Digital Signal Processing Reference
In-Depth Information
t
9
t
1
t
9
t
1
X
t
17
t
17
X
X
Illustration 74:
Standing sinusoidal wave on the string of an instrument
The sinusoidal deflection of the string is presented in a highly exaggerated way. In the above depiction the
length of the string is
/2. The top run of the curve is valid for the moment t
1
, the run below that for the
moment t
2
etc. Moment t
9
shows that the string is temporarily immobile. With moment t
17
the bottom run is
reached. After that the whole process reverses. At t
25
the string would be immobile again and at t
33
the
same situation as at t
1
would be reached. This means that the standing wave is a dynamic, i.e. time-
variable, condition.
λ
Those areas of the string which are permanently immobile are called nodes, the areas of greatest
deflection are called antinodes.
In the middle row the frequency is twice as high but the wavelength half as long as at the top. As you can
see only integer multiples of the base frequency (top) can form a standing wave on a string. That is why the
string of a guitar produces a (near) periodic sound with a characteristic timbre. The sinusoidal basic
"conditions" depicted above overlap each other (as you have already seen in connection with the
FOURIER Principle
FP
) when the string is plucked to produce a sawtooth or triangular deflection.
