Two persons X and Y are standing at a distance of
100 m from a high wall as shown in the given figure.
When X gives a clap, the time interval between the
two (direct and reflected) sounds heard by Y is 0.2 s.
If the speed of sound is 330 m s', then the distance
d between X and Y is
Answers
The distance between x and y is d = 270 m
Explanation:
The sound of the clap given by X travels directly to Y at time:
td = d / v = d / 330
- The sound that gets reflected by the wall travels, first to the wall at the point that corresponds to the middle point between X and Y, then travels to Y.
- The distance it travels can be calculated as:
l = 2 √ (100) ^2 + (d / 2)^ 2 = √ (200)^ 2 + d^ 2
This part of the sound reaches Y at time:
t r = l / v = √ (200)^ 2 + d^ 2 / 330
The reflected sound should reach Y 0.2 s later than the direct sound, we can solve for the distance "d".
t r − t d = 0.2
√ (200 )^2 + d^ 2 / 330 − d / 330 = 0.2
( 200)^ 2 + d ^2 − d = 66
√ (200)^ 2 + d^ 2 = d + 66
(200 )^2 + d^ 2 = d^ 2 + 66^ 2 + 132 d
(200 )^2 − 66^ 2 = 132 d
d = ( 200)^ 2 − 66 ^2 / 132
d = 270 m
Hence the distance between x and y is d = 270 m
Also learn more
Find the frequency of sound waves in air if the distance between a compression and an adjacent rarefaction is 0.5 mm . Speed of sound waves in air is 330 m/s ?
https://brainly.in/question/11503748
Answer:
270 m twuathzfjdykdykdykdyktsjstjysm