
The equation of a progressive wave where is the time in second is the distance in meter is . The phase difference (in SI unit) between two position apart is
A.40
B.20
C.10
D.5
Answer
490.8k+ views
Hint: We will use the definition of phase difference in this question. The lateral difference between two or more waveforms along a common axis and the same frequency sinusoidal waveforms is known as phase difference. The phase differential equation would therefore be: ,where propagation wave vector, angular frequency, time, position vector, maximum amplitude.
Formula used:
, where path difference, and .
Complete answer:
According to the question the equation for a progressive wave is , where is the time in second is the distance in meter.
So, we can also write the above equation as follows,
-------equation (1)
Now if we see the standard equation for the progressive wave, which is as
---------equation (2)
On comparing the equation (1) and equation (2), we see that
and
Now we have to find phase difference, formula for the phase difference is,
------equation (3), where path difference.
Here it is given in the question, the path difference = and we know that the , So putting the values in the equation (3), we get
Hence the phase difference (in SI unit) between two positions apart is .
So, option (C) is the correct answer.
Note:
In these types of questions it is best to consider the basic concepts such as progressive waves, i.e. a wave that moves in the same direction continuously in a medium without the change in its amplitude. Let's take one example on a string of a progressive wave. So, here we'll define the displacement relationship of any element on the string as a function of time, and the vibration of the string elements along the length at a given time.
Formula used:
Complete answer:
According to the question the equation for a progressive wave is
So, we can also write the above equation as follows,
Now if we see the standard equation for the progressive wave, which is as
On comparing the equation (1) and equation (2), we see that
Now we have to find phase difference, formula for the phase difference is,
Here it is given in the question, the path difference =
Hence the phase difference (in SI unit) between two positions
So, option (C) is the correct answer.
Note:
In these types of questions it is best to consider the basic concepts such as progressive waves, i.e. a wave that moves in the same direction continuously in a medium without the change in its amplitude. Let's take one example on a string of a progressive wave. So, here we'll define the displacement relationship of any element on the string as a function of time, and the vibration of the string elements along the length at a given time.
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