Building Acoustics

10 Building acoustics

-50 -40 -30 -20 -10 0 10 20 30 40 50

Time (ms)

0

25

50

75

100

125

150

x(

t)

Pulse duration

T= 10 ms

T= 1 ms

Figure 1.5 Time functions of rectangular pulses.

Figure 1.6 Modulus of the Fourier transforms of rectangular pulses.

10 100 1000

Frequency (Hz)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

|X

(f)|

Ampl.=100

T= 10 ms

T= 5 ms

T= 1 ms

B) The example above does not represent, for many reasons, an oscillatory motion
you will find in real life. It does, however, illustrate important relationships concerning
the form of a pulse and the corresponding frequency spectrum. The following example
uses a more realistic type of motion; the function used represents the amplitude
(displacement, velocity or acceleration) of a simple mass and spring system having a