1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
timofeeve [1]
3 years ago
7

Two transverse waves travel along the same taut string inopposite directions. the waves are described by following equations use

superposition to determine the standing wave function
Physics
1 answer:
Umnica [9.8K]3 years ago
4 0

Answer: y'=2Asin(kx)cos(wt)

Explanation:

Let y1=A sin (kx + wt) be the first wave

y2=A sin (kx - wt) be the second wave in the opposite direction (which we showed by putting a negative sign between the terms kx and wt)

Please do note that both wave have the same attributes (that's Amplitude, wave number and angular frequency) because they are formed on the same medium by the same source just that their directions are opposite.

By super imposing these 2 waves, we have a resulting singular wave representing both wave (law of superimposition) with a resulting value of vertical displacement y'.

Thus y' = y1 + y2.

Let us do the math.

y'=A sin (kx + wt) + A sin (kx - wt)

By factoring A out, we have that

y' = A [ sin (kx + wt) + sin (kx - wt)]

For simplicity let us use the substitution

Let (kx + wt) = a and (kx - wt) =b

Hence we have that

y' = A [sin a + sin b].

From trigonometric ratio

sin a + sin b = 2sin[(a+b)/2] * cos [(a - b)/2]

By recalling that (kx + wt) = a and (kx - wt) =b

sin a + sin b = 2sin [(kx +wt +kx-wt) /2] * cos [(kx +wt - (kx-wt))/2]

Thus we have that

sin a + sin b = 2sin [(kx+wt+kx-wt)/2] * cos[(kx+wt-kx+wt)/2]

By collecting like terms in the bracket we have that

sin a + sin b = 2sin[2kx/2] * cos [2wt/2]

By dividing

sin a + sin b = 2sin(kx) cos(wt)

Now let us get the final resultant vertical displacement (y')

Recall that

y' = A [sin a + sin b]. and we already deduced that

sin a + sin b = 2sin(kx) cos(wt)

Finally,

y' = A [2sin(kx) cos(wt)] which is

y'=2Asin(kx)cos(wt)...... Final answer

You might be interested in
What is a limited resource?
Artemon [7]
Something that there is only so many of or not enough of
7 0
3 years ago
Read 2 more answers
What is buoyant force on the ball? Question 9 on student exploration: Archimedes Princable
mariarad [96]
Mass of the displaced material. In water it would be the mass of the water that the volume of the ball displaces.
3 0
3 years ago
What causes the weight of an object to change depending on if it is on Earth or the Moon?
Gnoma [55]
The acceleration due to gravity



Brainliest please
7 0
2 years ago
What's the difference between mechanical waves and vibrations
OlgaM077 [116]

A mechanical wave is a wave that is an oscillation of matter, and therefore transfers energy through a medium. While waves can move over long distances, the movement of the medium of transmission—the material—is limited. Therefore, the oscillating material does not move far from its initial equilibrium position.

7 0
3 years ago
In the modern quantum–based atomic theory, what is the name given to a particular space around the nucleus in which an electron
Marina86 [1]
<span>The correct answer is: Atomic orbital

Explanation:
In the modern quantum-based atomic theory, an atomic orbital is a mathematical function that is used to explain the wave-like behavior of an electron in an atom. In other words, the space around the nucleus in which an electron moves is expressed by the atomic orbital. Hence, the correct answer is Atomic orbital.</span>
6 0
3 years ago
Read 2 more answers
Other questions:
  • A transverse wave on a rope is given by y(x,t)= (0.750cm)cos(π[(0.400cm−1)x+(250s−1)t]). part a part complete find the amplitude
    13·2 answers
  • The Tesla Roadster electric car is rated at 16.8kW how much energy does it use during a one hour car drive
    7·1 answer
  • Skateboard A Force: 33 N Time: 0.12 s Skateboard B Force: 33 N Time: 0.57 s Skateboard C Force: 33 N Time: 0.78 s Which skateboa
    9·2 answers
  • Think about a girl on a swing. When is the kinetic energy of the girl zero?
    8·2 answers
  • The given function represents the position of a particle traveling along a horizontal line. s(t) = 2t3 − 3t2 − 36t + 6 for t ≥ 0
    8·1 answer
  • What happens if you add additional,solid NaCl after the maximum has been reached?
    8·2 answers
  • A piston above a liquid in a closed container has an area of 1m2. The piston carries a load of 350 kg. What will be the external
    10·1 answer
  • While listening to operatic solos, musicians process the lyrics and the tunes in separate brain areas. This most clearly illustr
    9·1 answer
  • Please help me out i'm so depressed and such a failure
    12·1 answer
  • In young Goodman’s Brown hawthornes reveals his feelings about his Puritan ancestors when
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!