The strontium iridate Sr2IrO4 has recently received a special attention because of its closeresemblance to undoped high-Tc cuprate in terms of structural, electronic, and magnetic aspects.We have recently measured magnon dispersion using the resonant inelastic x-ray scattering(RIXS) technique. A dispersive magnon branch with a bandwidth of ~200 meV has beenobserved. However, due to insufficient energy resolution of the state-of-the-art RIXS instruments,the magnon gaps, of quantum and classical origins, have not been quantified. The proposed INSmeasurements are aimed (i) to quantitatively measure the magnon gap at the zone center andzone boundary, and (ii) to investigate the origin of the new high energy magnetic excitationsobserved in the RIXS. We propose to measure the magnetic excitation up to the energy transfer of~ 600 meV using the TOF Merlin spectrometer.