With the development of internet of things technologies, tremendous sensor audio data has been produced, which poses great challenges to audio-based event detection in smart cities. In this paper, we target a challenging audio-based event detection task, namely, text-to-audio grounding. In addition to precisely localizing all of the desired on- and off-sets in the untrimmed audio, this challenging new task requires extensive acoustic and linguistic comprehension as well as the reasoning for the crossmodal matching relations between the audio and query. The current approaches often treat the query as an entire one through a global query representation in order to address those issues. We contend that this strategy has several drawbacks. Firstly, the interactions between the query and the audio are not fully utilized. Secondly, it has not distinguished the importance of different keywords in a query. In addition, since the audio clips are of arbitrary lengths, there exist many segments which are irrelevant to the query but have not been filtered out in the approach. This further hinders the effective grounding of desired segments. Motivated by the above concerns, a novel Cross-modal Graph Interaction (CGI) model is proposed to comprehensively model the relations between the words in a query through a novel language graph. To capture the fine-grained relevances between the audio and query, a cross-modal attention module is introduced to generate snippet-specific query representations and automatically assign higher weights to keywords with more important semantics. Furthermore, we develop a cross-gating module for the audio and query to weaken irrelevant parts and emphasize the important ones.