The children waved goodbye as the train disappeared.

Meaning: The children said goodbye to the toy train as it went away from them.

Choice of Words: Waved means to move one's hand or arm back and forth in the air. Goodbye is a word or phrase said when parting. Disappeared means to become hidden from view.

Alternative Expressions

The children waved farewell as the train vanished.

Meaning: This means that the children were saying goodbye to the train as it was leaving very quickly.

Choice of Words: The children are still the ones doing the waving, but now they are saying farewell, which is a more formal way of saying goodbye. The train is still disappearing, but now it is called vanishing, which makes it sound like it is disappearing very quickly.

The kids bid farewell as the locomotive departed.

Meaning: This means that the children said goodbye to the train after it had already left.

Choice of Words: The children are now called kids, which is a more informal way of saying children. They are still saying farewell, but now the train is called a locomotive, which is a more formal way of saying train. Departed means that the train has already left.

Related Expressions