Question

A child standing between two large buildings claps and hears the echo from the first building in 0.2 seconds and the echo from the second building in 0.3 seconds. (Speed of sound in air = \(340\ \text{m/s}\))

• [(a)] What is the condition to produce an echo?
• [(b)] Calculate the distance between the two buildings.

Hint:

Echo distance formula: \( d = \frac{vt}{2} \)
Always divide by 2 because sound travels to the object and back.

Answer 1

Concept: Echo and Sound Reflection
An echo is produced due to reflection of sound waves from a distant surface. Part (a): Condition to produce an echo
Step 1: Time condition}
For a distinct echo to be heard, the reflected sound must reach the ear after at least: \[ 0.1 \text{ seconds} \] Step 2: Minimum distance condition}
Using speed of sound: \[ \text{Minimum distance} = \frac{v \times t}{2} = \frac{340 \times 0.1}{2} = 17 \text{ m} \] Conclusion (a): \[ \text{Reflecting surface must be at least 17 m away} \] Part (b): Distance between two buildings
Step 1: Distance to first building}
Echo time = \(0.2\) s (round trip) \[ d_1 = \frac{v \times t}{2} = \frac{340 \times 0.2}{2} = 34 \text{ m} \] Step 2: Distance to second building}
Echo time = \(0.3\) s \[ d_2 = \frac{340 \times 0.3}{2} = 51 \text{ m} \] Step 3: Total distance between buildings}
\[ \text{Distance} = d_1 + d_2 = 34 + 51 = 85 \text{ m} \] Conclusion (b): \[ \text{Distance between buildings} = 85 \text{ m} \]