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Question

Two travelling sinusoidal waves are described by the wave functions 
y1=10sin[π(8x1400t)]
and y2=10sin[π(8x1400t0.5)] Where x, y1, and y2 are in metres and t is in seconds . which of the following options is/are correct ?


Correct Answer
A
Amplitude of the resultant wave is 102 m
Correct Answer
B
Frequency of the resultant wave  is  700 Hz
Your Answer
C
Time period of the resultant wave is 0.1 s
Your Answer
D
None of these

Solution

The correct options are
A Amplitude of the resultant wave is 102 m
B Frequency of the resultant wave  is  700 Hz
Given wave functions are
y1=10sin[π(8x1400 t)]    .....(1)
y2=10sin[π(8x1400t0.5)]    ......(2)
Comparing these with the general equation, 

y=Asin(kxωt+ϕ) 

Phase difference between (1) and (2) is given by ϕ=π2

Now, According to the principle of superposition, the resultant wave function will be :
y=y1+y2

From (1) and (2), we can conclude that the waves are moving in the same direction, so we can write the above equation as 
yr=y1+y2

yr=2A0cos(ϕ2)sin(kxωtϕ2)

Using the given data,

yr=(2×10)cos(π4)sin[π(8x1400t)π4]

yr=102sin[π(8x1400t)π4]

So,
Resultant amplitude Ar=102 m
Resultant Angular frequency ωr=1400π
frequency of resultant wave  f=1400π2π=700 Hz
Time period (T)=1f=1700=0.0014 sec 

Thus, options (a) and (b) are the correct answers.

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