Answer :
Answer:
0.117 m
Explanation:
First of all, we can find the wavelength of the wave in the problem, by using the wave equation:
[tex]v=f\lambda[/tex]
where:
v = 350 m/s is the speed of the wave
f = 500 Hz is the frequency of the wave
[tex]\lambda[/tex] is the wavelength
Solving for [tex]\lambda[/tex],
[tex]\lambda=\frac{v}{f}=\frac{350}{500}=0.7 m[/tex]
This means that the distance between two consecutive points of the wave having a difference of phase of
[tex]\phi=2\pi[/tex]
is 0.7 m.
Here we want to find the distance between two points that have a difference of phase of
[tex]\phi'=\frac{\pi}{3}[/tex]
So, we can set up the following rule of three:
[tex]\frac{d}{\phi}=\frac{d'}{\phi'}[/tex]
where d' is the distance we are looking for. Solving for d',
[tex]d'=d\frac{\phi'}{\phi}=(0.7)\frac{\pi/3}{2\pi}=\frac{1}{6}(0.7)=0.117 m[/tex]