
A string has a mass per unit length of . The equation of the simple harmonic wave produced in it is 4=0.2 . The tension in the string is
A. 0.0016 N
B. 0.16 N
C. 16 N
D. 1.6 N
Answer
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Hint: We are provided with an equation of simple harmonic wave, which we can compare with the general equation of SHM of simple harmonic wave. We can compare with standard form . Tension acts on anybody when it is subjected to a pulling force. Additionally, because the string is under SHM has a velocity associated with it. Use the formula of tension in the string which has relation between velocity and mass, to find the required answer. When it is subjected to pull and while performing motion it has velocity so use a formula of tension in the string which will give a relation between velocity and mass.
Formula used:
Formula of tension in the string is given by,
Where,
= tension in the string
V = velocity of the waves
= linear density/mass per unit length
Complete step by step answer:
The definition of simple harmonic motion is given as a body of linear periodic motion in which the restoring forces/acceleration is always directly proportional to the displacement from the mean position (magnitude of restoring force) and directed towards the mean position.
The standard equation of S.H.M is given as,
--
Where, y= displacement
Spring constant/force constant
Angular velocity
Time
Amplitude
The equation of simple Harmonic motion or wave produced in it is given as,
--- (2)
Compare equation (2) with (1), we get
; ;
Now we need to calculate the velocity of the wave. So from above data we can calculate velocity of wave which is given as
---- (3)
Put the value in above equation (3), we get
Hence velocity of the wave is
In question we have given mass of string per unit length which is donated as
Therefore
Convert into
We get
Let be the tension then tension in the string
Therefore tension in the string is given as
Therefore option (B) is the correct option.
Note:
Tension does not possess any kind of component perpendicular to it. Tension (T) is always directed towards the line of string. Tension acts on the body on a string when it is subjected to pull. Tension is one of the types of force which acts on a string or body when weight or mass is applied to it and it gets pulled by that mass.
Formula used:
Formula of tension in the string is given by,
Where,
V = velocity of the waves
Complete step by step answer:
The definition of simple harmonic motion is given as a body of linear periodic motion in which the restoring forces/acceleration is always directly proportional to the displacement from the mean position (magnitude of restoring force) and directed towards the mean position.
The standard equation of S.H.M is given as,
Where, y= displacement
The equation of simple Harmonic motion or wave produced in it is given as,
Compare equation (2) with (1), we get
Now we need to calculate the velocity of the wave. So from above data we can calculate velocity of wave which is given as
Put the value in above equation (3), we get
Hence velocity of the wave is
In question we have given mass of string per unit length which is donated as
Therefore
Convert
We get
Let
Therefore tension in the string is given as
Therefore option (B) is the correct option.
Note:
Tension does not possess any kind of component perpendicular to it. Tension (T) is always directed towards the line of string. Tension acts on the body on a string when it is subjected to pull. Tension is one of the types of force which acts on a string or body when weight or mass is applied to it and it gets pulled by that mass.
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