Question

George yells from one side of the Grand Canyon and records the time it takes to hear an echo. He repeats the process in Antelope Canyon. The time recorded for Antelope Canyon is shorter than for the Grand Canyon. Which is the most likely conclusion based on this information?

A) The rock in the Grand Canyon is denser than the rock in Antelope Canyon.
B) The rock in the Grand Canyon is stiffer than the rock in Antelope Canyon.
C) The distance across Antelope Canyon is longer than the distance across the Grand Canyon.
D) The distance across the Grand Canyon is longer than the distance across Antelope Canyon.

Answer 1

The correct option D. The distance across the grand canyon is greater than the distance across the Antelope canyon.

Echoes occur due to reflection of sound. Sound is a mechanical wave which travels in air as a longitudinal wave. When sound wave falls on a smooth surface, it undergoes reflection. If the distance between the source of the sound and the reflector is d and if the sound takes a time t to travel from the source to the reflector and then back to the source, it travels a distance 2d in the time t. If the speed of sound in air is v, then,

`v=(2d)/(t)`

Therefore, the distance between the source and the reflector is given by,

`d= (vt)/(2)`

The speed of sound in any medium is a constant at a particular temperature. Both Grand canyon and Antelope Canyon are mad of rocks, which can reflect sound. Therefore, if the time taken for the echo to reach the person in Grand canyon is greater than the time taken for it to reach in Antelope Canyon, The distance across the Grand Canyon is greater than the distance across the Antelope Canyon.

The denseness or stiffness of a rock cannot change the time of travel of the sound wave. The time taken by a sound wave to travel a certain distance in a medium is governed by the speed of the sound wave in that medium, which is a constant. Hence options A and B are incorrect.

The correct option is therefore D.