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Unformatted text preview: . Tension at the point x is now given by T = Weight of Mass + Weight of string above. i.e. T = Mg + µxg Mg 0.5 µx 0.5
dx
T
Mg
=v =
=
+ xg = 1 + dt
µ
µ µ M
dx
So that ∫
0.5 =
0
µx 1 + M x Mg 0.5
∫ 0 µ dt t x µx 0.5 M Mg 0.5
21 + = t M µ 0 µ 0.5 M µx 0.5 ∴ t = 2 1 + − 1 µg M € € Now µ=m/L and when x=L we have for the total time τ: 0.5 ML m 0.5 τ = 2 1 + − 1 mg M L 0.5
0.5
= 2 ( M + m) − M 0.5 mg { € } Higher Physics 1A PHYS1131 2010T1, Solutions Q6 18 Marks (a) The sinusoidal oscillator is a pure tone generator; i.e. emitting at a single frequency that is desired. Set the two oscillators in operation, emitting their tones. If the two oscillators emit at the same frequency you will hear a single pitch. There will be no amplitude modulation in the sound. If the frequencies are different beats will be heard. Adjust the frequency of one oscillator; as the beat frequency decreases it approaches the frequency of the second oscillator. (b) € To get standing waves we have to have an integer number of half wavelengths if the string is fixed at both ends. λ
i.e. n = L 2 Suppose that f = v / λ with v = T /µ . Take n half wavelengths for mass mn. €
Then there will be n+1 half wavelengths for a mass mn+1 with mn+1 < mn,...
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This note was uploaded on 12/02/2012 for the course PHYS 1131 taught by Professor Angstman during the Three '12 term at University of New South Wales.
 Three '12
 Angstman
 Physics, Work

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