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A girl claps in front of a wall and wind blows from girls towards the wall at the speed of \[20m/s\]. If she is standing at a distance of \[50m\] from the wall, then she will hear an echo of claps sound after: (Speed of sound in air=\[330m/s\])
A) \[0.3s\]
B) \[0.6s\]
C) \[1.2s\]
D) \[0.9s\]

Last updated date: 20th Jun 2024
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Hint: In case of echo, distance travelled is twice as tice as the sound reflects back. The wind blows in the direction of the sound, therefore, the magnitude of resultant velocity increases. The speed of sound can be calculated by the distance travelled as per unit of time by the sound wave through an elastic medium.

Complete step by step answer:
The speed of wind blowing\[ = 20m/s\]
The speed of sound in still air=\[330m/s\]
Distance between girl and the cliff\[ = 50m\]
Now, here as we need to calculate the time taken to hear the echo, the sound must reflect, since the sound is reflected, it covers twice the distance\[ = 100m\].
Given the wind blows in the direction towards the wall. Therefore, the velocity of sound increases and the resultant velocity of sound becomes:
The velocity of sound in still air\[ + \]velocity of the wind.
Thus, the resultant velocity is \[(330 + 20 = 350m/s)\].
We know,
\[v = \dfrac{d}{t}\]
v= velocity
d=Distance travelled
t=Time taken

Rearranging the equation, we obtain:
\[t = \dfrac{d}{v}\]
Putting the known values in the above equation:
\[t = \dfrac{{100}}{{350}}\]
Thus, we obtain the time taken to be \[0.28s \cong 0.3s\].

Thus the required answer is option (B) =\[0.3s\].

Note: It is important to note that the distance covered is twice the distance between the girl and the wall as the sound is getting reflected. The conditions for echo to take place is that the distance between the source and the reflecting surface must not be less than \[17m\], and the time interval between hearing the original and reflected sound must be at least \[0.1s\].