Waves Test

Result

Waves Test - 64

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Weekly Quiz Competition

Question 1
1 / -0

Which of the following figure about reflection of transverse or longitudinal waves is CORRECT? $$ (V_w = velocity \ of \ wave, v_p = particle\ velocity) $$

A

B

C

D
Question 2
1 / -0

The displacement equation of a simple harmonic oscillator is given by
$$x = 6 \sin \left[\dfrac{\pi}{8} + \dfrac{\pi}{16}t\right] m $$ when t = 2 seconds is

A
1.3m

B
1.5m

C
$$3\sqrt{3} m$$

D
$$3 \sqrt{2}$$ m
Question 3
1 / -0

The displacement of a particle ( in meters ) from its mean position is given by the equation $$y = 0.2\left( {{{\cos }^2}\dfrac{{\pi t}}{2} - {{\sin }^2}\dfrac{{\pi t}}{2}} \right)$$. The motion of the above particle is.

A
not simple harmonic

B
Simple harmonic with amplitude of 0.2 m

C
Simple harmonic with a period equal double that of a second's pendulum

D
Simple harmonic with an amplitude of 0.4 m

Solution
Question 4
1 / -0

For a wave $$ y= y_0 sin ( \omega t - kx ) $$, for what value of $$ \lambda $$ , is the maximum particle velocity equal to two times the wave velocity :-

A
$$ \pi y_0 $$

B
$$ 2 \pi y_0 $$

C
$$ \pi y_0/2 $$

D
$$4 \pi y_0 $$

Solution
Question 5
1 / -0

Figure given showsa sinusoidal wave on a string.If the frequency of the wave is 150 Hz and the mass per unit length of the string is 0.2 g/s.the power transmitted by the wave is

A
2.34 W

B
3.84 W

C
4.80 W

D
5.78 W

Solution
Question 6
1 / -0

Number of waves of a light of wavelength $$5000 \mathrm { A } ^ { \circ } ,$$ in a thickness of $$0.2 \mathrm { mm } ,$$ of air is

A
$$100$$

B
$$200$$

C
$$250$$

D
$$400$$

Solution
Question 7
1 / -0

Equation $${ y }_{ 1 }=0.1sin\left( 100\pi t+\dfrac { \pi }{ 3 } \right) $$ and $${ y }_{ 2 }=0.1$$ cos $$\pi t$$ The phase difference of the velocity of particle 1, with respect to the velocity of particle 2 is

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

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

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

D
$$\dfrac { \pi }{ 6 } $$
Question 8
1 / -0

The equation of a progressive wave is $$Y= a sin(200 t-x)$$, where x is in meter and t is in second. The velocity of wave is

A
$$200 $$ m/sec

B
$$100 $$ m/sec

C
$$50 $$ m/sec

D
None

Solution
Question 9
1 / -0

The equation of a wave is given by
$$ Y\quad =\quad A\quad sin\quad \omega \left( \frac { x }{ v } -k \right) $$
Where $$ \omega $$ is the angular velocity and v is the linear velocity.The dimensions of K is

A
LT

B
T

C
$$ T^{-1} $$

D
$$ T^2 $$

Solution

From the principle of homogenity $$(\dfrac{x}{v})$$ has dimensions of T.
Question 10
1 / -0

If the amplitude of a wave at a distance $$r$$ from a point source is $$A$$, the amplitude at a distance $$2r$$ will be

A
$$2A$$

B
$$A$$

C
$$A/2$$

D
$$A/4$$

Solution

Intensity, $$I \propto (A)^2$$

Also, $$I \propto \dfrac{1}{r^2}$$

So, $$A \propto \dfrac{1}{r} $$

At distance r, amplitude is A, so at distance 2r amplitude will be $$\dfrac{A}{2}$$