Q#691: (Past Exam Paper – June 2013 Paper 23 Q5)
[Waves > Superposition]
(a) Explain the principle of superposition.
(b) Sound waves travel from source S to a point X along two paths SX and SPX, as shown in Fig.1.
(i) State phase difference between these waves at X for this to be the position of
1. a minimum,
2. a maximum.
(ii) Frequency of the sound from S is 400 Hz and speed of sound is 320 m s–1. Calculate wavelength of the sound waves.
(iii) Distance SP is 3.0 m and distance PX is 4.0 m. Angle SPX is 90°. Suggest whether a maximum or a minimum is detected at point X. Explain your answer.
Solution 691:
(a) When waves overlap / meet, the resultant displacement is the sum of the individual displacements of the waves.
(b)
(i)
1. Phase difference for minimum = 180 º / (n + ½) 360 º
2. Phase difference for maximum = 0 / 360 º / (n360 º)
(ii)
Speed v = f λ
Wavelength λ = 320 / 400 = 0.80 m
(iii)
{Path difference = 7 – 5 = 2m. Wavelength λ = 0.80m. In terms of λ, a path difference of 2m is equal to 2 × (λ / 0.80) = 2.5 λ.}
Path difference = 7 – 5 = 2 (m) = 2.5 λ
Hence a minimum is detected at point X.
OR maximum if phase change at P is suggested
{If a phase change occurred at point P, then a maximum could be obtained at point X. The condition for destructive interference: 180 º / (n + ½) 360 º is for coherent sources (waves from these sources are in phase)}
Post a Comment for " (a) Explain the principle of superposition. (b) Sound waves travel from source S to a point X along two "