Waves Test

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Waves Test - 11

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Weekly Quiz Competition

Question 1
1 / -0

The product of the time period of a wave and its frequency is

A
Infinite

B
Zero

C
More than unity but less than infinity

D
Unity

Solution

The relation between frequency (f) and time period(T) is
$$f=1/T or f \times T=1$$
Question 2
1 / -0

Which of the following quantity decrease as sound wave travels through a medium :

A
Amplitude

B
Frequency

C
Velocity

D
Wavelength

Solution

When sound wave propagates through a medium, the amplitude of vibration decreases due to the energy dissipation due to the resistance of the medium.
Question 3
1 / -0

Two waves $${y_1} = {A_1}\sin (\omega t - {\beta _1}){y_2} = {A_2}\sin (\omega t - {\beta _2})$$ superimpose to form a resultant wave whose amplitude is

A
$$\sqrt {A_1^2 + A_2^2 + 2{A_1}{A_2}\cos ({\beta _1} - {\beta _2})} $$

B
$$\sqrt {A_1^2 + A_2^2 + 2{A_1}{A_2}\sin ({\beta _1} - {\beta _2})} $$

C
$$A_1 + A_2$$

D
$$|A_1 + A_2|$$

Solution

$$y=y_1 +y_2$$
$$y=A Sin (wt - \beta)$$
$$A=\sqrt{A_1^2 + A_2^2 + 2A_1 A_2 Cos (\beta_1- \beta_2)}$$
Question 4
1 / -0

When two plane progressive waves travelling in same direction superimpose over each other, the velocity of the resultant wave will

A
increase

B
remain unchanged

C
be zero

D
decrease

Solution

When two plane progressive waves travelling in same direction superimpose over each other, the velocity of the resultant wave will remain unchanged. Velocity depends on the medium only.
Question 5
1 / -0

What will be the wave velocity, if the radar gives 54 waves per min and wavelength of the given wave is 10 m?

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

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

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

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

Solution

$$v = v \displaystyle \lambda = \frac{54}{60}H_z \times 10 m = 9 m s^{-1}$$
Question 6
1 / -0

The frequency of a man's voice is $$300\space Hz$$. If the velocity of sound waves is $$336\space ms^{-1}$$, the wavelength of the sound is

A
$$1.12\space m$$

B
$$300\times336\space m$$

C
$$330/336\space m$$

D
None of these

Solution

We are given, frequency $$f=300 Hz$$, and velocity $$v=336 ms^{-1}$$,

From the relation $$v=f \times \lambda$$,

$$\lambda = v/f =336/300=1.12 m$$

Option "A" is correct.
Question 7
1 / -0

If the energy density and velocity of a wave are $$u$$ and $$c$$ respectively then the energy propagating per second per unit area will be

A
$$u/c$$

B
$$c^2u$$

C
$$uc$$

D
$$c/u$$

Solution

If the energy density and velocity of a wave are $$u$$ and $$c$$ respectively then the energy propagating per second per unit area will be $$uc.$$
Question 8
1 / -0

An ultrasonic source emits sound of frequency 220 kHz in air. If this sound meets a water surface, what is the wavelength of the reflected sound?

A
$$1.6 \times 10^{-3} m$$

B
$$2.6 \times 10^{-3} m$$

C
$$3.6 \times 10^{-3} m$$

D
$$4.6 \times 10^{-3} m$$

Solution

Here, $$v=220 kHz = 220 \times 10^3$$
$$=2.2 \times 10^5 Hz$$;
Speed of sound in air, $$v_a = 352 m s^{-1}$$
Speed of sound in water, $$v_w = 1.496 m s^{-1}$$
The reflected sound: After reflection, the ultrasonic sound continues to travel in air. If $$\lambda_a$$ is wave length in air, then
$$\lambda_a = \displaystyle \frac{v_a}{v} = \frac{352}{2.2 \times 10^5} = 1.6 \times 10^{-3} m$$
Question 9
1 / -0

A piezo - electric quartz plate is vibrating to produce wavelength of $$10^{-1}$$ m. Find the frequency if for quartz $$Y=8 \times 10^{10} N m^{-2}$$ and $$\rho = 2.65 \times 10^3 kg m^{-3}$$

A
350 kHz

B
450 kHz

C
550 kHz

D
650 kHz

Solution

We know that for longitudinal waves in solids,
$$v = \displaystyle \sqrt{\frac{Y}{\rho}}$$, so, $$v = \displaystyle \sqrt{\frac{8 \times 10^{10}}{2.65 \times 10^3}}$$
$$ = 5.5 \times 10^3 m/s$$
So, $$10^{-2}m$$
But as $$v=f \lambda$$, i.e., $$f = (\frac{v}{\lambda})$$
so f $$[5.5 \times 10^3 / 10^{-2}] = 5.5 \times 10^5 Hz$$
$$=550 kHz$$
Question 10
1 / -0

The particle of a medium vibrates about their mean position whenever a wave travels through that medium. The phase difference between the vibrations of two such particles

A
varies with time only

B
varies with distance separating them only

C
varies with time as well as distance

D
is always zero

Solution

The phase difference between the vibrations of two particles of the medium is given by :
$$\Delta \phi=\dfrac{2\pi}{\lambda}\Delta x$$
it is clear that phase difference varies as the path difference between the particles varies, which is the distance, separating the particles.

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Waves Test - 11

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Waves Test - 11

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SHARING IS CARING

Question 1

Infinite

Zero

More than unity but less than infinity

Unity

Solution

Question 2

Amplitude

Frequency

Velocity

Wavelength

Solution

Question 3

$$\sqrt {A_1^2 + A_2^2 + 2{A_1}{A_2}\cos ({\beta _1} - {\beta _2})} $$

$$\sqrt {A_1^2 + A_2^2 + 2{A_1}{A_2}\sin ({\beta _1} - {\beta _2})} $$

$$A_1 + A_2$$

$$|A_1 + A_2|$$

Solution

Question 4

increase

remain unchanged

be zero

decrease

Solution

Question 5

4 m s$$^{-1}$$

6 m s$$^{-1}$$

9 m s$$^{-1}$$

5 m s$$^{-1}$$

Solution

Question 6

$$1.12\space m$$

$$300\times336\space m$$

$$330/336\space m$$

None of these

Solution

Question 7

$$u/c$$

$$c^2u$$

$$uc$$

$$c/u$$

Solution

Question 8

$$1.6 \times 10^{-3} m$$

$$2.6 \times 10^{-3} m$$

$$3.6 \times 10^{-3} m$$

$$4.6 \times 10^{-3} m$$

Solution

Question 9

350 kHz

450 kHz

550 kHz

650 kHz

Solution

Question 10

varies with time only

varies with distance separating them only

varies with time as well as distance

is always zero

Solution

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