Question

Speakers A and B are vibrating in phase. They are directly facing each other, are 8.2 m apart, and are each playing a 78.0 Hz tone. The speed of sound is 343 m/s. On the line between the speakers there are three points where constructive interference occurs. What is the distance of the farthest point from speaker A?

Answer 1

Answer:6.298,4.1,1.9015

Explanation:

Wavelength=$\frac{velocity of sound }{frequency}$

=$\frac{343}{78}$=4.397 m

Distance of 3rd speaker from speaker A is x

From B 78-x

Difference between the distances must be a whole number of wavelengths

First

$x-\left ( 8.2-x\right )=4.397$    for 1 st wavelength

2x=8.2+4.397=12.597

x=6.298m

second

For zero wavelength

$x-\left ( 8.2-x\right )=0$

2x=8.2

x=4.1m

Third

$\left ( 8.2-x\right )-x=4.397$

x=1.9015 m