Waves
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Question : 9
Total: 27
For the wave described in question no. 8, plot the displacement (y) versus (t) graphs for x = 0, 2 and 4 cm. What are the shapes of these graphs? In which aspects does the oscillatory motion in travelling wave differ from one point to another : amplitude, frequency or phase?
Solution:
The transverse harmonic wave is
y ( x , t ) = 3.0 sin [ 36 t + 0.018 x +
]
Forx = 0
y ( 0 , t ) = 3.0 s i n [ 36 t +
)
Here,ω =
= 36 , T =
=
s e c
On plotting y versus t graph, we obtain a sinusoidal curve as shown in above figure.
Similar graphs are obtained for x = 2 cm and x = 4 cm.
The oscillatory motion in travelling wave differs from one point to another only in terms of phase. Amplitude and frequency of oscillatory motion remain the same in all the three cases.
For
Here,
For different values of t, we calculate y using equation (i). These values are tabulated below :
On plotting y versus t graph, we obtain a sinusoidal curve as shown in above figure.
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The oscillatory motion in travelling wave differs from one point to another only in terms of phase. Amplitude and frequency of oscillatory motion remain the same in all the three cases.
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