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A wave of frequency 500Hz has a wave velocity of 350ms1 .
1) Find the distance between the two points which has 600 out of phase.
2) Find the phase difference between two displacements at a certain point of time 103s apart?

Answer
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Hint: In this question, we will first calculate the wavelength of the wave from the velocity and the frequency already given to us. Then we shall use the relation that a phase difference of 2π is equivalent to a path difference of λ and calculate the path difference by substituting the required values in the formula x=ϕλ2π . Further we shall calculate the distance travelled by the wave using the time given to us. Again, making proper substitutions, we will get our answer.

Complete step by step answer:
The velocity of the wave is given to be V=350ms1
Also, frequency of the wave is given to be υ=500Hz
The wavelength, frequency and the velocity of the wave are related as V=λυ where V is the velocity of the wave, λ is the wavelength of the wave and υ is the frequency of the wave.
 Substituting the known values, we get,
350500=λ
λ=0.7m
 1) We are supposed to calculate the distance between the two points given that they have a phase of 600
The same phase difference expressed in radians is equal to ϕ=π3
A phase difference of 2π is equivalent to a path difference of λ
Hence, we can say that if the path difference is x for a phase difference of ϕ=π3
ϕ=2πxλ
This can be rewritten as
x=ϕλ2π
Substituting the known values, we get,
x=π×0.76π
x=0.116m
 2) The velocity of the wave is given to be V=350ms1
The time taken is given as t=103s
So, the distance travelled by the wave is equal to x=vt where x is the distance travelled.
Substituting in the equation, we get,
x=350×103
x=0.35m
So, now we know the path difference and we are supposed to calculate the phase difference.
Using the same relation as used before, we have,
 ϕ=2πxλ
Substituting the values, we get,
ϕ=2π×0.350.7
ϕ=π

Note: The phase difference refers to the magnitude of the difference in the phase. It can be both leading or lagging. It should be specified which quantity is leading and which is lagging. In this particular question, we didn’t specify the lead or lag because we were supposed to deal with quantities that could be calculated without knowing whether it is a lead or lag.