A man stands one-third of the way between two walls and claps his hands, He hears two distinct echoes 1s apart. If…

JAMB 1980

A man stands one-third of the way between two walls and claps his hands, He hears two distinct echoes 1s apart. If the speed of sound is 330ms-1 the distance between the wall is

A. 33m

B. 110m

C. 220m

D. 330m

E. 495m

Correct Answer: Option E

Explanation

the man was standing at one third of d(distance between two walls), that means that he is 2/3 d from the other wall, and the echo were distinct echoes (not same reflection)

so since the v is same, make v subject for the two echoes

first echo distance=1/3d, time =x,

for second echo distance=2/3d, time =(x+1)seconds

from eqn v=2d/t

therefore (2(1/3d))/x =(2(2/3d))/x+1

after solving this u would get x =1

then sub 1 for x in the equation v=2d/t to get ur d, so 330=2(1/3d)/1, d =495

Or 

v=2d/t

but the man stands one third of his distance =⅓d

Therefore, v=2×⅓d/t

330=2×⅓d/1

330=2d/3

Making d the subject formula

2d=330×2

d=990/2

d=495

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