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A string of mass 100 gm is clamped between two rigid supports a wave of amplitude 2 mm is generated in strong if angular frequency of wave is 5000 rad/s then total energy of the wave in the string is?
Most Upvoted Answer
A string of mass 100 gm is clamped between two rigid supports a wave o...
Given:
Mass of the string, m = 100 gm = 0.1 kg
Amplitude of the wave, A = 2 mm = 0.002 m
Angular frequency of the wave, ω = 5000 rad/s
To find:
Total energy of the wave in the string
Formula:
Total energy of a wave on a string = 1/2 * μ * v² * A² * ω²
Where, μ = mass per unit length of the string
v = velocity of the wave in the string
Calculation:
1. Calculation of μ:
Mass per unit length of the string, μ = m / L
Where, L = length of the string
As the length of the string is not given, let's assume it to be 1 m (as it doesn't affect the final answer)
μ = 0.1 kg / 1 m = 0.1 kg/m
2. Calculation of v:
The velocity of the wave in the string, v = ω * λ
Where, λ = wavelength of the wave
As the wavelength is not given, we can use the relation between λ and A:
λ = 2 * π * A
λ = 2 * π * 0.002 m
λ = 0.01256 m
v = 5000 rad/s * 0.01256 m = 62.8 m/s
3. Calculation of Total energy:
Total energy of the wave in the string = 1/2 * μ * v² * A² * ω²
Total energy = 0.5 * 0.1 kg/m * (62.8 m/s)² * (0.002 m)² * (5000 rad/s)²
Total energy = 0.5 * 0.1 * 62.8² * 0.002² * 5000²
Total energy = 31.4 J
Therefore, the total energy of the wave in the string is 31.4 J.
Mass of the string, m = 100 gm = 0.1 kg
Amplitude of the wave, A = 2 mm = 0.002 m
Angular frequency of the wave, ω = 5000 rad/s
To find:
Total energy of the wave in the string
Formula:
Total energy of a wave on a string = 1/2 * μ * v² * A² * ω²
Where, μ = mass per unit length of the string
v = velocity of the wave in the string
Calculation:
1. Calculation of μ:
Mass per unit length of the string, μ = m / L
Where, L = length of the string
As the length of the string is not given, let's assume it to be 1 m (as it doesn't affect the final answer)
μ = 0.1 kg / 1 m = 0.1 kg/m
2. Calculation of v:
The velocity of the wave in the string, v = ω * λ
Where, λ = wavelength of the wave
As the wavelength is not given, we can use the relation between λ and A:
λ = 2 * π * A
λ = 2 * π * 0.002 m
λ = 0.01256 m
v = 5000 rad/s * 0.01256 m = 62.8 m/s
3. Calculation of Total energy:
Total energy of the wave in the string = 1/2 * μ * v² * A² * ω²
Total energy = 0.5 * 0.1 kg/m * (62.8 m/s)² * (0.002 m)² * (5000 rad/s)²
Total energy = 0.5 * 0.1 * 62.8² * 0.002² * 5000²
Total energy = 31.4 J
Therefore, the total energy of the wave in the string is 31.4 J.
Community Answer
A string of mass 100 gm is clamped between two rigid supports a wave o...
The total energy of stationary wave in the string is 1/4KA^2=1/4mw^2A^2
now after putting the values we will get answer =2.5J
with regards
now after putting the values we will get answer =2.5J
with regards
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A string of mass 100 gm is clamped between two rigid supports a wave of amplitude 2 mm is generated in strong if angular frequency of wave is 5000 rad/s then total energy of the wave in the string is?
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A string of mass 100 gm is clamped between two rigid supports a wave of amplitude 2 mm is generated in strong if angular frequency of wave is 5000 rad/s then total energy of the wave in the string is? 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 A string of mass 100 gm is clamped between two rigid supports a wave of amplitude 2 mm is generated in strong if angular frequency of wave is 5000 rad/s then total energy of the wave in the string is? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A string of mass 100 gm is clamped between two rigid supports a wave of amplitude 2 mm is generated in strong if angular frequency of wave is 5000 rad/s then total energy of the wave in the string is?.
A string of mass 100 gm is clamped between two rigid supports a wave of amplitude 2 mm is generated in strong if angular frequency of wave is 5000 rad/s then total energy of the wave in the string is? 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 A string of mass 100 gm is clamped between two rigid supports a wave of amplitude 2 mm is generated in strong if angular frequency of wave is 5000 rad/s then total energy of the wave in the string is? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A string of mass 100 gm is clamped between two rigid supports a wave of amplitude 2 mm is generated in strong if angular frequency of wave is 5000 rad/s then total energy of the wave in the string is?.
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