Trial version. Microphone Sensitivity

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1 Microphone Sensitivity Contents 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? Initial Problem Statement 2 Narrative 3-8 Solutions 9-2 Appendix 3 Microphone Sensitivity page: of 3

2 Microphone Sensitivity Initial Problem Statement Sound recording engineers use different microphone designs depending on whether they wish to capture sound from all around or only from a particular direction. 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? Microphone Sensitivity page: 2 of 3

3 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? 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. Figure. The strongest signal recorded by the microphone, corresponding to the highest sensitivity, is given a value of. 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 means that the microphone is half as sensitive as it would be if it were pointing in its most favourable direction. Microphone Sensitivity page: 3 of 3

4 Activity A measurement of how the relative sensitivity of a microphone varies with the sound source angle gives the following results Sketch these data on the following graph. Sensitivity Angle (θ ) Sensitivity (r ) Microphone Sensitivity page: 4 of Angle (degrees) Figure 2.

5 Discussion What shape is the graph? Discussion What does it tell you about the sensitivity of the microphone as the direction of the sound source changes? Discussion Do you think the graph shows the sensitivity of the microphone in an obvious way? Microphone Sensitivity page: 5 of 3

6 2. A polar graph The recorded data for a microphone are plotted below. Sensitivity Angle (degrees) Figure 3. 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? Discussion Where is the polar point (.8, 3 ) on the above graph? Microphone Sensitivity page: 6 of 3

7 Activity 2 Sketch the relative sensitivity data as a polar plot on the above graph. Discussion Angle (θ ) Relative Sensitivity (r ) How does the polar graph compare with the Cartesian graph in terms of clarity of information? Microphone Sensitivity page: 7 of 3

8 Discussion 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. Sensitivity Angle (degrees) Figure 5. Figure 6. Microphone Sensitivity page: 8 of 3

9 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. 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. Activity solution The recorded data are plotted below Sensitivity Angle (degrees) Discussion solution Figure 7. The curve looks like a cosine curve that has been stretched in the y-direction with a scale factor and moved up so that all values are above the x-axis. You can see this in the following. Microphone Sensitivity page: 9 of 3

10 Discussion solution The curve looks like a cosine curve that has been stretched in the y-direction with a scale factor and moved up so that all values are above the x-axis. You can see this in the following sequence y x y - y = cos x y = x 2 cos Figure 8. x Figure 9. Microphone Sensitivity page: of 3

y.75 y = + x 2 2 cos.25 -.25 - -.75 - x 3 6 9 2 5 8 2 24 27 3 33 36 Figure. The last graph looks like the microphone sensitivity curve.

11 y.75 y = + x 2 2 cos x Figure. The last graph looks like the microphone sensitivity curve. Discussion solution 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. Discussion solution 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 = is the same as x = 36, which can be done by wrapping the graph of results around the experiment. Figure. Microphone Sensitivity page: of 3

2. A polar graph Discussion solution The origin of a polar graph is the point where r = and q =. This is at the centre of the circles. The point (.8, 3 ) means that r =.8 and q = 3.

12 2. A polar graph Discussion solution The origin of a polar graph is the point where r = and q =. This is at the centre of the circles. The point (.8, 3 ) means that r =.8 and q = 3. This is a point on a circle of radius.8 centred on the origin and 3 around the circle relative to the line. Activity 2 solution Figure 2. Plotting the microphone sensitivity data on a polar graph gives the following Discussion solution Figure 3. 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. Microphone Sensitivity page: 2 of 3

13 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 Use algebra to solve engineering problems Work with cartesian (x, y) and polar (r, θ ) coordinates and graphs, and convert between these forms Microphone Sensitivity page: 3 of 3

1 Graphs of Sine and Cosine

1 Graphs of Sine and Cosine Exercise 1 Sketch a graph of y = cos(t). Label the multiples of π 2 and π 4 on your plot, as well as the amplitude and the period of the function. (Feel free to sketch the unit