Abstract : Junctions on cosmic string loops give rise to the proliferation of sharp kinks. We study the effect of this proliferation on the gravitational wave (GW) signals emitted from string networks with junctions, assuming a scaling solution. We calculate the rate of occurrence and the distribution in amplitude of the GW bursts emitted at cusps and kinks in the frequency bands of LIGO/VIRGO and LISA as a function of the string tension, the number of sharp kinks on loops with junctions, and the fraction of loops in the cosmological network which have junctions. Combining our results with current observational constraints, we find that pulsar data rule out a significant number of kinks on loops for strings with tensions Gμ≳10-12. By contrast, for smaller tensions current observations allow for a large number of kinks on loops. If this is the case, the incoherent superposition of small bursts emitted at kink-kink encounters leads to an enhanced GW background that hides the strong individual bursts from kinks and cusps.