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3 years ago

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Two harmonic waves traveling in opposite directions interfere to produce a standing wave described by y = 3 sin (2x) cos 5t wher

e x is in m and t is in s. What is the wavelength of the interfering waves?

1 answer:

Nostrana [21]3 years ago

8 0

Answer:

The wavelength of the interfering waves is 3.14 meters.

Explanation:

Given that,

The equation of standing wave that is formed by interfering two harmonic waves (travelling opposite direction) is given by :

$y=3\ sin(2x)\ cos(5t)$ ........(1)

The general equation of standing wave is given by :

$y=2A\ sin(kx)\ cos(\omega t)$ ..............(2)

On comparing equation (1) and (2), we get :

k = 2

We know that,

$\dfrac{2\pi}{\lambda}=k$

$\dfrac{2\pi}{\lambda}=2$

$\lambda=3.14\ m$

So, the wavelength of the interfering wave is 3.14 meters. Hence, this is the required solution.

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Likurg_2 [28]

Answer:

1) $t=2.26\: s$

2) $S=33.9\: m$

3) $v=26.77\: m/s$

4) $\alpha=55.92$

Explanation:

1)

We can use the following equation:

$y_{f}=y_{0}+v_{iy}t-0.5*g*t^{2}$

Here, the initial velocity in the y-direction is zero, the final y position is zero and the initial y position is 25 m.

$0=25-0.5*9.81*t^{2}$

$t=2.26\: s$

2)

The equation of the motion in the x-direction is:

$v_{ix}=\frac{S}{t}$

$15=\frac{S}{2.26}$

$S=33.9\: m$

3)

The velocity in the y-direction of the stone will be:

$v_{fy}=v_{iy}-gt$

$v_{fy}=0-(9.81*2.26)$

$v_{fy}=-22.17\: m/s$

Now, the velocity in the x-direction is 15 m/s then the velocity will be:

$v=\sqrt{v_{x}^{2}+v_{fy}^{2}}=\sqrt{15^{2}+(-22.17)^{2}}$

$v=26.77\: m/s$

4)

The angle of this velocity is:

$tan(\alpha)=\frac{22.17}{15}$

$\alpha=tan^{-1}(\frac{22.17}{15})$

$\alpha=55.92$

Then α=55.92° negative from the x-direction.

I hope it helps you!

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