Two identical speakers are mounted on a wall and sparated by 3.77m as shown in t

Question

Two identical speakers are mounted on a wall and sparated by 3.77m as shown in the diagram below. They emit sounds coherently of exactly same frequency of 114 Hz.

A) Will a person at point 'ear' hear a loud or quite sounds? Support your clam with calculations.

B) You now increase the frequency slowly. Find the next frequency at which the person at 'Ear' hears an opposite type of interference as in part (A)?

Two identical speakers are mounted on a wall and separated by 3.77m as shown in the diagram below. They emit sounds coherently of exactly same frequency of 114 Hz. Will a person at point 'ear' hear a loud or quite sound? Support your clam with calculations. You now increase the frequency slowly. Find the next frequency at which the person at 'Ear' hears an opposite type of interference as in part (A)?

Explanation / Answer

1) we first try to find the wavelength of the sound wave which is

=v/f = 3m here we have taken speed of sound to be 342m/s

now we calculate the path travelled by the second speaker

= root(4^2 + 3.77^2) = 5.5 m

thus the path difference between the sound from first and the second speaker

= 5.5m - 4m = 1.5 m

phase difference between the two waves = 2*(pi)*delta(L) / Lamda = 1.5 m/ 3m = pi

thus the twowaves interfere with phase difference of pi. Thus they destructively interfere and thus we observe very less sound.

2) now for the sound to be loud the wavelength sould be satisfy

2*(pi)*delta(L) / Lamda = 2*pi

thus delta(L) = Lamda = 1.5m

thus frequency = v/lamda= 342 / 1.5 = 228 Hz.

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