The time taken by echo to be heard

t = \(\frac{2d}{v}\)

where d = distance between the reflecting surface and source of sound and v = speed of sound in air. As we know that speed of sound increases with increase in temperature. So on a hotter day speed of sound will be higher, so the time after which echo is heard will decrease.

If time taken by the reflected sound is less than 0.15 after the production of original sound, then echo is not heard.

The speed of sound increases on a hotter day (when the temperature is high) and it requires a larger distance from the reflecting surface for the eacho to be hard. Since the distance between the reflecting surface and the source of sound remains the same, no echo can be heard on a hotter day.

The minimum distance (d) for the distinct echo to be heard (say at `22^@ C`) is `17.2 m` (as `2 d = v t = 344 xx 0.1 = 34.4 m`). On a hotter day, the temperature increases and the speed of sound in air also increases. For example, at `40^@ C`, speed of sound i.e., `v ~= 356 m//s` and as such `2 d = 356 xx 0.1 = 35.6 m` or `d = 17.8 m`. Thus, if the distance of the reflecting surfece and the source of sound remains the same `(i.e., 17.2 m)`, no echo is heard on the hotter day as the minimum distance noe required is `17.8 m`.