Teacher
Microphone Sensitivity
To select a suitable microphone a sound
engineer will look at a graph of directional
sensitivity. How can the directional sensitivity
of a microphone be plotted in a clear way?
Contents
Initial Problem Statement 2
Narrative 3-8
Solutions 9-12
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Microphone
Sensitivity
Appendix 13
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Teacher
Microphone Sensitivity
Sound recording engineers use different
microphone designs depending on whether they
wish to capture sound from all around or only
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from a particular direction.
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To select a suitable microphone
a sound engineer will look at a
graph of directional sensitivity.
How can the directional
sensitivity of a microphone be
plotted in a clear way?
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Initial Problem Statement
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Microphone Sensitivity
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Narrative
Introduction
Discussion
When might it be useful to have a microphone that picks up sounds from all
directions? When might it be useful to have a microphone that only picks up
sound from the direction in which it is pointing?
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Figure 1.
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The strongest signal recorded by the microphone, corresponding to the highest sensitivity, is given
a value of 1. If no sound is recorded by the microphone the sensitivity is given a value of zero. All
other measurements are made relative to these points. A relative sensitivity of 0.5 means that the
microphone is half as sensitive as it would be if it were pointing in its most favourable direction.
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Microphone Sensitivity
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One way to measure the directional sensitivity of a microphone is to play a sound of fixed volume at
a fixed distance from it and measure the signal strength that it records. By moving the sound source
around the microphone (but keeping the volume and distance fixed), measurements can be made of
the recorded signal strength as a function of the angle between the source and the direction of the
microphone.
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A measurement of how the relative sensitivity of a microphone varies with the sound
source angle gives the following results
Sensitivity (r )
0
1.00
15
0.98
30
0.93
45
0.85
60
0.75
75
0.63
90
0.50
105
0.37
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Angle (θ )
120
0.25
135
0.15
150
0.07
0.02
180
0.00
0.02
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195
210
0.07
0.15
240
Microphone Sensitivity
225
0.25
0.37
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255
0.50
285
0.63
300
0.75
315
0.85
330
0.93
345
0.98
360
1.00
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270
Sketch these data on the following graph.
Sensitivity
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1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
30
60
90
120
150
Figure 2.
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180
210
240
270
300
330
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0
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Activity 1
360
Angle (degrees)
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Discussion
What shape is the graph?
Discussion
Discussion
Microphone Sensitivity
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Do you think the graph
shows the sensitivity of the
microphone in an obvious
way?
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What does it tell you
about the sensitivity of
the microphone as the
direction of the sound
source changes?
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2. A polar graph
The recorded data for a microphone are plotted below.
Sensitivity
1
0.9
0.8
0.7
0.6
0.2
0.1
0
30
60
90
120
150
180
210
240
270
300
330
360
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0
Angle (degrees)
Figure 3.
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While the directional sensitivity information can be read from the graph it does not give an intuitive
indication; you have to study the graph rather than “see it at a glance”. The reason is the data have
been plotted using Cartesian (x, y) coordinates (in this case x is the angle and y is the sensitivity).
Instead of using a Cartesian plot, a polar plot can be made. This uses polar (r, θ ) coordinates on
axes that show radius and angle from the origin as shown below.
Figure 4.
Discussion
Where is the origin on the
above graph?
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Discussion
Where is the polar point
(0.8, 30°) on the above
graph?
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0.3
Microphone Sensitivity
0.4
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0.5
Teacher
Activity 2
Sketch the relative sensitivity data as a polar plot on the above graph.
Relative Sensitivity (r )
Angle (θ )
1.00
0.98
30
0.93
45
0.85
60
0.75
75
0.63
90
0.50
105
0.37
120
0.25
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0
15
135
0.15
150
0.07
165
0.02
0.00
225
240
255
0.15
0.25
0.37
0.50
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270
0.07
Microphone Sensitivity
210
0.02
si
195
0.63
300
0.75
315
0.85
330
0.93
345
0.98
360
1.00
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Discussion
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How does the polar graph compare with the Cartesian graph in terms of clarity of
information?
