Space-time parametric instability in a soft string

When a system is subjected to parametric forcing, its response occurs at half the excitation frequency. This effect was observed by Faraday on vertically vibrated liquids and by Melde in his studies of string resonances. In this presentation, we introduce an experiment similar to Melde's, but using a string made of a soft material (i.e. with a low Young's modulus). We observe an atypical response, different from the Faraday-type sub-harmonic instability: pairs of sub-harmonic frequencies are created (e.g., f/3 and 2f/3 or f/4 and 3f/4, where f is the forcing frequency). By varying f, the unstable pairs are modified. A theoretical model based on multi-scale development is used to predict these observations and describe the dynamics of the instability.