9702/May Jun/13/2015/Q29

Wave generators at points X and Y produce water waves of the same wavelength. At point Z, the
waves from X have the same amplitude as the waves from Y. Distances XZ and YZ are as
shown.

When the wave generators operate in phase, the amplitude of oscillation at Z is zero.
What could be the wavelength of the waves?

A 2 cm
B 3 cm
C 4 cm
D 6 cm

Solution:

Answer: C.

The amplitude of oscillation at Z is zero, so destructive interference occurs at Z and the difference between lengths XZ and YZ must be an odd number of half-wavelengths.

Path difference between XY and YZ = 34 – 24 = 10cm

This path difference must be an odd number of half-wavelengths.

(n + ½) λ = 10cm

Wavelength λ = 10 / (n + 0.5)

Put n = 0, Wavelength λ = 10 / (0 + 0.5) = 20cm 

Put n = 1, Wavelength λ = 10 / (1 + 0.5) = 6.67cm

Put n = 2, Wavelength λ = 10 / (2 + 0.5) = 4cm [C is correct]

Put n = 3, Wavelength λ = 10 / (3 + 0.5) = 2.86cm

… 

Reference: PYQ - May/Jun 2015 Paper 13 Q29