DOUBLE SOURCE 



23 



At a very small distance 



A 

 u <x — cos a 



2.15 



The transverse component of the particle velocity is 



'1 



-\-jk 



^J^Mct~r) sin a 



Retaining the real parts of equation 2.16 



"=-^[7= 



cos k{ct — r) sin k {ct 



— r) sin a 



2.16 



2.17 



At a very large distance 



Ak . 

 u <x — sm a 



At a very small distance 



A . 

 « a: — sm a 



2.18 



2.19 



Figure 2.2 shows the velocity com- 

 ponents and the pressure for various 

 points around a doublet source. A com- 

 mon example of a doublet source is a 

 direct radiator loud speaker mounted in 

 a small baffle. (Dimensions of the baffle 

 small compared to the wavelength.) If 

 the response of such a loud speaker is 

 measured with a pressure microphone 

 for various angles at a constant distance 

 the result will be a cosine characteristic. 

 If the response is measured with a vel- 

 ocity microphone keeping the axis pointed 

 towards the loud speaker the result will 

 be a cosine directional characteristic. If 

 the same is repeated keeping the axis of 

 the velocity microphone normal to the 

 line joining the microphone and the loud 

 directional characteristic. 



Fig. 2.2. The pressure and particle 

 velocity at a constant distance from 

 a doublet source. The magnitude 

 of the pressure is indicated by the 

 diameter of the circle. The particle 

 velocity has two components: a 

 radial and transverse component. 

 The direction and magnitude of 

 these two components are indicated 

 by vectors. 



speaker the result will be a sine 



