With reference to the reflection of sound, what is the condition for hearing a distinct echo?

Correct Option

The correct option is

The total distance covered by sound must be at least 34.4 m (at 22°C).

Explanation

An echo is a distinct repetition of sound produced by the reflection of sound waves from a hard surface. For the human ear to distinguish the reflected sound (echo) from the original sound, the time gap between the reception of the two sounds must exceed the duration of the "persistence of hearing."

Detailed Analysis

• Persistence of Hearing: The sensation of any sound persists in the human brain for approximately 0.1 seconds. If a reflected sound reaches the ear within this interval, it merges with the original sound, causing reverberation rather than a distinct echo. Therefore, the time interval between the original sound and the reflected sound must be at least 0.1 seconds.
• Calculation of Distance:
  • The speed of sound in air at 22°C is approximately 344 m/s.
  • To satisfy the time condition ($t \ge 0.1$ s), the total distance covered by the sound must be calculated using the formula: $\text{Distance} = \text{Speed} \times \text{Time}$.
  • $\text{Total Distance} = 344 \, \text{m/s} \times 0.1 \, \text{s} = 34.4 \, \text{m}$.
• Path of Sound: The sound travels from the source to the reflecting surface and back to the listener. If $d$ is the distance between the source and the reflecting surface, the total distance covered is $2d$.
  • Therefore, $2d \ge 34.4 \, \text{m}$.
  • This implies the reflecting surface must be at a minimum distance ($d$) of 17.2 m.

Evaluation of Options:

• The reflecting surface must be at a distance of at least 344 m. is Incorrect: The reflecting surface needs to be at a minimum distance of approximately 17.2 m, not 344 m.
• The time interval between original and reflected sound must be less than 0.1 s. is Incorrect: The time interval must be at least 0.1 s. If it is less than 0.1 s, the sounds will overlap.
• The total distance covered by sound must be at least 34.4 m (at 22°C). is Correct: As calculated, the total distance traveled by the sound (to the obstacle and back) must be at least 34.4 m.
• The temperature of the air must be 0°C. is Incorrect: Echoes can be heard at various temperatures. Temperature affects the speed of sound, which slightly alters the minimum distance required, but 0°C is not a mandatory condition for the phenomenon itself.

Key Takeaway: To hear a distinct echo, the reflected sound must reach the ear at least 0.1 seconds after the original sound. At 22°C, this requires the total distance traveled by the sound to be at least 34.4 m, meaning the obstacle must be at least 17.2 m away.