Question

Two waves leave the same source in phase. The waves travel along different paths and then meet. The wavelength of the waves is 8.0 cm. Which of the following would cause constructive interference when the waves meet?

A path difference of 16.0 cm
B path difference of 3λ/2
C phase difference of 180°
D phase difference of 3π radians

Answer 1

Constructive interference occurs when the waves are in phase and their amplitudes add up.

A path difference of one wavelength (λ) corresponds to a phase difference of 2π radians, so a path difference of 2λ corresponds to a phase difference of 4π radians, and so on.

Therefore, a path difference of 16.0 cm corresponds to a phase difference of 2π x 16.0 cm / 8.0 cm = 4π radians, which is a multiple of 2π and results in constructive interference.

A path difference of 3λ/2 corresponds to a phase difference of 3π radians, which is also a multiple of 2π and results in constructive interference.

A phase difference of 180° corresponds to a path difference of λ/2, which is not a multiple of the wavelength and results in destructive interference.

A phase difference of 3π radians corresponds to a path difference of 3λ/2, which we already determined results in constructive interference.

Therefore, the answers that would cause constructive interference when the waves meet are A and D.

Answer 2

A path difference of 16.0 cm would cause constructive interference when the waves meet.

Step-by-step explanation:

For constructive interference to occur, the path difference between the waves must be equal to an integer number of wavelengths. In this case, the wavelength is given as 8.0 cm.

Option A gives a path difference of 16.0 cm, which is equal to two wavelengths. Therefore, the two waves will arrive at the meeting point in phase and will reinforce each other, resulting in constructive interference.

Option B gives a path difference of 12.0 cm, which is equal to 1.5 wavelengths. This will result in destructive interference rather than constructive interference.

Option C and D refer to phase differences rather than path differences, and alone they are not enough to determine whether constructive or destructive interference will occur.