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A sinusoidal progressive wave is generated in a string . It's equation is given by Y = (2mm) sin(2πx-100πt π/3 ). The time when particle at x=4m first pass thru mean position,will be (A) 1/150sec (B) 1/300sec (C) 1/12sec (D) 1/100sec?
Verified Answer
A sinusoidal progressive wave is generated in a string . It's equation...
We have , y= (2mm)sin(2pix-100pit+ pi/3)
This equation is of the form
y= Asin(kx-wt+phi),
where A =2mm ,k= 2pi, w= 100pi, and
phi = pi/3
So, wave velocity,v = w/k
=> v = 100pi/2pi
=> v = 50m/s
So, at x = 4m, v= 50m/s
t = x/v
=> t = 4/ 50
=> t = 0.08 second
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Most Upvoted Answer
A sinusoidal progressive wave is generated in a string . It's equation...
Given:
The equation of the sinusoidal progressive wave is given as:
Y = (2mm) sin(2πx-100πt π/3)
To find:
The time when the particle at x=4m first passes through the mean position.
Solution:
Step 1: Identify the Mean Position
The mean position of a wave is the position where the displacement is zero. In this case, when the particle is at the mean position, the value of Y will be zero.
Step 2: Set up the Equation
We can set up the equation by substituting the given values into the equation and solving for t.
0 = (2mm) sin(2πx - 100πt π/3)
Step 3: Simplify the Equation
To simplify the equation, we can divide both sides by 2mm:
0 = sin(2πx - 100πt π/3)
Step 4: Determine the Angle
We know that sin(θ) = 0 when θ = nπ, where n is an integer. In this case, we have:
2πx - 100πt π/3 = nπ
Simplifying further, we get:
2x - 100t/3 = n
Step 5: Substitute the Given Value
Substituting x = 4m into the equation, we have:
8 - 100t/3 = n
Since we are looking for the time when the particle first passes through the mean position, the value of n should be zero.
8 - 100t/3 = 0
Simplifying, we get:
100t/3 = 8
Step 6: Solve for t
To solve for t, we can multiply both sides of the equation by 3/100:
t = 8 * 3/100
Simplifying, we get:
t = 24/100
Converting to seconds, we have:
t = 0.24 seconds
Answer:
The time when the particle at x=4m first passes through the mean position is 0.24 seconds, which is equivalent to 1/4 seconds or 1/100 seconds.
Key Points:
- The mean position of a wave is where the displacement is zero.
- Set up the equation by substituting the given values into the wave equation.
- Determine the angle at which the sine function is zero.
- Simplify the equation by solving for t.
- Substitute the given value of x into the equation.
- Solve for t to find the time when the particle first passes through the mean position.
The equation of the sinusoidal progressive wave is given as:
Y = (2mm) sin(2πx-100πt π/3)
To find:
The time when the particle at x=4m first passes through the mean position.
Solution:
Step 1: Identify the Mean Position
The mean position of a wave is the position where the displacement is zero. In this case, when the particle is at the mean position, the value of Y will be zero.
Step 2: Set up the Equation
We can set up the equation by substituting the given values into the equation and solving for t.
0 = (2mm) sin(2πx - 100πt π/3)
Step 3: Simplify the Equation
To simplify the equation, we can divide both sides by 2mm:
0 = sin(2πx - 100πt π/3)
Step 4: Determine the Angle
We know that sin(θ) = 0 when θ = nπ, where n is an integer. In this case, we have:
2πx - 100πt π/3 = nπ
Simplifying further, we get:
2x - 100t/3 = n
Step 5: Substitute the Given Value
Substituting x = 4m into the equation, we have:
8 - 100t/3 = n
Since we are looking for the time when the particle first passes through the mean position, the value of n should be zero.
8 - 100t/3 = 0
Simplifying, we get:
100t/3 = 8
Step 6: Solve for t
To solve for t, we can multiply both sides of the equation by 3/100:
t = 8 * 3/100
Simplifying, we get:
t = 24/100
Converting to seconds, we have:
t = 0.24 seconds
Answer:
The time when the particle at x=4m first passes through the mean position is 0.24 seconds, which is equivalent to 1/4 seconds or 1/100 seconds.
Key Points:
- The mean position of a wave is where the displacement is zero.
- Set up the equation by substituting the given values into the wave equation.
- Determine the angle at which the sine function is zero.
- Simplify the equation by solving for t.
- Substitute the given value of x into the equation.
- Solve for t to find the time when the particle first passes through the mean position.
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A sinusoidal progressive wave is generated in a string . It's equation is given by Y = (2mm) sin(2πx-100πt π/3 ). The time when particle at x=4m first pass thru mean position,will be (A) 1/150sec (B) 1/300sec (C) 1/12sec (D) 1/100sec?
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A sinusoidal progressive wave is generated in a string . It's equation is given by Y = (2mm) sin(2πx-100πt π/3 ). The time when particle at x=4m first pass thru mean position,will be (A) 1/150sec (B) 1/300sec (C) 1/12sec (D) 1/100sec? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A sinusoidal progressive wave is generated in a string . It's equation is given by Y = (2mm) sin(2πx-100πt π/3 ). The time when particle at x=4m first pass thru mean position,will be (A) 1/150sec (B) 1/300sec (C) 1/12sec (D) 1/100sec? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A sinusoidal progressive wave is generated in a string . It's equation is given by Y = (2mm) sin(2πx-100πt π/3 ). The time when particle at x=4m first pass thru mean position,will be (A) 1/150sec (B) 1/300sec (C) 1/12sec (D) 1/100sec?.
A sinusoidal progressive wave is generated in a string . It's equation is given by Y = (2mm) sin(2πx-100πt π/3 ). The time when particle at x=4m first pass thru mean position,will be (A) 1/150sec (B) 1/300sec (C) 1/12sec (D) 1/100sec? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A sinusoidal progressive wave is generated in a string . It's equation is given by Y = (2mm) sin(2πx-100πt π/3 ). The time when particle at x=4m first pass thru mean position,will be (A) 1/150sec (B) 1/300sec (C) 1/12sec (D) 1/100sec? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A sinusoidal progressive wave is generated in a string . It's equation is given by Y = (2mm) sin(2πx-100πt π/3 ). The time when particle at x=4m first pass thru mean position,will be (A) 1/150sec (B) 1/300sec (C) 1/12sec (D) 1/100sec?.
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