During early morning hours a layer of mist forms close to the ground, making the air near the surface humid while the air just above remains comparatively dry. A farmer standing 1000m from a temple hears the first stroke of the temple bell.
Take the following average speeds at 15∘C:
Speed of sound in dry air =340m/s
Speed of sound in humid air =343m/s
(i) Calculate the time taken for the sound to reach the farmer (a) through the dry air layer and (b) through the humid layer, assuming each layer extends the full 1000m separately.
(ii) Find the percentage difference between the two times obtained in part (i).
(iii) The farmer actually hears the bell after a time closer to the value calculated for humid air even though both layers are present. Write a reasoned account, in about 80–100 words, to explain how humidity influences the density of air and thereby the speed of sound, helping the humid layer to dominate the overall travel time.