Similar to a sigh, but not exactly a sigh.
Sighlike things might make people feel tired or bored.
Examples:
Her yawn was sighlike.
The sound was sighlike, but not quite a sigh.
The music was sighlike and made me want to sleep.
The cat's meow was sighlike, as if it was tired of waiting for food.
The teacher's voice was sighlike, making the students feel sleepy.
The room was filled with a sighlike silence.