Question

A syllable can be uttered in 1/5 s. It is given that an echo represents two syllables. If the velocity of sound is 330 m/s, then the distance of the reflecting surface is:
A. 66.0 m
B. 33.0 m
C. 99.0 m
D. 16.5 m

Answer 1

We know that, for an echo the distance travelled by the sound is twice the distance between source and reflecting surface. Use the relation between distance, velocity and time to determine the distance of the reflecting surface.

Formula Used:
$d = vt$
Here, d is the distance, v is the velocity and t is the time.

Complete step by step answer:
We know that, for an echo the distance travelled by the sound is twice the distance between source and reflecting surface.
Therefore, we can use the relation between distance, velocity and time as follows,
$d = vt$
Here, d is the distance, v is the velocity and t is the time.
We can express the distance travelled by the sound wave as follows,
$2d = {v_s}t$
$\Rightarrow d = \dfrac{{{v_s}t}}{2}$
Here, ${v_s}$ is the velocity of sound and t is the time to utter the syllable.
In the above equation, the term $2d$ represents the distance for an echo of the sound.
We can substitute 330 m/s for ${v_s}$ and 1/5 s for t in the above equation.
$d = \dfrac{{\left( {330\,m/s} \right)\left( {\dfrac{1}{5}\,s} \right)}}{2}$
$\Rightarrow d = 33.0\,m$

Therefore, the distance of the reflecting surface is 33.0 meter.

Hence, the correct answer is option (B).

Note: Remember, the distance for an echo is twice the distance between the source of sound and reflecting surface. The velocity of sound is different for different mediums. It is 330 m/s for the sound wave moving through the air medium. To solve such types of questions, students only need to remember the distance, velocity and time relation. If the time is given in minutes, you need to convert it in seconds as the velocity of sound is usually given in m/s.