# Digital Waveguides: String with Losses

## Introducing Losses¶

Real strings, however, introduce losses when reflecting the waves at either end. These losses are caused be the coupling between string and body, as well as the resonant behavior of the body itself. Thus, they contribute significantly to the individual sound of an instrument. In physical modeling, these losses can be implemented by inserting filters between the delay lines:

## Plucked String Sound¶

The result of the waveguide synthesis has the characteristics of a plucked string with a crisp onset and a sinusoidal decay:

## Smoothing¶

With an additional lowpass between the waveguides, the signal will get smoother with every iteration, resulting in a crisp onset with a sinusoidal decay. This example works with a basic moving average filter (FIR with boxcar frequency response) with a length of $N=20$. The slow version shows the smoothing of the excitation function for both delay lines even during the first iterations:

Once Loop Reflect