Waves
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Question : 10
Total: 27
For the travelling harmonic wave
y ( x , t ) = 2.0 c o s 2 π ( 10 t − 0.0080 x + 0.35 )
Where x and y are in cm and t in s. Calculate the phase difference between oscillatory motion of two points separated by a distance of
(a) 4 m
(b) 0.5 m
(c)
(d)
Where x and y are in cm and t in s. Calculate the phase difference between oscillatory motion of two points separated by a distance of
(a) 4 m
(b) 0.5 m
(c)
(d)
Solution:
Given equation of a travelling harmonic wave is
y ( x , t ) = 2.0 c o s 2 π ( 10 t – 0.0080 x + 0.35 )
The standard equation of a travelling harmonic wave is
y ( x , t ) = A cos [
t −
x + ϕ 0 ]
Comparing equation(i) and (ii), we get
= 2 π × 0.0080 c m − 1
= 2 π × 10 ϕ 0 = 0.35
We know that,
phase difference =
×
(a) When path difference = 4m = 400 cm, then from (iv)
phasedifference =
× 400 = 6.4 π
(b) When path difference = 0.5 m = 50 cm, then
phase difference= 2 π × 0.0080 × 50 = 0.8 π
(c) When path difference =
phase difference =
×
= π
(d)When path difference=
phase difference =
×
=
= ( π +
)
∴ effective phase difference =
The standard equation of a travelling harmonic wave is
Comparing equation(i) and (ii), we get
We know that,
phase difference =
(a) When path difference = 4m = 400 cm, then from (iv)
phasedifference =
(b) When path difference = 0.5 m = 50 cm, then
phase difference
(c) When path difference =
phase difference =
(d)When path difference
phase difference =
∴ effective phase difference =
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