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A piano wire of length 50 cm and mass of 6.5 gm is stretched so that the frequency of its fundamental modes of vibration is 80 cycles/ sec . find the streatching force in gm-wt?
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A piano wire of length 50 cm and mass of 6.5 gm is stretched so that t...
To determine the stretching force on a piano wire given its dimensions and frequency of vibration, we can use the relationship between the frequency, tension, length, and mass per unit length of the wire.
Given Parameters
- Length of the wire (L): 50 cm = 0.5 m
- Mass of the wire (m): 6.5 gm = 0.0065 kg
- Frequency of fundamental mode (f): 80 cycles/sec
Calculating Mass per Unit Length
- The mass per unit length (μ) can be calculated using:
Using the Frequency Formula
- The frequency of the fundamental mode for a stretched wire is given by:
- Rearranging to find tension (T):
Substituting Values
- Now, substituting the values into the equation:
Converting Tension to gm-wt
- To convert the tension from Newtons to gram-force (gm-wt):
Final Result
- The stretching force in the wire is approximately 8476.78 gm-wt.
Given Parameters
- Length of the wire (L): 50 cm = 0.5 m
- Mass of the wire (m): 6.5 gm = 0.0065 kg
- Frequency of fundamental mode (f): 80 cycles/sec
Calculating Mass per Unit Length
- The mass per unit length (μ) can be calculated using:
- μ = m / L
- μ = 0.0065 kg / 0.5 m = 0.013 kg/m
Using the Frequency Formula
- The frequency of the fundamental mode for a stretched wire is given by:
- f = (1/2L) * √(T/μ)
- Rearranging to find tension (T):
- T = (2Lf)² * μ
Substituting Values
- Now, substituting the values into the equation:
- T = (2 * 0.5 m * 80 Hz)² * 0.013 kg/m
- T = (80 m/s)² * 0.013 kg/m
- T = 6400 * 0.013 = 83.2 N
Converting Tension to gm-wt
- To convert the tension from Newtons to gram-force (gm-wt):
- 1 N = 101.97 gm-wt
- Force in gm-wt = 83.2 N * 101.97 gm-wt/N = 8476.784 gm-wt
Final Result
- The stretching force in the wire is approximately 8476.78 gm-wt.
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A piano wire of length 50 cm and mass of 6.5 gm is stretched so that the frequency of its fundamental modes of vibration is 80 cycles/ sec . find the streatching force in gm-wt?
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A piano wire of length 50 cm and mass of 6.5 gm is stretched so that the frequency of its fundamental modes of vibration is 80 cycles/ sec . find the streatching force in gm-wt? for Chemistry 2024 is part of Chemistry preparation. The Question and answers have been prepared according to the Chemistry exam syllabus. Information about A piano wire of length 50 cm and mass of 6.5 gm is stretched so that the frequency of its fundamental modes of vibration is 80 cycles/ sec . find the streatching force in gm-wt? covers all topics & solutions for Chemistry 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A piano wire of length 50 cm and mass of 6.5 gm is stretched so that the frequency of its fundamental modes of vibration is 80 cycles/ sec . find the streatching force in gm-wt?.
A piano wire of length 50 cm and mass of 6.5 gm is stretched so that the frequency of its fundamental modes of vibration is 80 cycles/ sec . find the streatching force in gm-wt? for Chemistry 2024 is part of Chemistry preparation. The Question and answers have been prepared according to the Chemistry exam syllabus. Information about A piano wire of length 50 cm and mass of 6.5 gm is stretched so that the frequency of its fundamental modes of vibration is 80 cycles/ sec . find the streatching force in gm-wt? covers all topics & solutions for Chemistry 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A piano wire of length 50 cm and mass of 6.5 gm is stretched so that the frequency of its fundamental modes of vibration is 80 cycles/ sec . find the streatching force in gm-wt?.
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