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A transverse wave propagating on a stechted string of linear density 3 ×10 powe of 4 kgm inverse is represented by equation y =0•2sin (1•5+60t) where x is in metre and t in seconds .the tension in string is N?
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A transverse wave propagating on a stechted string of linear density 3...
Wave Equation Analysis
The wave equation given is \( y = 0.2 \sin(1.5x + 60t) \). Here, \( y \) represents the displacement of the string, \( x \) is the position along the string, and \( t \) is the time.
Identifying Parameters
- Amplitude (A): The coefficient before the sine function, which is \( A = 0.2 \) m.
- Wave Number (k): The coefficient of \( x \) in the argument of the sine function:
\[
k = 1.5 \, \text{rad/m}
\]
- Angular Frequency (ω): The coefficient of \( t \):
\[
\omega = 60 \, \text{rad/s}
\]
Calculating Wave Speed (v)
The wave speed \( v \) can be calculated using the relationship:
\[
v = \frac{\omega}{k}
\]
Substituting the values:
\[
v = \frac{60}{1.5} = 40 \, \text{m/s}
\]
Tension in the String (T)
The tension \( T \) in the string can be found using the formula:
\[
v = \sqrt{\frac{T}{\mu}}
\]
where \( \mu \) is the linear density. Given \( \mu = 3 \times 10^{-4} \, \text{kg/m} \):
\[
v^2 = \frac{T}{\mu} \implies T = \mu v^2
\]
Substituting the known values:
\[
T = (3 \times 10^{-4}) \times (40^2) = (3 \times 10^{-4}) \times 1600 = 0.48 \, \text{N}
\]
Conclusion
The tension in the string is \( 0.48 \, \text{N} \). This calculation highlights the relationship between wave parameters and the physical properties of the medium in which the wave propagates.
The wave equation given is \( y = 0.2 \sin(1.5x + 60t) \). Here, \( y \) represents the displacement of the string, \( x \) is the position along the string, and \( t \) is the time.
Identifying Parameters
- Amplitude (A): The coefficient before the sine function, which is \( A = 0.2 \) m.
- Wave Number (k): The coefficient of \( x \) in the argument of the sine function:
\[
k = 1.5 \, \text{rad/m}
\]
- Angular Frequency (ω): The coefficient of \( t \):
\[
\omega = 60 \, \text{rad/s}
\]
Calculating Wave Speed (v)
The wave speed \( v \) can be calculated using the relationship:
\[
v = \frac{\omega}{k}
\]
Substituting the values:
\[
v = \frac{60}{1.5} = 40 \, \text{m/s}
\]
Tension in the String (T)
The tension \( T \) in the string can be found using the formula:
\[
v = \sqrt{\frac{T}{\mu}}
\]
where \( \mu \) is the linear density. Given \( \mu = 3 \times 10^{-4} \, \text{kg/m} \):
\[
v^2 = \frac{T}{\mu} \implies T = \mu v^2
\]
Substituting the known values:
\[
T = (3 \times 10^{-4}) \times (40^2) = (3 \times 10^{-4}) \times 1600 = 0.48 \, \text{N}
\]
Conclusion
The tension in the string is \( 0.48 \, \text{N} \). This calculation highlights the relationship between wave parameters and the physical properties of the medium in which the wave propagates.
Community Answer
A transverse wave propagating on a stechted string of linear density 3...
V=√T/u = W/k
=} T= (w/k)^2 u
T is tension
U is linear density
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A transverse wave propagating on a stechted string of linear density 3 ×10 powe of 4 kgm inverse is represented by equation y =0•2sin (1•5+60t) where x is in metre and t in seconds .the tension in string is N?
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A transverse wave propagating on a stechted string of linear density 3 ×10 powe of 4 kgm inverse is represented by equation y =0•2sin (1•5+60t) where x is in metre and t in seconds .the tension in string is N? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about A transverse wave propagating on a stechted string of linear density 3 ×10 powe of 4 kgm inverse is represented by equation y =0•2sin (1•5+60t) where x is in metre and t in seconds .the tension in string is N? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A transverse wave propagating on a stechted string of linear density 3 ×10 powe of 4 kgm inverse is represented by equation y =0•2sin (1•5+60t) where x is in metre and t in seconds .the tension in string is N?.
A transverse wave propagating on a stechted string of linear density 3 ×10 powe of 4 kgm inverse is represented by equation y =0•2sin (1•5+60t) where x is in metre and t in seconds .the tension in string is N? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about A transverse wave propagating on a stechted string of linear density 3 ×10 powe of 4 kgm inverse is represented by equation y =0•2sin (1•5+60t) where x is in metre and t in seconds .the tension in string is N? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A transverse wave propagating on a stechted string of linear density 3 ×10 powe of 4 kgm inverse is represented by equation y =0•2sin (1•5+60t) where x is in metre and t in seconds .the tension in string is N?.
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