Physics

Physics

Problem

On a winter morning at 0∘C0^{\circ}\text{C}, an echo from a cliff is heard 0.90 s0.90\,\text{s} after a shout. If the observer remains at the same place, how long (in s) will the echo take on a summer afternoon when the air temperature is 25∘C25^{\circ}\text{C}? a) 0.900.90 b) 1.041.04 c) 0.860.86 d) 0.940.94
Intuitive explanation

The key insight is that sound travels faster in warmer air because molecules move more energetically, so the speed of sound increases with temperature. Since the distance to the cliff stays fixed, a faster sound speed means the round-trip journey takes less time. You'll need to find how sound speed depends on temperature, then use the ratio of speeds to find the new echo delay.

Intuitive explanation

The key insight is that sound travels faster in warmer air because molecules move more energetically, so the speed of sound increases with temperature. Since the distance to the cliff stays fixed, a faster sound speed means the round-trip journey takes less time. You'll need to find how sound speed depends on temperature, then use the ratio of speeds to find the new echo delay.

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