In this study of the twin paradox, the periods of acceleration necessary for the astronaut to start the journey, turn around, and return to rest at the starting point are investigated. Each twin sends a light beam of frequencyf0to the other one. The waves received by each twin have a constantly changing Doppler‐shifted frequency due to the astronaut’s acceleration. The stay‐at‐home twin (SAHT) receivesKcycles sent by the astronaut and the astronaut receivesK′ cycles sent by SAHT, whereK≠K′.KandK′ are calculated by integrating the observed instantaneous frequency with respect to time. Then the time for the round trip recorded by the astronaut,TA, and by SAHT,TS, can be compared, whereTA=K/f0andTS=K′/f0. The relationships derived are identical to those obtained by using the concept of proper time. The results are illustrated with numerical examples.