Physics

Problem

20^{\circ}\text{C}

, a student standing at a distance

d

from a vertical cliff claps and hears the echo after

2.4\,\text{s}

. Two weeks later, when the temperature is

40^{\circ}\text{C}

, he moves

60\,\text{m}

closer to the cliff and now hears the echo after

2.0\,\text{s}

. Taking the temperature dependence of sound speed into account, calculate the original distance

d

(in m). a)

400

433

412

500

Intuitive explanation

The key is recognizing that sound speed changes with temperature—it increases as $v = v_0 + kT$ for some constant $k$ . Each scenario gives you a relationship between distance, time, and speed: the sound travels to the cliff and back, so $2d = v \cdot t$ . Set up two equations (one for each temperature and position), use the temperature dependence to link the two speeds, and solve the system to find $d$ .

Intuitive explanation

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