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180
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If you were looking for a microphone that had bi-directional sensitivity, i.e. it was
sensitive to sounds in front of and behind it but not sensitive to sounds from the
sides, which of the two graphs shown below would you find easier to use. Note,
they both show the same information. The one on the left shows the data plotted
on a Cartesian graph while the one on the right shows the data plotted using a
polar graph.
Teacher
Discussion
Sensitivity
1
0.9
0.8
0.7
0.6
0.3
0.2
0.1
0
0
30
60
90
120
150
180
210
240
270
300
330
360
Angle (degrees)
Figure 6.
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Microphone Sensitivity
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Figure 5.
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0.4
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0.5
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Solutions
Introduction
Discussion solution
A microphone that picks up sounds from all directions would be useful for
recording sound from, for example, a group. In this situation the engineer wants
every voice to be recorded with equal clarity.
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Activity 1 solution
The recorded data are plotted below
Sensitivity
1
0.9
0.7
0.6
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0.5
Microphone Sensitivity
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0.8
0.4
0.3
0.2
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0.1
0
0
30
60
90
120
150
180
Figure 7.
210
240
270
300
330
360
Angle (degrees)
Discussion solution
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The curve looks like a cosine curve that has been stretched in the y-direction with
a scale factor 0.5 and moved up so that all values are above the x-axis. You can
see this in the following.
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A microphone that is only sensitive in a particular direction would be useful for an outside TV
interview where the engineer wants to hear the voice of the person talking but does not want sounds
from other sources, such as traffic or nearby people, to be picked up.
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The curve looks like a cosine curve that has been stretched in the y-direction with
a scale factor 0.5 and moved up so that all values are above the x-axis. You can
see this in the following sequence
Teacher
Discussion solution
y
1
0.75
y = cos x
0.5
0.25
60
90
120
150
180
210
240
-0.25
-0.5
-0.75
y
1
0
0
x
30
60
90
120
150
180
210
240
270
300
330
360
x
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-0.75
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0.25
-0.5
360
1
y = cos x
2
0.5
-0.25
330
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0.75
300
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-1
Figure 8.
270
Microphone Sensitivity
30
on
0
-1
Figure 9.
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y
1
0.75
y=
0.5
1 1
+ cos x
2 2
0.25
0
0
30
60
90
120
150
180
210
240
270
300
330
360
x
-0.25
Figure 10.
The last graph looks like the microphone sensitivity curve.
Discussion solution
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The graph shows you that the microphone is most sensitive when the sound is
directly in front of it. The sensitivity falls as the source moves towards the back of
the microphone and reaches zero when the sound source is directly behind the
microphone.
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Discussion solution
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While the directional sensitivity information can be read from the graph it does
not give an intuitive indication; you have to study the graph rather than “see it at
a glance”. To make sense of the graph you have to note that x = 0 is the same
as x = 360, which can be done by wrapping the graph of results around the
experiment.
Figure 11.
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Microphone Sensitivity
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-0.5
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2. A polar graph
Discussion solution
The origin of a polar graph is the point where r = 0 and q = 0. This is at the centre
of the circles. The point (0.8, 30°) means that r = 0.8 and q = 30°. This is a point
on a circle of radius 0.8 centred on the origin and 30° around the circle relative to
the 0° line.
Activity 2 solution
Microphone Sensitivity
Figure 12.
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Plotting the microphone sensitivity data on a polar graph gives the following
Figure 13.
Discussion solution
This diagram very clearly shows how the sensitivity varies with the angle and
demonstrates why polar plots are sometimes preferred to Cartesian ones. Using
such a plot, a sound engineer can quickly determine the sensitivity characteristics
of a microphone. This shape is called a cardioid (as it somewhat resembles
a heart) and a microphone with this type of sensitivity is called a cardioid
microphone.
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Appendix
mathematical coverage
PL objectives
Use trigonometry and coordinate geometry to solve engineering problems
• Know the graphs of y = sinx, y = cosx and y = tanx for all values of x
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Use algebra to solve engineering problems
• Work with cartesian (x, y) and polar (r, θ ) coordinates and graphs, and convert between these
forms
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