The Doctor Worries Klausner is Mentally Unstable (Dramatic Irony)
Whenever the narrative point of view shifts to the doctor, the reader learns that the doctor is constantly reading Klausner's frantic, obsessive behavior and trying to assess whether Klausner is having a psychotic episode. With this instance of dramatic irony, Dahl generates tension and introduces conflict to the story by giving the reader insight into details of which Klausner remains unaware.
The Tree Branch Smashes the Machine (Situational Irony)
After Klausner hears the tree in the park make a low growl of pain when it is struck with an axe, he attempts to recreate the experiment by asking the doctor to listen. However, the second axe strike causes one of the tree's largest branches to crackle away from the trunk and land on the machine. In this instance of situational irony, the question of whether Klausner truly heard what he thinks he heard will remain unanswered because the machine is now unusable and the doctor was too distracted by the falling branch to notice whether the tree growled. Adding to the irony, the falling branch follows the theme of personification by suggesting that the tree intentionally ruined Klausner's machine as retribution for wounding it with the axe.