This function might represent the lateral displacement of a string, a local electric field, the position of the surface of a body of water, or any of a number of other physical manifestations of waves.
1. Find ye(x) and yt(t). Keep in mind that yt(t) should be a trigonometric function of unit amplitude.
2. At the position x=0, what is the displacement of the string (assuming that the standing wave ys(x,t) is present)?
3. At certain times, the string will be perfectly straight. Find the first time t1>0 when this is true.
4. Which one of the following statements about the wave described in the problem introduction is correct?
A. The wave is traveling in the +x direction.
B. The wave is traveling in the −x direction.
C. The wave is oscillating but not traveling.
D. The wave is traveling but not oscillating.
Which of the expressions given is a mathematical expression for a wave of the same amplitude that is traveling in the opposite direction? At time t=0this new wave should have the same displacement as y1(x,t), the wave described in the problem introduction.
A. Acos(kx−ωt)
B. Acos(kx+ωt)
C. Asin(kx−ωt)
D. Asin(kx+ωt)
The definition of standing wave and trigonometry allows to find the results for the questions about the waves are:
1. For the standing wave its parts are: spatial and
temporal part
2. The string moves with an oscillating motion y = A’ cos wt.
3. Thefirst displacement is zero for
4. the correct result is:
A. The wave is traveling in the +x direction.
5. The correct result is:
D. Asin(kx+ωt)
Traveling waves are periodic movements of the media that transport energy, but not matter, the expression to describe it is:
y₁ = A sin (kx -wt)
Where A is the amplitude of the wave k the wave vector, w the angular velocity and x the position and t the time.
1. Ask us to find the spatial and temporal part of the standing wave.
To form the standing wave, two waves must be added, the reflected wave is:
y₂ = A sin (kx + wt)
The sum of a waves
y = y₁ + y₂
y = A (sin kx-wt + sin kx + wt)
We develop the sine function and add.
Sin (a ± b) = sin a cos b ± sin b cos a
The result is:
y = 2A sin kx cos wt
They ask that the function be unitary therefore
The amplitude of each string
A_ {chord} = A_ {standing wave} / 2
The spatial part is
= A 'sin kx
The temporary part is:
= A ’cos wt
2. At position x = 0, what is the displacement of the string?
y = A ’cos wt
The string moves in an oscillating motion.
3. At what point the string is straight.
When the string is straight its displacement is zero x = 0, the position remains.
y = A ’cos wt
For the amplitude of the chord to be zero, the cosine function must be zero.
wt = (2n + 1)
the first zero occurs for n = 0
wt =
t =
4) The traveling wave described in the statement is traveling in the positive direction of the x axis, therefore the correct statement is:
A. The wave is traveling in the +x direction.
5) The wave traveling in the opposite direction is
y₂ = A sin (kx + wt)
The correct answer is:
D. Asin(kx+ωt)
In conclusion using the definition of standing wave and trigonometry we can find the results for the questions about the waves are:
1. For the standing wave its parts are: spatial and
temporal part
2. The string moves with an oscillating motion y = A’ cos wt.
3. Thefirst displacement is zero for
4. the correct result is:
A. The wave is traveling in the +x direction.
5. The correct result is:
D. Asin(kx+ωt)
Learn more about standing waves here: brainly.com/question/1121886
Answer:
Time taken for 1 swing = 3.81 second
Explanation:
Given:
Time taken for 1 swing = 2.20 Sec
Find:
Time taken for 1 swing , when triple the length(T2)
Computation:
Time taken for 1 swing = 2π[√l/g]
2.20 = 2π[√l/g].......Eq1
Time taken for 1 swing , when triple the length (3L)
Time taken for 1 swing = 2π[√3l/g].......Eq2
Squaring and dividing the eq(1) by (2)
4.84 / T2² = 1 / 3
T2 = 3.81 second
Time taken for 1 swing = 3.81 second
Answer: ∆p2 = 2* ∆p1
Explanation:
Given that all other factors remain constant. The pressure drop across the pipeline is directly proportional to the length.
i.e ∆p ~ L
Therefore,
∆p2/L2 = ∆p1/L1
Since L2 = 2 * L1
∆p2/2*L1 = ∆p1/L1
Eliminating L1 we have,
∆p2/2 = ∆p1
Multiplying both sides by 2
∆p2 = 2 * ∆p1
Answer:
wavelength of the standing wave will be equal to 30 cm
Explanation:
We have given length of the guitar string L = 60 cm
Mass per unit length
Frequency is given f = 660 Hz
We have to find the wavelength of the standing wave
Length of the string will be 2 times of the wavelength of the wave
So
So wavelength of the standing wave will be equal to 30 cm
B. 60 cm
C. 75 cm
D. 90 cm
Answer:
See the explaination for the details.
Explanation:
Gauss Law states that the total electric flux out of a closed surface is equal to the charge enclosed divided by the permittivity. The electric flux in an area is defined as the electric field multiplied by the area of the surface projected in a plane and perpendicular to the field.
According to the Gauss law, the total flux linked with a closed surface is 1/ε0 times the charge enclosed by the closed surface.
Please kindly check attachment for the step by step explaination of the answer.