A mountaineer standing on the rim of a deep canyon shouts loudly. The air inside the canyon is filled with cold fog in which the speed of sound is 300m/s, while the warmer air above the rim has a speed of sound of 343m/s. The mountaineer hears two distinct echoes:
• the first echo, from the canyon floor directly below, after 1.8s,
• the second echo, from the opposite vertical rock face at the same rim level, exactly 0.5s after the first echo.
(a) Calculate the depth of the canyon.
(b) Assuming the sound that produces the second echo travels entirely through the warmer air layer, determine the horizontal width of the canyon between the mountaineer and the opposite rock face. Show all stages of your reasoning.