Your brother is insisting that you'll never hear a sound produced behind a barrier wall at the end of your yard. you notice that the door within the wall is open and quickly explain to him that the sound will be able to reach you due to

Explanation:

The sound is a longitudinal wave that when it hits an obstacle is reflected, but in the part where the door is open it does not find the obstacle, so the diffraction phenomenon can occur if the incident wavelength is less than or equal to the size of the opening.

This diffraction phenomenon is well known and gives rise to part where the sound has a high intensity and others where it is attenuated, following the relationship

   sin θ = λ / a

Where the angle is measured from the center of the opening, a  is the width of the door and λ is the wavelenght of sound.

If we analyze the audible frequencies a little, they are in the range of 20 Hz to 20000Hz, and since the sound velocity is of the order of 343m / s, we can look for its wavelength range

    v = λ f

    λ = v / f

Therefore, the wave languages are in the range of 17 m to 0.017 m, so we can see that almost all wavelengths can pass through the diffraction phenomenon.

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