Question

When the door of Chapel of mausoleum in Hamilton, Scotland, is slammed shut, the last echo heard by someone standing just inside the door reportedly comes after 15 s later.
(A) If that echo were due to a single reflection off a wall opposite the door, how far from the door is the wall?
(B) If, instead, the wall is 25.7m away, how many reflections (back and forth) occur?

Answer 1

Since the echo was due to reflection from the wall, this means sound has travelled the distance between door to wall twice. To calculate the distance between door and wall use formula for speed i.e. distance=speed x time. Since the echo was due to single reflection therefore no. of echoes produced will be 1.

Complete step by step solution:
The echo is defined as the bouncing back of a sound wave after striking from a surface. An echo is heard when the source and reflecting surface has a minimum distance of 17 meters. Less than this distance echo cannot be distinguished properly. According to the question it is given that, time=15sec.
Part (A)
Since the echo was due to single reflection therefore it covered the distance twice
$D = (n + 1)d = v \times t = 343 \times 15 = 5160m$ [Speed of sound in air is 343m/s]
$d$ = $\dfrac{5160}{2}$ = $2580m$ [Distance between door and wall is half the distance travelled by sound]
Here n=1 because reflection is single.

Part (B)
In this part we have to find the number of reflections
$(n + 1)d = 5160$ Given, d=25.7m
On putting the value of d. we get,
$n = 199.9 \approx 200$times
The reflection of sound is the same as the reflection of light. Sound is reflected from almost all surfaces. After reflection sound travels the distance twice if it is reflected once. And if sound reflects n times then it is given by $D = (n + 1)d$. Sound travels in a wave form and has different speed in different mediums. Sound travels fastest in metals.

Note: To calculate the distance of the source from the reflecting surface basic formula of speed distance relation is used. Also the number of reflections is multiplied with single distance. The medium of propagation also matters in which sound travels. Speed of sound is more in denser medium than in rarer medium.