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At t= 0, a transverse wave pulse travelling in the positive x direction with a speed of 2 m/s in a wire is described by the function y = 6/x2 given that x ≠ 0. Transverse velocity of a particle at x = 2 m and t = 2 s is
- a)3 m/s
- b)-3 m/s
- c)8 m/s
- d)-8 m/s
Correct answer is option 'B'. Can you explain this answer?
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At t= 0, a transverse wave pulse travelling in the positive x directio...
Any transverse wave travelling in positive x-direction is of the form y = f (ax - bt) (and y = f (ax + bt) if it is travelling in negative x-direction) and has a wave speed equal to b/a.
Given a = 1 ⇒ b = 2
Given a = 1 ⇒ b = 2
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At t= 0, a transverse wave pulse travelling in the positive x directio...
Any transverse wave travelling in positive x-direction is of the form y = f(ax - bt) (and y = f(ax + bt) if it is travelling in negative x-direction) and has a wave speed equal to b/a. 
Given a = 1 => b = 2
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At t= 0, a transverse wave pulse travelling in the positive x directio...
Given information:
- At t=0, a transverse wave pulse is travelling in the positive x direction with a speed of 2 m/s in a wire.
- The wave pulse is described by the function y = 6/x^2, where x is greater than 0.
To find: Transverse velocity of a particle at x = 2 m and t = 2 s.
Let's solve this step by step:
Step 1: Understanding the given function y = 6/x^2
The given function represents the displacement of the wave pulse as a function of position (x). The expression y = 6/x^2 indicates that the displacement decreases as x increases. This suggests that the wave pulse is spreading out as it travels.
Step 2: Finding the position of the particle at t = 2 s
Since the wave pulse is travelling at a speed of 2 m/s, we can determine the position of the particle at t = 2 s using the formula x = vt, where v is the velocity and t is the time.
Given v = 2 m/s and t = 2 s, substituting these values into the formula, we get:
x = 2 m/s * 2 s = 4 m
Step 3: Finding the transverse velocity at x = 2 m and t = 2 s
To find the transverse velocity of the particle at x = 2 m and t = 2 s, we need to differentiate the given function with respect to time (t) and then substitute the values of x and t into the derivative.
Differentiating y = 6/x^2 with respect to t:
(dy/dt) = 0 (since there is no explicit dependence on time in the given function)
Substituting x = 2 m and t = 2 s into (dy/dt), we get:
(dy/dt)|x=2,t=2 = 0
Therefore, the transverse velocity of the particle at x = 2 m and t = 2 s is 0 m/s.
Step 4: Comparing the result with the given options
The correct answer is option 'B' (-3 m/s), which is not the same as the result obtained in Step 3. It seems that there might be an error in the options or a misinterpretation of the problem. Please double-check the options or provide additional information to resolve the discrepancy.
- At t=0, a transverse wave pulse is travelling in the positive x direction with a speed of 2 m/s in a wire.
- The wave pulse is described by the function y = 6/x^2, where x is greater than 0.
To find: Transverse velocity of a particle at x = 2 m and t = 2 s.
Let's solve this step by step:
Step 1: Understanding the given function y = 6/x^2
The given function represents the displacement of the wave pulse as a function of position (x). The expression y = 6/x^2 indicates that the displacement decreases as x increases. This suggests that the wave pulse is spreading out as it travels.
Step 2: Finding the position of the particle at t = 2 s
Since the wave pulse is travelling at a speed of 2 m/s, we can determine the position of the particle at t = 2 s using the formula x = vt, where v is the velocity and t is the time.
Given v = 2 m/s and t = 2 s, substituting these values into the formula, we get:
x = 2 m/s * 2 s = 4 m
Step 3: Finding the transverse velocity at x = 2 m and t = 2 s
To find the transverse velocity of the particle at x = 2 m and t = 2 s, we need to differentiate the given function with respect to time (t) and then substitute the values of x and t into the derivative.
Differentiating y = 6/x^2 with respect to t:
(dy/dt) = 0 (since there is no explicit dependence on time in the given function)
Substituting x = 2 m and t = 2 s into (dy/dt), we get:
(dy/dt)|x=2,t=2 = 0
Therefore, the transverse velocity of the particle at x = 2 m and t = 2 s is 0 m/s.
Step 4: Comparing the result with the given options
The correct answer is option 'B' (-3 m/s), which is not the same as the result obtained in Step 3. It seems that there might be an error in the options or a misinterpretation of the problem. Please double-check the options or provide additional information to resolve the discrepancy.
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ample number of questions to practice At t= 0, a transverse wave pulse travelling in the positive x direction with a speed of 2 m/s in a wire is described by the function y = 6/x2 given that x ≠ 0. Transverse velocity of a particle at x = 2 m and t = 2 s isa)3 m/sb)-3 m/sc)8 m/sd)-8 m/sCorrect answer is option 'B'. Can you explain this answer? tests, examples and also practice Class 11 tests.
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