physicstutor - york university
TRANSCRIPT
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PhysicsTutor
Guitar string.
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Problem:
• A guitar B string of vibrating length 63.5 cm is made of steel wire (diameter 0.406 mm, mass density: 7800 kg/m3) to play the B3 note (247 Hz) as a fundamental.
• What is the tension of the string?
• The string is now tuned down from B3 to A3
(220 Hz). What is the percentage decrease in the tension?
2
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Relevant ideas:
3
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Relevant ideas:
• Standing wave on a string of length L with n=1.
4
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Relevant ideas:
5
• Standing wave on a string of length L with n=1.
• Wave propagation speed relates wavelength and frequency.
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Relevant ideas:
• Standing wave on a string of length L with n=1.
• Wave propagation speed relates wavelength and frequency.
• Propagation speed depends on tension force and on linear mass density.
6
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Relevant ideas:
• Standing wave on a string of length L with n=1.
• Wave propagation speed relates wavelength and frequency.
• Propagation speed depends on tension force and on linear mass density.
• Volume of the string is known, as is material mass density; linear mass density should follow.
7
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Equations associated with ideas:
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Strategy
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Strategy
• Given L, n=1 we find the wavelength _______
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Strategy
• Given L, n=1 we find the wavelength _______
• From wavelength and frequency we find the propagation speed ______________
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Strategy
• Given L, n=1 we find the wavelength _______
• From wavelength and frequency we find the propagation speed ______________
• The tension force will follow from _________, if we find the linear mass density =M/L.
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Strategy
• Given L, n=1 we find the wavelength _______
• From wavelength and frequency we find the propagation speed ______________
• The tension force will follow from _________, if we find the linear mass density =M/L.
• The mass M follows from __________, where the volume is that of a cylinder _______.
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Solution
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Solution
• _______________________
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Solution
• _______________________
• _______________________
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Solution
• _______________________
• _______________________
• _______________________
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Solution
• _______________________
• _______________________
• _______________________
• _______________________