A hunter fires a gun at a point 408 m away from a cliff. If he hears an echo 2.4 s later, determine the speed of the sound wave

Analyze the question: Sound travels from the hunter to the cliff and back again, so the total distance covered is twice the distance to the cliff.

Concept: For an echo,

speed = total distance ÷ time = 2d / t

Solution:

• Distance to cliff, d = 408 m
• Time for echo, t = 2.4 s
• Total distance = 2 × 408 = 816 m

v = 816 / 2.4 = 340 m/s

Answer: The speed of the sound wave is 340 m/s.

Why not D? Option D (680 m/s) is what you get if you forget that the sound travels there and back and use 408/2.4 × 4, or a similar slip. The most common mistake is using 408 m alone, which gives 170 m/s. That isn't an option, but it shows why you must double the distance.

Tip: In every echo question, remember "there and back": use 2d = vt. Also, 340 m/s is the typical speed of sound in air, so if your answer lands near this value, it's a good sign you've done it right.