The phrase "make a buzzing sound" can be substituted with a variety of engaging synonyms, depending on the context in which it is being used. For instance, we can use words like "hum," "whir," "vibrate," and "drone" to convey the same meaning. "Buzz" is another common synonym that is widely used to describe a low humming or vibrating sound. Similarly, "whistle" can be used to describe a high-pitched buzzing sound. In addition, "zing" and "zinging" can be used to describe a sharp, buzzing sound that is often heard in nature. All these synonyms effectively convey the sense of a buzzing sound while adding a touch of variation and flair to the language.