The pulse tube cooler (PTC) driven by a thermoacoustic engine can completely eliminate mechanical moving parts, and then achieves a simpler and more reliable device. A Stirling thermoacoustic heat engine has been constructed and tested. The heat engine can generate a maximal pressure ratio of 1.19, which makes it possible to drive a PTC and get good performance. Frequency is one of the key operating parameters, not only for the heat engine but also for the PTC. In order to adapt to the relatively low design frequency of the PTC, the operating frequency of the thermoacoustic heat engine was regulated by varying the length of the resonance tube. Driven by the thermoacoustic engine, a single stage double-inlet PTC obtained the lowest refrigeration temperature of 80.9K with an operating frequency of 45Hz, which is regarded as a new record for the reported thermoacoustically driven refrigerators.