  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 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 G\mu > 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.
