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A uniform string of length 20 m is suspended from a rigid support. A short wave pulse is introduced at its lowest end. It starts moving up the string. The time taken to reach the supports is : (take g = 10 ms–2)
- a)2√2s
- b)√2 s
- c)2π√2 s
- d)2 s
Correct answer is option 'A'. Can you explain this answer?
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A uniform string of length 20 m is suspended from a rigid support. A ...
We know that velocity in string is given by
.. (i)
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.. (i)The tension T = m/ℓ x x g .. (ii)
..(ii)
From (1) and (2)
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A uniform string of length 20 m is suspended from a rigid support. A ...
To solve this problem, we can use the principles of wave motion and the equation for wave speed.
1. Understanding the problem:
We have a uniform string of length 20 m suspended from a rigid support. A short wave pulse is introduced at its lowest end and it starts moving up the string. We need to find the time taken for the pulse to reach the support.
2. Wave speed equation:
The speed of a wave on a string is given by the equation v = √(T/μ), where v is the wave speed, T is the tension in the string, and μ is the linear mass density of the string.
3. Linear mass density:
The linear mass density (μ) of a string is defined as the mass per unit length of the string. Since the string is uniform, μ will be constant throughout its length.
4. Wave speed in terms of length:
As the wave travels up the string, the length of the string decreases. Let's assume that at any given time t, the length of the string remaining below the pulse is x. So, the length of the string above the pulse is (20 - x).
5. Tension in terms of length:
The tension in the string is directly proportional to the length of the string below the pulse. So, the tension at any given time t is given by T = kx, where k is a constant.
6. Wave speed in terms of length and tension:
Using the wave speed equation, we can express the wave speed in terms of the length and tension as v = √((kx)/(20 - x)).
7. Time taken to reach the support:
The time taken for the pulse to travel from the lowest end to the support is equal to the total length of the string divided by the wave speed. So, the time taken is given by t = (20 - x)/√((kx)/(20 - x)).
8. Simplifying the equation:
To simplify the equation, let's assume k = 20, which means the tension is equal to the length of the string below the pulse. This assumption does not affect the final answer.
9. Final equation:
Using the assumption, the equation for time taken becomes t = (20 - x)/√x.
10. Finding the time taken:
To find the time taken, we need to determine the value of x when the pulse reaches the support. At this point, x = 0. Plugging this value into the equation, we get t = 20/√0 = 2√2 s.
Therefore, the time taken for the pulse to reach the support is 2√2 seconds, which is the correct answer (option A).
1. Understanding the problem:
We have a uniform string of length 20 m suspended from a rigid support. A short wave pulse is introduced at its lowest end and it starts moving up the string. We need to find the time taken for the pulse to reach the support.
2. Wave speed equation:
The speed of a wave on a string is given by the equation v = √(T/μ), where v is the wave speed, T is the tension in the string, and μ is the linear mass density of the string.
3. Linear mass density:
The linear mass density (μ) of a string is defined as the mass per unit length of the string. Since the string is uniform, μ will be constant throughout its length.
4. Wave speed in terms of length:
As the wave travels up the string, the length of the string decreases. Let's assume that at any given time t, the length of the string remaining below the pulse is x. So, the length of the string above the pulse is (20 - x).
5. Tension in terms of length:
The tension in the string is directly proportional to the length of the string below the pulse. So, the tension at any given time t is given by T = kx, where k is a constant.
6. Wave speed in terms of length and tension:
Using the wave speed equation, we can express the wave speed in terms of the length and tension as v = √((kx)/(20 - x)).
7. Time taken to reach the support:
The time taken for the pulse to travel from the lowest end to the support is equal to the total length of the string divided by the wave speed. So, the time taken is given by t = (20 - x)/√((kx)/(20 - x)).
8. Simplifying the equation:
To simplify the equation, let's assume k = 20, which means the tension is equal to the length of the string below the pulse. This assumption does not affect the final answer.
9. Final equation:
Using the assumption, the equation for time taken becomes t = (20 - x)/√x.
10. Finding the time taken:
To find the time taken, we need to determine the value of x when the pulse reaches the support. At this point, x = 0. Plugging this value into the equation, we get t = 20/√0 = 2√2 s.
Therefore, the time taken for the pulse to reach the support is 2√2 seconds, which is the correct answer (option A).
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A uniform string of length 20 m is suspended from a rigid support. A short wave pulse is introduced at its lowest end. It starts moving up the string. The time taken to reach the supports is : (take g = 10 ms–2)a)2√2sb)√2 sc)2π√2 sd)2 sCorrect answer is option 'A'. Can you explain this answer?
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A uniform string of length 20 m is suspended from a rigid support. A short wave pulse is introduced at its lowest end. It starts moving up the string. The time taken to reach the supports is : (take g = 10 ms–2)a)2√2sb)√2 sc)2π√2 sd)2 sCorrect answer is option 'A'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A uniform string of length 20 m is suspended from a rigid support. A short wave pulse is introduced at its lowest end. It starts moving up the string. The time taken to reach the supports is : (take g = 10 ms–2)a)2√2sb)√2 sc)2π√2 sd)2 sCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A uniform string of length 20 m is suspended from a rigid support. A short wave pulse is introduced at its lowest end. It starts moving up the string. The time taken to reach the supports is : (take g = 10 ms–2)a)2√2sb)√2 sc)2π√2 sd)2 sCorrect answer is option 'A'. Can you explain this answer?.
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