Question

The drawing shows a loudspeaker A and point C, where a listeer is positioned. A second loudspeaker B is located somewhere to the right of A. Both speakers vibrate in phase and are playing a 62.8-Hz tone. The speed of sound is 349 m/s. What is the closest to speaker A that speaker B can be located, so that the listener hears no sound?

Answer 1

Answer: 4.17m

Explanation:

The observer at C will hear a sound on no sound upon whether the interference is constructive or destructive.

If the listeners hears sounds it is caled constructive interference but if he hears no sound its called destructive interference.

So

d2 - d1 = (n *lamba)/ 2

Where n=1,3,5

lamda=v/f =349/62.8

lamda=5.56m

d2= d1 + nlamda/2

d2= 1 + 5.56/2

d2= 3.78m

X'= 1 cos 60= 0.5m

Y= 1 sin60= 0.866m

X"^2 + Y^2 =d2^2

X" =√(y^2 - d2^2)

X"=√(3.78^2 - 0.886^2)

X"= 3.67m

So therefore the closest that speaker A can be to speaker B so the listener does not hear any sound is X' + X"= 0.5 + 3.67

4.17m