Answer :
Answer:
1) [tex]x_{1}=x_{n}-d=0.518-0.204=0.314 m[/tex]
2) [tex]x_{2}=x_{1}-d=0.314-0.204=0.11 m[/tex]
3) [tex]x_{2}=x_{1}-d=0.518+0.204=0.722 m[/tex]
4) [tex]x_{2}=x_{1}-d=0.722+0.204=0.926 m[/tex]
Explanation:
Let's recall that two antinodes are required for a complete wavelength in standing waves which are produced by the facing speakers.
The equation for the spacing between two nodes of a stationaty wave is:
[tex]d=\frac{\lambda}{2}[/tex] (1)
Now, we know that velocity of a sound wave is:
[tex]v=f\lambda[/tex] (2)
We can solve the equation 1 for λ and put it on equation 2
[tex]v=2fd[/tex]
[tex]d=\frac{v}{2f}=\frac{343}{2*840}=0.204m[/tex]
The antinode is formed in the half distance between both speakers, so:
x = 1.24/2 = 0.62 m
The location of the node will be:
[tex]x_{n}=x-d/2=0.62-(0.204/2)=0.518 m[/tex]
Therefore the nodes will be:
1) [tex]x_{1}=x_{n}-d=0.518-0.204=0.314 m[/tex]
2) [tex]x_{2}=x_{1}-d=0.314-0.204=0.11 m[/tex]
3) [tex]x_{2}=x_{1}-d=0.518+0.204=0.722 m[/tex]
4) [tex]x_{2}=x_{1}-d=0.722+0.204=0.926 m[/tex]
I hope it helps you!