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Question

Two point sources of sound are kept at a separation of 10cm. They vibrate in phase to produce waves of wavelength 5cm. What would be the phase difference between the two waves arriving at a point 20cm from the source.

  1. on the line joining the sources and
  2. on the perpendicular bisector of the line joining the sources?

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Solution

Step 1: Given data

Wavelength, λ=5cm

Distance between the slits=10cm

Step 2: To find

We have to find the phase difference between the two waves arriving at a point 20cm from one source.

Step 3: Formula used

Path difference,

x=x1-x2

Phase difference,

ϕ=2π×xλ

where λ is the wavelength

Step 4: The phase difference between the two waves arriving at a point 20cm from one source on a line joining the sources.

x1=20+10=30cmx2=20cm

Path difference,

x=x1-x2=30-20=10cm

Phase difference,

ϕ=2π×xλϕ=2π×105ϕ=2π×2

Since it is a multiple of 2π, the phase difference will be 0

Step 5: The phase difference between the two waves arriving at a point 20 cm from on the perpendicular bisector of the line joining the sources.

From, the figure, it is clear that y1=y2

Therefore, path difference,

y=y1-y2=0

Phase difference,

ϕ=2π×yλϕ=2π×0λϕ=0

Here the phase difference is 0.

In both cases, a and b, the phase difference is 0.


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