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Solution to HW4_2007

# Solution to HW4_2007 - Solution to Homework 4 Acoustics I...

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Solution to Homework 4 Acoustics I 2007 The figure shown below shows a typical sound power measurement setup in semi- anechoic chamber (all five surfaces of the room are anechoic, while the floor is rigid. In the figure, Q above the rigid surface is the actual sound source idealized as an acoustic monopole, Q below the rigid surface is the image source of the former. Q Q h r 1 r 2 R h A B θ (1) Show that the rigid surface condition (particle velocity normal to the surface = 0) is satisfied automatically by considering an image source as shown above. As ( , ) 4 jkr j t r Qk u r t j e e e r ω π = r r , the particle velocity at any point on the reflective surface is the vector sum of and which are of the same magnitude because r 1 u r 2 u r 1 = r 2 and symmetric about the surface. Therefore the particle velocity at a point on the surface has no normal velocity component to the surface, which satisfies the boundary condition.

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Solution to HW4_2007 - Solution to Homework 4 Acoustics I...

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