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TOPIC 11: Sound
Echo problems are teachers' favourites in exams because they are usually more challenging. Remember to multiply by a factor of '2' to the distance between the source and the reflecting wall, in order to get the distance traveled by the sound wave.
Example: I stand between two opposite-facing walls separated by 425m and shout. The time interval between hearing the first echo and second echo is 1.5 seconds. How far am I standing from each wall?
Solution: Let x be the distance from me to the nearer wall; and y the distance from me to the further wall. Therefore x + y = 425m
The distance travelled by the first echo was 2x (towards the wall and then back to me), so the time it took was 2x/340 seconds (speed of sound is taken as 340 m s-1). Similarly, the distance traveled by the second echo was 2y, so the time it took was 2y/340 seconds. The time interval (1.5 seconds) was the difference between 2y/340 and 2x/340. Therefore 2y/340 - 2x/340 = 1.5
Equation 1: x + y = 425
Equation 2: 2y/340 - 2x/340 = 1.5
Two equations, two unknowns. Solving by simultaneous equation, we get x = 85m and y = 340m.
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