Benthowave Instrument Inc.

BENTHOWAVE INSTRUMENT INC. Acoustic Transducer & System 

Linear and Nonlinear Acoustics

Unit Conversion

Receiving Sensitivity: (xx) V/μPa = ((xx)*1000000) V/Pa = (20*log(xx)) dB V/μPa = (20*log(xx) + 120) dB V/Pa
(xx) dB V/μPa = ((xx) + 120) dB V/Pa = (10^((xx)/20)) V/μPa = ((10^((xx)/20))*1000000) V/Pa
Transmitting Voltage Response: (xx) μPa/V@1m = (20*log(xx)) dB μPa/V@1m = (20*log(xx) - 120) dB Pa/V@1m
(xx) dB μPa/V@1m = (10^((xx)/20)) μPa/V@1m = ((10^((xx)/20))/1000000) Pa/V@1m

Impedance and Admittance

Impedance Z=R+jX=G/(G*G+B*B) -jB/(G*G+B*B)
Admittance Y=G+jB=R/(R*R+X*X)+jX/(R*R+X*X)
Impedance Phase θ=arctan(X/R)=-arctan(B/G)
R: Resistance; X: Reactance; G: Conductance; B: Susceptance

Useful Acoustic Formulae:

Planar Transducer: 33 kHz
Cavitation Threshold:
at Sea Surface, (dB uPa)
203 206 209 214 214 217.5 220 212

Transducer SL (Source Level): SL = TVR + 20*log (Vrms)   (dB re µPa @ 1m)
TVR - Transmitting Voltage Response of Transducers;
Vrms - (Root Mean Square) Driving Voltage of Transducers
Transducer SL (Source Level): SL = 10*log(Pe) + 10*log(Efficiency) + DI + 170.8   (dB re uPa@1m)
Pe - Electrical Power Driving Transducers; Efficiency - Transducer Electroacoustic Efficiency.
DI - Directivity Index of Transducer
Acoustic Far Field: ≥ Area/λ (Planar)
≥ (Length*Length)/λ and ≥ Length (Line or thin cylinder)
Hydrophone/Acoustic Sensor
Output Vrms:
Vrms = SPL + OCV   (dBV)
SPL - Sound Pressure Level (dB re µPa); OCV - Receiving Sensitivity (dB re V/uPa);
dBV = 20*log(Voltage)
Impedance Matching Transformer: Zp = Zt/(N*N)   (Ω)
Zp - Transformed Load Impedance; Zt - Transducer Impedance.
N - Turn Ration of Secondary to Primary Winding
Signal Loss Over Extension Cable: 20*log[Ch/(Ch+Cc)]    (dB)
Ch - Hydrophone Capacitance; Cc - Extension Cable Capacitance
Sound Transmission loss: Spherical Spreading: TL = 20 * log R;   R - Range (m)
Absorption Coefficient below 50 kHz:
    Absorption Coefficient (dB/km)) = 1.0936 [0.1*f*f/(1 + f*f) + 40*f*f/(4100 + f*f)]
    f - Frequency (kHz)
Electrical Power Loss over Cable: Power Loss over cable = 2*Irms*Irms*R*L
Irms: RMS cable current, from 0.1A to 7A;
R: Nominal Conductor Resistance, about 0.035ohms/meter; L: Cable Length (meter)
Constants Free Dielectric ε0 = 8.842 x 10^-12 C/mV
Sound Speed in Sea Water:
C = 1449.2+4.6T-0.055T^2+0.00029T^3+(1.34-0.010T)*(S-35)+0.012z (m/s).
T - Temperature, °C; S - Salinity, parts per thousand of dissolved weight of salts; z - Depth, meter.
Sound Speed in Fresh Water: C = 1481 m/s;
Density of Sea Water: 1026 kg/m^3;      Density of Fresh Water: 998 kg/m^3.

Ocean Sound Sources Frequency Range (Hz)
Vessel Traffic 5 to 500
Air-Gun (Seismic Reflection Profiling) 5 to 1,000
Earthquake Up to 100
Drill Ship 10 to 20,000
Ice 10 to 1,000
Ocean Surfaces 1 to 50,000