amplitude 1μPa (0.667·10-18w/m2). | Transmitting Loss | TL | dB | TL=20log(r)+α(r-1) | The drop in acoustic intensity caused by spherical spreading and attenuation |
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