Answer:
a) Δφ = 1.51 rad
, b) x = 21.17 m
Explanation:
This is an interference problem, as they indicate that the distance AP is on the x-axis the antennas must be on the y-axis, the phase difference is
Δr /λ = Δfi / 2π
Δfi = Δr /λ 2π
Δr = r₂-r₁
let's look the distances
r₁ = 57.0 m
We use Pythagoras' theorem for the other distance
r₂ = √ (x² + y²)
r₂ = √(57² + 9.3²)
r₂ = 57.75 m
The difference is
Δr = 57.75 - 57.0
Δr = 0.75 m
Let's look for the wavelength
c = λ f
λ = c / f
λ = 3 10⁸ / 96.0 10⁶
λ = 3.12 m
Let's calculate
Δφ = 0.75 / 3.12 2π
Δφ = 1.51 rad
b) for destructive interference the path difference must be λ/2, the equation for destructive interference with φ = π remains
Δr = (2n + 1) λ / 2
For the first interference n = 0
Δr = λ / 2
Δr = r₂ - r₁
We substitute the values
√ (x² + y²) - x = 3.12 / 2
Let's solve for distance x
√ (x² + y²) = 1.56 + x
x² + y² = (1.56 + x)²
x² + y² = 1.56² + 2 1.56 x + x²
y2 = 20.4336 +3.12 x
x = (y² -20.4336) /3.12
x = (9.3² -20.4336) /3.12
x = 21.17 m
This is the distance for the first minimum
The frequency of oscillation on the frictionless floor is 28 Hz.
<h3>
Frequency of the simple harmonic motion</h3>
The frequency of the oscillation is calculated as follows;
f = (1/2π)(√k/m)
where;
- k is the spring constant
- m is mass of the block
f = (1/2π)(√7580/0.245)
f = 28 Hz
Thus, the frequency of oscillation on the frictionless floor is 28 Hz.
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The image distance is 33.3 cm while the image height is 14.2 cm.
<h3>What is a converging lens?</h3>
A converging lens will always have a positive focal length hence, we have to find the object distance as follows;
1/f = 1/v + 1/u
1/12 = 1/v + 1/20
1/v = 1/12 - 1/20
1/v = 0.08 - 0.05
v =33.3 cm
Now;
Magnification = 33.3 cm/20.0 cm =1.67
M = Image height/Object height
1.67 = Image height/8.50 cm
Image height = 1.67 * 8.50 cm
Image height = 14.2 cm
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The final atmospheric pressure is
Explanation:
Assuming that the temperature of the air does not change, we can use Boyle's law, which states that for a gas kept at constant temperature, the pressure of the gas is inversely proportional to its volume. In formula,
where
p is the gas pressure
V is the volume
The equation can also be rewritten as
where in our problem we have:
is the initial pressure (the atmospheric pressure at sea level)
is the initial volume
is the final pressure
is the final volume
Solving the equation for p2, we find the final pressure:
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