A wave pulse in a string is described by the equation y 1 = 5 3 x - 4 t 2 + 2 and another wave pulse in the same string is described by y 2 = - 5 3 x + 4 t - 6 2 + 2 . The values of y 1 , y 2 and x are in metres and t is in seconds. Which of the following statement is correct?

At x = 1 m , y 1 and y 2 always cancel

y 1 travels along - x -direction and y 2 along + x -direction

Both y 1 and y 2 travel along + x -direction

At time t = 1 s , y 1 and y 2 exactly cancel everywhere

At time t = 3 s , y 1 and y 2 exactly cancel everywhere

A typical plane electromagnetic wave propagating along the Z - direction is shown in figure. Write the equation for electric and magnetic fields.

Electromagnetic waves are also known as EM waves. Electromagnetic radiations are composed of electromagnetic waves that are produced when an electric field comes in contact with the magnetic field. It can also be said that electromagnetic waves are the composition of oscillating electric and magnetic fields. A plane Electromagnetic wave travelling in the Z-direction is of the form E z , t = E max cos kz - ωt + ϕ and B z , t = B max cos kz - ωt + ϕ Where E , is the electric field and B , is the magnetic field vector of the electromagnetic waves.For electromagnetic waves E and B , are perpendicular to each other and perpendicular to the direction of propagation.The direction of propagation is the direction of E × B .

Match the following: Column - I Column - II (a) Transverse wave through a steel rod (i) B + 4 3 η ρ (b) Longitudinal waves in earth's crust (ii) η ρ (c) Longitudinal waves through a steel rod (iii) 2 π T g λ (d) Ripples (iv) λ ρ

( a − i i ) , ( b − i ) , ( c − i v ) , ( d − i i i )

( a − i ) , ( b − i i i ) , ( c − i v ) , ( d − i i )

( a − i i i ) , ( b − i v ) , ( c − i ) , ( d − i i )

( a − i i ) , ( b − i v ) , ( c − i ) , ( d − i i i )

What are transverse waves Describe theessential conditions for the propagation of transverse waves

EASY

Physical Sciences>Waves and Their Applications in Technologies for Information Transfer>Use mathematical representations to support a claim regarding relationships among the frequency, wavelength,and speed of waves traveling in various media.>Wave Properties - The wavelength and frequency of a wave are related to one another by the speed of travel of the wave, which depends on the type of wave and the medium through which it is passing.

The displacement of a wave is represented by

y = 0.6 \times 10^{- 3} \sin (500 t - 0.05 x),

where all the quantities are in their proper units. The maximum particle velocity

(i n m s^{- 1})

of the medium is

EASY

Physical Sciences>Waves and Their Applications in Technologies for Information Transfer>Use mathematical representations to support a claim regarding relationships among the frequency, wavelength,and speed of waves traveling in various media.>Wave Properties - The wavelength and frequency of a wave are related to one another by the speed of travel of the wave, which depends on the type of wave and the medium through which it is passing.

Consider a wire with density

(d)

and stress

(σ) .

For the same density, if the stress increases

2

times, the speed of the transverse waves along the wire changes by

MEDIUM

Physical Sciences>Waves and Their Applications in Technologies for Information Transfer>Use mathematical representations to support a claim regarding relationships among the frequency, wavelength,and speed of waves traveling in various media.>Wave Properties - The wavelength and frequency of a wave are related to one another by the speed of travel of the wave, which depends on the type of wave and the medium through which it is passing.

A wave pulse in a string is described by the equation

y_{1} = \frac{5}{{(3 x - 4 t)}^{2} + 2}

and another wave pulse in the same string is described by

y_{2} = \frac{- 5}{{(3 x + 4 t - 6)}^{2} + 2}

. The values of

y_{1}, y_{2}

and

x

are in metres and

t

is in seconds. Which of the following statement is correct?

EASY

Physical Sciences>Waves and Their Applications in Technologies for Information Transfer>Use mathematical representations to support a claim regarding relationships among the frequency, wavelength,and speed of waves traveling in various media.>Wave Properties - The wavelength and frequency of a wave are related to one another by the speed of travel of the wave, which depends on the type of wave and the medium through which it is passing.

A simple harmonic progressive wave is represented as

y = 0.03 s i n π (2 t - 0.01 x) m

. At a given instant of time, the phase difference between two particles

25 m

apart is

EASY

Physical Sciences>Waves and Their Applications in Technologies for Information Transfer>Use mathematical representations to support a claim regarding relationships among the frequency, wavelength,and speed of waves traveling in various media.>Wave Properties - The wavelength and frequency of a wave are related to one another by the speed of travel of the wave, which depends on the type of wave and the medium through which it is passing.

