Building Acoustics

160 Building acoustics

As derived in Chapter 3 (section 3.5.1.1), the RMS-value of the sound pressure at a
given frequency may be expressed as

1

ˆi (^22)
() 1 2 cos(2 )
2
pp ,
p
px=++⎡⎢R R kx+δ
⎣⎦

 ⎤

⎥ (5.1)

where Rp is the pressure reflection factor having phase angle δ.

Figure 5.3 Sketch of the set-up for the “classical” standing wave tube measurement method.

Loudspeaker Probe Specimen

From the ratio of the maximum and the minimum sound pressure amplitudes, these
amplitudes are given by

()

()

i

max

i

min

ˆ

1

2

ˆ

and 1 ,

2

p

p

p

pR

p

pR

=+⎡ ⎤

⎣ ⎦

=−⎡ ⎤

⎣ ⎦





(5.2)

we may then determine the modulus of the pressure reflection factor Rp. The phase angle
δ is determined by the position of the first minimum pressure close to the specimen. (Can
you set up the expression for this phase angle using Equation (5.1)?). From these data
both the input impedance Zg and the absorption factor α are determined from the
equations

(^) g00 0

11

11

p

pp

RR

Zc Z

RR

ρ p

+ +

==

−−

(5.3)

and

g

0

2

gg

00

.

4Re

2Re 1

Z

Z

ZZ

ZZ

α

⎧⎫⎪⎪

⎨⎬

⎪⎪⎩⎭

=

⎧⎫⎪⎪

+ ⎨⎬+

⎪⎪⎩⎭

(5.4)

A sketch of the sound pressure level, given by the expression