On a calm evening a temperature inversion forms a sharp horizontal boundary between a warm layer of air near the ground (medium A) and a cooler layer above it (medium B). The speed of sound is 349ms−1 in the warm layer and 331ms−1 in the cool layer. A loudspeaker located just below the boundary emits a steady 440Hz tone directly upward.
(a) Explain why the frequency of the sound does not change as the wave crosses from medium A into medium B, even though its speed does.
(b) Without performing numerical calculations, describe qualitatively how the wavelength of the sound in medium B compares with that in medium A. State which medium has the shorter wavelength and provide reasoning.
(c) An observer standing well above the boundary hears the tone. Discuss whether the perceived pitch differs from that heard by someone beside the loudspeaker, and justify your answer.