A wave of frequency 20 Hz has a velocity of 80 m/s. a. How far apart are two points whose displacements are 30°apart in phase?b. At a given point, what is the phase difference between two displacements occurringat times separated by 0.01 s

The two points are 0.33 m  far apart

The phase difference between two displacements occurring at times separated by 0.01 s = 72°

Explanation:

Given that:

frequency of the wave (n) = 20 Hz

the velocity of the wave = 80 m/s

We can determine the wavelength () =

() =

() = 4 m

In order to determine how far apart the two points whose displacements are 30°apart in phase; we have the phase difference (∅) at  30° = rads

For path difference () , there is phase difference of 2π

Therefore, we can say that:

∅ =

x =

x =

x = 0.33 m

b)

At a given point, what is the phase difference between two displacements occurring at times separated by 0.01 s

If (t) = 0.01 seconds

Then; path difference (x) = v × t = 80 ×  0.01

= 0.8 m

phase difference can therefore be calculated as:

=

= 72°

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