Waves Test

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Waves Test - 65

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Weekly Quiz Competition

Question 1
1 / -0

Two points are located at a distance of $$10\ m$$ and $$15\ m$$ from the source of oscillation. The period of oscillation is $$0.05\sec$$ and the velocity of the wave is $$300\ m/\sec$$. What is the phase difference between the oscillations of two points?

A
$$\dfrac {\pi}{6}$$

B
$$\dfrac {\pi}{3}$$

C
$$\dfrac {2\pi}{3}$$

D
$$\pi$$

Solution
Question 2
1 / -0

The equation $$y =A\cos^2\left(2\pi\, nt -2\pi \dfrac{x}{\lambda}\right)$$ represents a wave with

A
amplitude $$A/2$$, frequency $$2n$$& wavelength $$\lambda/2$$

B
amplitude $$A/2$$, frequency $$2n$$& wavelength $$\lambda$$

C
amplitude $$A$$, frequency $$2n$$& wavelength $$2\lambda$$

D
amplitude $$A$$, frequency $$n$$& wavelength $$\lambda$$

Solution
Question 3
1 / -0

The phase difference between two particles executing SHM of the same amplitudes and frequency along same straight line while passing one another when going in opposite directions with equal displacement from their respective starting point is $$2\pi/3$$. If the phase of one particle is $$\pi/6$$, find the displacement at this instant, if amplitude is $$A$$.

A
$$A/3$$

B
$$2A/3$$

C
$$3A/4$$

D
$$A/2$$
Question 4
1 / -0

Which of the following statement is incorrect superposition of waves?
(i) After superposition frequency,wavelength and velocity of resultant wave remains same
(ii) After superposition amplitude of resultant wave is equal to amplitude of either wave
(iii) Mechanical wave cannot superposed with electromagnetic wave
(iv) For superposition two waves should have equal wavelength,frequency and amplitude

A
I & III Only

B
I & II Only

C
I,II, & III Only

D
II & IV Only

Solution

If both the waves have same frequency wavelength and velocity then only superposition frequency, wavelength and velocity of resultant wave remains same.
Superposition amplitude of resultant wave is given by, $$A = \sqrt{A_1^2+A_2^2 +2A_1A_2\cos{\theta}}$$, which may of may not be equal to amplitude of either wave.
Question 5
1 / -0

The equation $$y = a \sin^2 \left(2 \pi nt - \dfrac{2\pi x}{\lambda}\right)$$ represents a wave with

A
Amplitude $$a$$, frequency $$n$$ and wavelength $$\lambda$$

B
Amplitude $$a$$, frequency $$2n$$ and wavelength $$2\lambda$$

C
Amplitude $$a/2$$, frequency $$2n$$ and wavelength $$\lambda$$

D
Amplitude $$a/2$$, frequency $$2n$$ and wavelength $$\lambda/2$$
Question 6
1 / -0

A wave has a wavelength of 3m. The distance between a crest and adjacent trough is

A
0.75 m

B
1.5 m

C
3 m

D
1 m

Solution

Distance between two adjacent crest or trough is wavelength, and distance between a crest and adjacent trough is half of wavelength.
Given, $$\lambda = 3m$$
Distance between a crest and adjacent trough$$= \dfrac{\lambda}{2} = \dfrac32 = 1.5m$$
Question 7
1 / -0

The displacement equation of a progressive wave is y = 3 sin (200 t-5 x), Where the distance x and y are in meter and time t in second. The speed of the wave is:

A
$$ 20 m s^{-1} $$

B
$$ 40 m s^{-1} $$

C
$$ 60 m s^{-1} $$

D
$$ 80 m s^{-1} $$

Solution

Given: $$y = 3\sin(200t-5x)$$

Comparing it with standard wave equation, $$y = A \sin(\omega t -kx)$$
$$\omega = 200$$ $$s^{-1}$$
$$k = 5$$ $$m^{-1}$$

Velocity of wave is given by, $$v =\dfrac{\omega}{k}$$

$$v = \dfrac{200}{5} = 40$$ $$m/s$$
Question 8
1 / -0

A sinusoidal wave travelling in the same direction have amplitude of $$3\ cm$$ and $$4\ cm$$ and difference in phase by $$\pi/2$$. The resultant amplitude of the superimposed wave is :

A
$$7\ cm$$

B
$$5\ cm$$

C
$$2\ cm$$

D
$$0.5\ cm$$

Solution
Question 9
1 / -0

At any instant a wave travelling along the string is shown in fig. Here, point $$'A'$$ is moving upward. Which of the following statements is true?

A
The wave is travelling to the right

B
The displacement amplitude of wave is equal to displacement of $$B$$ at this instant

C
At this instant $$'C'$$ also directed upward

D
None of these

Solution

A) there is no guarantee that the wave is moving to the right. The particles can perform oscillatory motion about the mean position without moving forward.

B)As given in the question point A is moving up. That means point C is moving down. In between these two points there should be a maxima which is represented by point B. An this maximum displacement is called the amplitude.

C) point C is directed downwards because it is on the decreasing side of the sinusoidal curve.
Question 10
1 / -0

Velocity of sound waves in air is $$330\ m/s$$. For a particular sound in air, a path difference of $$40\ cm$$ is equivalent to a phase difference of $$1.6\ \pi$$. The frequency of this wave is:

A
$$165\ Hz$$

B
$$150\ Hz$$

C
$$660\ Hz$$

D
$$330\ Hz$$

Solution