Bioacoustics Project S2, 2008
Hydrophonic doppler speed determination:
Objective: To use passive recordings of underwater sound in the Swan River to
determine the speed of passing motorised watercraft.
Theory:
The engine of a motorised boat produces a sound of a roughly constant frequency that
can be recorded using a hydrophone (underwater microphone) and digital recorder
(DAT) and the signal analysed using Fourier techniques. The doppler frequency shift
due to the relative motion between the source (the engine) and the observer (the
hydrophone) provides a way to calculate the speed of the boat relative to the land.
Consider a boat passing along the linear path A  B.
Let B be closest point to observer at O. Speed of sound in water = c.
d  b tan   a sin 
For a ferry traveling at constant speed vo producing a constant source frequency fo the
frequency at the observer f is given by the doppler relation:
frequency ratio:
r 
f
fo

c
c  vo sin 
Let the time origin (t = 0) be when boat is at B:
boat:
x(t) = vo t , y = b
observer:
x = 0, y=0

v t
( t )  tan 1  o 
 b 
Sound leaving the boat at time t reaches the observer at:
a
t  t  t 
c
Thus:
 t
r ( t  t ) 
vo t 2  b2
c
c
c  vo sin ( t )

c

 v t 
c  vo sin  arctan  o  
 b 

The extremes of the ratio r correspond to the limiting cases of approach (t  - ) and
retreat (t  + ):
maximum ratio:
rmax
minimum ratio:
rmin
relative difference:
f
fo
c
c  vo
c

c  vo
c
c


c  vo c  vo


2 c vo
c  vo 2
2
If c and f are known then v can be found:
v 
c
2
 1    1


where we define  
f
fo
For a particular recording then if the extreme frequencies are f1 (appraoching) and f2
(retreating) we have:
fo 
f1  f 2
2
and
 
2 f1  f 2 
f1  f 2
FFT constraints:
To detect a frequency shift of f requires a sampling frequency fs and number of
points N such that:
f 
fs
1

N
T
where T is the time of the sample to which the FFT is applied to determine f1 and f2.
Speed of sound measurements:
Using Igor Pro:
SOS_08.pxp
1)
From the Menu select
Data/Load Waves/Load sound WAV file...
browse to find and select sound files sosNmk.wav
where N = 1, 2, 3, ... 8; and k = 1,2
2)
From the Menu "macros" select 'start'
this displays two tables and panel:
parameters:
p_name:
ppp:
describes each variable used in calculations
contains parameter values for each variable
values can be entered directly or from the 'master' control panel
some are internally generated (written as * =)
results:
show stored values and parameter settings (see below)
master:
'select sound file'
pop-up menu displays all sound files starting with 's'
selecting a particluar sound file (eg: sos6m1) copies the stereo data to
ch_L
(left channel) displayed in top graph
ch_R
(right channel) displayed below
on the top graph 'left' are are diplayed two vertical lines
green for start of region of interest
blue for end
adjust start and end on 'master' panel to restrict to data subset
click on blue 'extract' button to copy the chosen subset to new graph:
eg: for sos6m1: start = 67680, end = 67960
the 'adjust zero' checkbox adjusts the initial few points of each subset to zero
as determined by ppp[5]
the 'gap (cm)' control allows for time compensation for the sound from the brass
rod crossing the air-gap to the air microphone.
extracted selection:
this graph shows the left and right selected subsets
adjust the 'master' controls:
L pt and R pt to correspond to first positive peak
on each trace.
the speed of sound (c) is then automatically calculated and displayed in the
yellow box from the time difference between the two traces in accordance with
the hydrophone-rod distance (automatically read from the sound file name – eg:
6 m for the file sos6m1.wav) as well as the air-gap distance (assuming speed of
sound in air as 340 m/s) as set in ppp[13].
The green 'store' button writes the parameters and result into the 'results' table:
file_name:
selected data file
P_start:
start point of extract
P_end:
end point of extract
P_L:
L pt
P_R:
R pt
distance:
in m, from file name
sos:
speed of sound (c) in m/s
air_gap_cm:
chosen value for estimate of bar-microphone distance
The number to the right of the store button shows the current location for writing
results (called 'flag' and shown also in ppp[11])
The purple 'clear last' button undoes the last stored values from the results table.
The red 'reset' button clears all previously stored values
(NOTE: can't undo this step so be careful!)
_____________________________________________________
Doppler sound analysis:
Implementation in Igor Pro: RiverSoundAnalysis08.pxp
________________________________________________________________
Instructions for use:
1)
Load sample:
sound should be mono 16 bit *.wav
Menu: Data/Load Waves/Load WAV Sound File ...
Name can be changed – must be alpha-numeric, can't start with number, can use _
instead of 'space'.
Menu: Macros/start
brings up graphs and a table:
parameters:
p_name describes global variables in ppp
ppp contains current value for variables
- can be set by direct typing into ppp
- or from controls on graphs
- sometimes calculated internally (indicated by * =)
sample:
displays sample to be analysed
select sound file from pop-up menu top right
set start point and FFT size (multiple of 2 for speed)
set sampling frequency (rate) in Hz
optional Hanning filter
- not required for noise
- good to identify signals
selection:
displays the selection from the sound sample
as determined by
- controls on graph 'sample'
spectrum:
displays power spectrum (in dB) of selection from sample
Update by clicking on purple 'FFT' button
Can smooth spectrum by clicking 'smooth' checkbox and choosing number to the right
of it. Bigger number  more smoothing.
For noise can reduce number of frequency bins by factor in 'bin' pop-up
eg: FFT size = 8192, bin = 1
 4096
2)
Sonagram:
Once a sound file is loaded and FFT size and smoothing is chosen, a sonagram can be
performed on a specified portion of the sample wave. Controls on the Spectrum graph
determine:
- start: point number for start of first spectrum
- end: point number for end of sonagram analysis
- overlap (%): amount of overlap between successive spectra in sonagram
For these values the number of individual spectra in the sonagram (called 'slices') are
calculated and displayed on the spectrum graph. There may be some points at the end
of the specified range that are excluded depending on the FFT size chosen etc.
Click on the red button 'sonagram' to perform the analysis.
When the calculations are completed two new graphs are displayed:
sonagram:
with frequency as the y-axis and time (of the start of each
separate slice) as the x-axis. A colour scale indicates the spectrum values in dB.
3)
________________________________________________________________
Other Graphs and Tables:
Window/GraphMacros/g_ends
ends:
displays the start (green) and end (blue) points in the selection
number of points included is set by ppp[3]
Window/GraphMacros/g_spec_extracted
extracted spectrum:
displays individual slices of the sonagram as a spectrum
shows time for point at start of slice
Window/TableMacros/t_SPL_values
SPL values: contains data calculated for dBA, dBC and dBF vs t_axis for
each slice of the sonagram.