Answer:
Explanation:
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Answer:
x = D (M/M-m) 2.41
Explanation:
a) Let's apply Newton's second law to find the summation of force, where each force is given by the law of universal gravitation
F = g m₁m₂ / r²
Σ F = 0
F1- F2 = 0
F1 = F2
We set the reference system in the body of greatest mass (M) the planet
F1 = g m₁ M / x²
F2 = G m1 m / (D-x)²
G m₁ M / x² = G m₁ m / (D-x)²
M (D-x)² = m x²
MD² -2MD x + M x² = m x²
x² (M-m) -2MD x + MD² = 0
We solve the second degree equation
x = [2MD ±√ (4M²D² - 4 (M-m) MD²)] / 2 (M-m)
x = {2MD ± 2D √ (M² + (M-m) M)} / 2 (M-m)
x = D {M ± Ra (2M²-mM)} / (M-m)
x = D (M ± M √ (2-m/M)) / (M-m)
x = D (M / (M-m)) (1 ±√ (2-m/M)
Let's analyze this result, the value of M-m >> 1, so if we take the negative root, the value of x would be negative, it is out of the point between the two bodies, so the correct result must be taken with the positive root
x = D (M / (M-m)) (1 + √2)
x = D (M/M-m) 2.41
b) X = 2/3 D
x = D (M/M-m) 2.41
2/3 D = D (M/(M-m)) 2.41
2/3 (M-m) = M 2.41
2/3 M - 2/3 m = 2.41 M
1.743 M = 0.667 m
M/m = 0.667/1.743
M/m = 0.38
The wavelength for C1 note is 10.40 m, for A6 note is 0.193 m and for B7 note 0.086 m.
Answer:
Explanation:
Since, wavelength, frequency and speed of sound waves are related to each other, we can determine a single parameter with the help of other two parameters. So in this case, the frequency of different notes are given along with their common speed. So as the frequency is inversely proportional to the wavelength then in this case, the wavelength of the notes will be maximum for C1 and minimum for 3951.1 Hz.
Wavelength = Speed / Frequency
Wavelength for C1 note = 340 / 32.7 =10.40 m
Similarly, the wavelength for A6 note = 340/1760=0.193 m
And, the wavelength for B7 note = 340/3951.1 = 0.086 m
So, the wavelength for C1 note is 10.40 m, for A6 note is 0.193 m and for B7 note 0.086 m.