Question

Two in-phase loudspeakers, which emit sound in all directions, are sitting side by side. One of them is moved sideways by 3.0 m, then forward by 7.0 m. Afterward, constructive interference is observed 14, 12, and 34 the distance between the speakers along the line that joins them, and at no other positions along this line.

What is the maximum possible wavelength of the sound waves?

Express your answer with the appropriate units.

Answer 1

Solution

In the figure show below is ilustrated the case of loudspeakers

In case initial, of differance phase between of the loudspeakers is cero. However for a distance, as follows

In reference in the last figure, the distance between of the loudspeakers is calculated as follows

Now , along the line that the joins them. We see, three points( P, Q and R), with the distance respectivaly 12m , 14m and 34m. In this moment occur the constructive interferance.

In other han the P point( the differance phase)

The Q point

t

The R point

The difference of the phases for both waves.

1) For the P, Q points

But , and the phase difference for both waves is for n=1

Finally for the Q, R points and n=1