A typical plane electromagnetic wave propagating along the $Z$ - direction is shown in figure.

Question Image

Write the equation for electric and magnetic fields.

EASY

Physical Sciences>Waves and Their Applications in Technologies for Information Transfer>Use mathematical representations to support a claim regarding relationships among the frequency, wavelength,and speed of waves traveling in various media.>Wave Properties - The wavelength and frequency of a wave are related to one another by the speed of travel of the wave, which depends on the type of wave and the medium through which it is passing.

A progressive wave travelling along the positive

x -

direction is represented by

y (x, t) = A s i n (k x - ω t + ϕ)

. Its snapshot at

t = 0

is given in the figure.
Question Image

For this wave, the phase

ϕ

is:

EASY

Physical Sciences>Waves and Their Applications in Technologies for Information Transfer>Use mathematical representations to support a claim regarding relationships among the frequency, wavelength,and speed of waves traveling in various media.>Wave Properties - The wavelength and frequency of a wave are related to one another by the speed of travel of the wave, which depends on the type of wave and the medium through which it is passing.

The maximum transverse velocity and maximum transverse acceleration of a harmonic wave in a

o n e - d i m e n s i o n a l

string are

1 m s^{- 1}

and

1 m s^{- 2}

respectively. The phase velocity of the wave is

1 m s^{- 1}

. The waveform is

EASY

Physical Sciences>Waves and Their Applications in Technologies for Information Transfer>Use mathematical representations to support a claim regarding relationships among the frequency, wavelength,and speed of waves traveling in various media.>Wave Properties - The wavelength and frequency of a wave are related to one another by the speed of travel of the wave, which depends on the type of wave and the medium through which it is passing.

Let $f (x) = \sin x + \cos a x$ be a periodic function. Then,

MEDIUM

Physical Sciences>Waves and Their Applications in Technologies for Information Transfer>Use mathematical representations to support a claim regarding relationships among the frequency, wavelength,and speed of waves traveling in various media.>Wave Properties - The wavelength and frequency of a wave are related to one another by the speed of travel of the wave, which depends on the type of wave and the medium through which it is passing.

A simple harmonic motion is represented by:

y = 5 (\sin 3 π t + \sqrt{3} \cos 3 π t) cm

The amplitude and time period of the motion are:

HARD

Physical Sciences>Waves and Their Applications in Technologies for Information Transfer>Use mathematical representations to support a claim regarding relationships among the frequency, wavelength,and speed of waves traveling in various media.>Wave Properties - The wavelength and frequency of a wave are related to one another by the speed of travel of the wave, which depends on the type of wave and the medium through which it is passing.

Two vectors

\vec{A}

and

\vec{B}

are defined as

\vec{A} = a \hat{i}

and

\vec{B} = a (\cos ω t \hat{i} + \sin ω t \hat{j})

, where a is a constant and

ω = \frac{π}{6} rad s^{- 1} .

If

|\vec{A} + \vec{B}| = \sqrt{3} |\vec{A} - \vec{B}|

at time

t = τ

for the first time, the value of

τ

in seconds, is_______

MEDIUM

Physical Sciences>Waves and Their Applications in Technologies for Information Transfer>Use mathematical representations to support a claim regarding relationships among the frequency, wavelength,and speed of waves traveling in various media.>Wave Properties - The wavelength and frequency of a wave are related to one another by the speed of travel of the wave, which depends on the type of wave and the medium through which it is passing.

A travelling wave in a medium is given by the equation

y = asin (ωt - kx)

. The maximum acceleration of the particle in the medium is

MEDIUM

Physical Sciences>Waves and Their Applications in Technologies for Information Transfer>Use mathematical representations to support a claim regarding relationships among the frequency, wavelength,and speed of waves traveling in various media.>Wave Properties - The wavelength and frequency of a wave are related to one another by the speed of travel of the wave, which depends on the type of wave and the medium through which it is passing.

