Waves Test

Result

Waves Test - 66

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Weekly Quiz Competition

Question 1
1 / -0

A wave pulse in a string is described by the equation $$y_1=\dfrac{5}{(3x-4t)^2+2}$$ and another wave pulse in the same string is described by $$y_2=\dfrac{-5}{(3x+4t-6)^2+2}$$. The values of $$y_1,y_2$$ and $$x$$ are in metres and $$t$$ in seconds. Which of the following statement is correct?

A
$$y_1$$ travels along -x- direction and $$y_2$$ along +x-direction

B
Both $$y_1$$ and $$y_2$$ travel along -x-direction

C
Both $$y_1$$ and $$y_2$$ travel along +x-direction

D
At $$x=1m,y_1$$ and $$y_2$$ always cancel

E
At time $$t=1s,y_1$$ and $$y_2$$ exactly cancel everywhere

Solution

$$y_1=\dfrac{5}{(3x-4t)^2+2}, y_2=\dfrac{-5}{(3x+4t-6)^2+2}$$
According option (d), at $$x=1$$
$$y_1=\dfrac{5}{(3-4t)^2+2}$$
$$y_2=\dfrac{-5}{(3+4t-6)^2+2}$$
$$=\dfrac{-5}{(3-4t)^2+2}$$
Both wave pulse equation are existing in same string therefore resultant equation of wave pulse.
$$y=y_1+y_2=0$$
At $$x=1m,y_1$$ and $$y_2$$ always cancel.
So, the correct option is $$(D)$$
Question 2
1 / -0

A wave pulse moves along a stretched rope in the direction shown.
Which diagram shows the variation with time t of the displacement s of the particle P in the rope?

A

B

C

D

Solution

The particles can only vibrate vertically – that is, they move up and down. Thus, particle P will only move up and down, it is not moving horizontally.
After some time, the vertical part (on the right) will be at P – particle would move according to the form of the wave.

So, at the earliest time there is a sudden jump up, followed by a constant high value of displacement s and finishing with the negative peak.

The answer is therefore D.
Question 3
1 / -0

Two simple harmonic motions are represented by the equations
$$y_1=10\sin \left(3\pi t+\dfrac{\pi}{4}\right)$$
and $$y_2=5(3\sin 3\pi t+\sqrt 3 \cos 3\pi t)$$ Their amplitudes are in the ratio of :

A
$$\sqrt 3$$

B
$$1/\sqrt 3$$

C
$$2$$

D
$$1/6$$

Solution
Question 4
1 / -0

The wavelength of the first line of Lyman series is $$\lambda$$. The wavelength of the first line in Paschen series is ________.

A
$$108/7$$

B
$$27/5$$

C
$$7/108$$

D
$$5/27$$

Solution

Formula for Lyman series is:
Where, n = 2,3,4,5,.....
Where, R = Rydbergg constant,
$$\dfrac{1}{\lambda}=R\left(\dfrac{1}{1^2}-\dfrac{1}{2^2}\right)$$ and
Paschen series in $$\lambda_1$$,
$$\Rightarrow \dfrac{1}{\lambda_1}=R\left(\dfrac{1}{3^2}-\dfrac{1}{4^2}\right)$$

$$\Rightarrow \dfrac{\lambda_1}{\lambda}=\dfrac{\dfrac{3}{4}}{\dfrac{7}{16\times 9}}$$

$$\Rightarrow \lambda_1=\dfrac{3}{4}\times \dfrac{16\times 9}{7}\lambda$$

$$\Rightarrow \lambda_1=\dfrac{108}{7}\lambda$$.
Question 5
1 / -0

The number of waves each of wavelength $$10\ cm$$ produced in string of $$100\ cm$$ length, is:

A
$$1$$

B
$$10$$

C
$$20$$

D
$$30$$

Solution
Question 6
1 / -0

The equation of standing wave is $$y=a\cos kx \sin \omega t$$ which one of following graphs is for the wave at $$t=\dfrac{T}{4}$$?

A

B

C

D
none of the above

Solution
Question 7
1 / -0

Equation of a plane wave is given by $$4\sin \dfrac{\pi}{4}\left[2t+\dfrac{x}{8}\right]$$. The phase difference at any given instant of two particles $$16\ cm$$ apart is :

A
$$60^o$$

B
$$90^o$$

C
$$30^o$$

D
$$120^o$$

Solution
Question 8
1 / -0

Wave of frequency $$500\ Hz$$ has a phase velocity $$360\ m/s$$. The phase difference between two displacement at a certain point at time $$10^{-3}\ s$$ apart will be :

A
$$\pi$$ radian

B
$$\dfrac{\pi}{2}$$ radian

C
$$\dfrac{\pi}{4}$$ radian

D
$$2\ pi$$ radian

Solution
Question 9
1 / -0

The phase change between incident and reflected sound wave from a fixed wall is:

A
$$0$$

B
$$\pi$$

C
$$3\pi$$

D
$$\dfrac{\pi}{2}$$

Solution
Question 10
1 / -0

Two waves represented by $$y = a \sin (\omega t - kx)$$ and $$y = a \cos (\omega t - kx)$$ are superposed. The resultant waves will have an amplitude.

A
$$a$$

B
$$\sqrt{2a}$$

C
$$2a$$

D
$$0$$

Solution