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The speed v of a transverse wave travelling on a string depends on tension force (T) and mass per unit length. Using Dimensional method derived the formula of speed?
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The speed v of a transverse wave travelling on a string depends on ten...
Let the tension in the string be F and mass per unit length be u.
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The speed v of a transverse wave travelling on a string depends on ten...
Derivation of the Formula for Speed of a Transverse Wave
- Given Parameters:
Let the speed of the transverse wave be represented by v, tension force by T, and mass per unit length by μ.
- Formula:
The speed of a transverse wave is given by the formula:
\[ v = \sqrt{\frac{T}{\mu}} \]
- Using Dimensional Analysis:
1. Write the dimensions of each parameter:
\[ [v] = LT^{-1} \]
\[ [T] = MLT^{-2} \]
\[ [\mu] = ML^{-1} \]
2. Substitute the dimensions into the formula:
\[ LT^{-1} = \sqrt{\frac{MLT^{-2}}{ML^{-1}}} \]
3. Simplify the equation:
\[ LT^{-1} = \sqrt{\frac{LT^{-2}}{L^{-1}}} \]
\[ LT^{-1} = \sqrt{L^2T^{-2}} \]
\[ LT^{-1} = LT^{-1} \]
- Conclusion:
By using dimensional analysis, we have derived the formula for the speed of a transverse wave:
\[ v = \sqrt{\frac{T}{\mu}} \]
This formula shows that the speed of a transverse wave is directly proportional to the square root of the tension force and inversely proportional to the square root of the mass per unit length of the string.
- Given Parameters:
Let the speed of the transverse wave be represented by v, tension force by T, and mass per unit length by μ.
- Formula:
The speed of a transverse wave is given by the formula:
\[ v = \sqrt{\frac{T}{\mu}} \]
- Using Dimensional Analysis:
1. Write the dimensions of each parameter:
\[ [v] = LT^{-1} \]
\[ [T] = MLT^{-2} \]
\[ [\mu] = ML^{-1} \]
2. Substitute the dimensions into the formula:
\[ LT^{-1} = \sqrt{\frac{MLT^{-2}}{ML^{-1}}} \]
3. Simplify the equation:
\[ LT^{-1} = \sqrt{\frac{LT^{-2}}{L^{-1}}} \]
\[ LT^{-1} = \sqrt{L^2T^{-2}} \]
\[ LT^{-1} = LT^{-1} \]
- Conclusion:
By using dimensional analysis, we have derived the formula for the speed of a transverse wave:
\[ v = \sqrt{\frac{T}{\mu}} \]
This formula shows that the speed of a transverse wave is directly proportional to the square root of the tension force and inversely proportional to the square root of the mass per unit length of the string.
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The speed v of a transverse wave travelling on a string depends on tension force (T) and mass per unit length. Using Dimensional method derived the formula of speed?
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The speed v of a transverse wave travelling on a string depends on tension force (T) and mass per unit length. Using Dimensional method derived the formula of speed? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about The speed v of a transverse wave travelling on a string depends on tension force (T) and mass per unit length. Using Dimensional method derived the formula of speed? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The speed v of a transverse wave travelling on a string depends on tension force (T) and mass per unit length. Using Dimensional method derived the formula of speed?.
The speed v of a transverse wave travelling on a string depends on tension force (T) and mass per unit length. Using Dimensional method derived the formula of speed? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about The speed v of a transverse wave travelling on a string depends on tension force (T) and mass per unit length. Using Dimensional method derived the formula of speed? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The speed v of a transverse wave travelling on a string depends on tension force (T) and mass per unit length. Using Dimensional method derived the formula of speed?.
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