Match the following:

	Column $- I$		Column $- II$
(a)	Transverse wave through a steel rod	(i)	$\sqrt{B + (\frac{4}{3}) \frac{η}{ρ}}$
(b)	Longitudinal waves in earth's crust	(ii)	$\sqrt{\frac{η}{ρ}}$
(c)	Longitudinal waves through a steel rod	(iii)	$\sqrt{\frac{2 π T}{g λ}}$
(d)	Ripples	(iv)	$\sqrt{\frac{λ}{ρ}}$

MEDIUM

Physical Sciences>Waves and Their Applications in Technologies for Information Transfer>Use mathematical representations to support a claim regarding relationships among the frequency, wavelength,and speed of waves traveling in various media.>Wave Properties - The wavelength and frequency of a wave are related to one another by the speed of travel of the wave, which depends on the type of wave and the medium through which it is passing.

For a transvers wave travelling, along a straight line, the distance between two peaks (crests) is

5 m

, while the distance between one crest and one trough is

1.5 m

. The possible wavelengths (in

m

) of the waves are:

MEDIUM

Physical Sciences>Waves and Their Applications in Technologies for Information Transfer>Use mathematical representations to support a claim regarding relationships among the frequency, wavelength,and speed of waves traveling in various media.>Wave Properties - The wavelength and frequency of a wave are related to one another by the speed of travel of the wave, which depends on the type of wave and the medium through which it is passing.

A transverse wave is represented by :

y = \frac{10}{π} sin (\frac{2 π}{T} t - \frac{2 π}{λ} x)

For what value of the wavelength the wave velocity is twice the maximum particle velocity?

EASY

Physical Sciences>Waves and Their Applications in Technologies for Information Transfer>Use mathematical representations to support a claim regarding relationships among the frequency, wavelength,and speed of waves traveling in various media.>Wave Properties - The wavelength and frequency of a wave are related to one another by the speed of travel of the wave, which depends on the type of wave and the medium through which it is passing.

The phase difference between the following two waves $y_{2}$ and $y_{1}$ is:

$y_{1} = a \sin (ω t - k x)$

$y_{2} = b \cos (ω t - k x + \frac{π}{3})$

EASY

Physical Sciences>Waves and Their Applications in Technologies for Information Transfer>Use mathematical representations to support a claim regarding relationships among the frequency, wavelength,and speed of waves traveling in various media.>Wave Properties - The wavelength and frequency of a wave are related to one another by the speed of travel of the wave, which depends on the type of wave and the medium through which it is passing.

The distance between two points differing in phase by

60 °

on a wave having wave velocity

360 m s^{- 1}

and frequency

500 Hz

is

HARD

Physical Sciences>Waves and Their Applications in Technologies for Information Transfer>Use mathematical representations to support a claim regarding relationships among the frequency, wavelength,and speed of waves traveling in various media.>Wave Properties - The wavelength and frequency of a wave are related to one another by the speed of travel of the wave, which depends on the type of wave and the medium through which it is passing.

A particle of mass

\frac{2}{3} kg

with velocity

v = - 15 m s^{- 1}

at

t = - 2 s

is acted upon by a force

F = k - β t^{2}

. Here,

k = 8 N

and

β = 2 N s^{- 2}

. The motion is one-dimensional. Then, the speed at which the particle acceleration is zero again, is

HARD

Physical Sciences>Waves and Their Applications in Technologies for Information Transfer>Use mathematical representations to support a claim regarding relationships among the frequency, wavelength,and speed of waves traveling in various media.>Wave Properties - The wavelength and frequency of a wave are related to one another by the speed of travel of the wave, which depends on the type of wave and the medium through which it is passing.

A particle performing S.H.M. starts from the equilibrium position and its time period is

16 s

. After

2 s

its velocity is

π m s^{- 1} .

Amplitude of oscillation is

(\cos 45^{o} = \frac{1}{\sqrt 2})

EASY

Physical Sciences>Waves and Their Applications in Technologies for Information Transfer>Use mathematical representations to support a claim regarding relationships among the frequency, wavelength,and speed of waves traveling in various media.>Wave Properties - The wavelength and frequency of a wave are related to one another by the speed of travel of the wave, which depends on the type of wave and the medium through which it is passing.

Write two properties and two uses of X-rays.

EASY

Physical Sciences>Waves and Their Applications in Technologies for Information Transfer>Use mathematical representations to support a claim regarding relationships among the frequency, wavelength,and speed of waves traveling in various media.>Wave Properties - The wavelength and frequency of a wave are related to one another by the speed of travel of the wave, which depends on the type of wave and the medium through which it is passing.

To propagate both longitudinal and transverse waves, a material must have

What are transverse waves? Describe the essential conditions for the propagation of transverse waves.

Important Questions on Use mathematical representations to support a claim regarding relationships among the frequency, wavelength,and speed of waves traveling in various media.

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