How far must the wall be?

The idea

Two sounds are heard separately only if they arrive at least 0.1 s apart, so with sound at 340 m s⁻¹ (34 m there and back) an echo needs a reflecting surface at least 17 m away.

Small room, big hall

You clap in a small room and hear nothing but the clap. You clap facing a far wall in a big empty hall and hear the clap again.

Why do you think the small room gives no echo?

• The reflected sound returns too quickly to be heard as separate
• Small rooms have no walls
• Sound cannot reflect indoors

Move the wall

Use the slider to change the distance to the wall. Sound travels at 340 m s⁻¹.

At least 0.1 s, at least 17 m

If the time gap between two sounds is at least 0.1 s, we hear them as separate sounds. In 0.1 s, sound at 340 m s⁻¹ travels 340 × 0.1 = 34 m. This is the distance to the surface and back, so the surface must be at least half of it, 17 m, away.

We hear two sounds as separate only if they arrive at least 0.1 s apart. With sound at 340 m s⁻¹, it travels 34 m in 0.1 s, to the surface and back, so an echo needs a reflecting surface at least 17 m away.

Notes

For an echo, the gap must be at least 0.1 s. At 340 m s⁻¹ sound travels 34 m (there and back) in 0.1 s, so the surface must be at least 17 m away.

Check yourself

What is the least time gap for hearing two sounds as separate?

Sound travels at 340 m s⁻¹. How far does it travel in 0.1 s, in m?

Answer: 34 m

Distance = 340 m s⁻¹ × 0.1 s = 34 m.

The sound travels 34 m from the source to the surface and back. What is the minimum distance of the reflecting surface from the source, in m?

Answer: 17 m

The 34 m is there and back, so the surface is 34 ÷ 2 = 17 m away.

A wall is 10 m from you. Will you hear a separate echo of a clap?

• 0.1 s — correct. Yes!
• 0.01 s. If the time gap is less than 0.1 s, we cannot clearly tell the two sounds apart.
• 1 s. A gap of at least 0.1 s is enough to hear two sounds as separate.
• Yes, because the wall is hard. The wall must also be at least 17 m away. At 10 m the sound goes there and back in less than 0.1 s.
• No, because the sound returns in less than 0.1 s — correct. Yes!
• Yes, because a wall reflects sound. An echo needs a time gap of at least 0.1 s, so the surface must be at least 17 m away.