25 mL of water is poured into a graduated cylinder. Several coins are dropped into the water, and the new volume is measured to
2 answers:
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To solve this problem it is necessary to take into account the concepts related to frequency and period, and how they are related to each other.
The relationship that defines both agreements is given by the equation,
Then the frequency for the previous period given (2sec) is
The beat frequency of two frequencies is equal to the difference between the two frequencies, then
<em>Hence option A is incorrect.</em>
We can do this process for 254Hz as and 258 Hz for
, then
<em>Hence option B is incorrect. </em>
We can also do this process for 255Hz as and 257 Hz for
, then
<em>Hence option C is incorrect. </em>
We can also do this process for 255.5Hz as f_1 and 256.5 Hz for f_2, then
<em>Hence option D is incorrect. </em>
We can also do this process for 255.75Hz as and 256.25 Hz for
, then
<em>Hence option E is incorrect. </em>
Therefore the sum of the frequencies in the sound wave would be 256.25Hz and 255.75Hz
1) Analyze the equation
Vₓ = α + β t²
Vₓ = 3.00 + 0.100 t²
That is a quadratic equation, so the graph is a parabola.
2) Therefore, take into account that the main points to draw a parabola are:
i) vertex
ii) concavity
iii) y-intercepts
iv) x - intercepts
Also, for all graphs you need the domain and the range.
3) Find the y-intercept (t = 0)
t = 0 ⇒ Vₓ = 3.00 + 0.100 (0)² = 3.00
4) Find the x-intercepts (Vₓ = 0)
Vₓ = 0 ⇒ 0 = 3.00 + 0.100 t²
⇒ t² = - 3.00 / 0.100 = -30.0. Since t² cannot be negative, there is not x-intercepts.
5) Concavity
Since, the coefficient of t² is positive, the parabola open upwards.
6) Vertex
It is the local minimum of the equation. You can find it by the first derivative
Vₓ' = 2×0.100 t = 0 ⇒ t = 0
Vₓ = 3.00 + 0.100 (0)² = 3.00 m/s
⇒ vertex = (0,3.00)
7) The domain is given t ∈ [0,5.00]
8) You can also build a table with several points in the domain
t =0; Vₓ = 3.00 + 0.100 (0)² = 0
t = 1; Vₓ = 3.00 + 0.100 (1)² = 3.10
t = 2; Vₓ = 3.00 + 0.100 (2)² = 3.40
t = 3; Vₓ = 3.00 + 0.100 (3)² = 3.90
t = 4; Vₓ = 3.00 + 0.100 (4)² = 4.60
t = 5; Vₓ = 3.00 + 0.100 (5)² = 5.50
9) Range: Vₓ ∈ [ 3.00, 5.50]
10) All that information permits you to put several points in a coordinate sysment and sketch the same graph as the shown in the figure attached.
