QBManager

WAVES (NCERT)

274454 Which of the following equations correctly represents a travelling wave having wavelength $λ = 4.0 cm$ , frequency $v = 100 Hz$ and travelling in positive $x$ -axis direction?

1

y = A sin [(0.50 π c m^{- 1}) x - (100 π s^{- 1}) t]

2

y = A sin 2 π [(0.25 c m^{- 1}) x - (50 s^{- 1}) t]

3

y = A sin [(\frac{2 π}{4} c m^{- 1}) x - (\frac{2 π}{100} s^{- 1}) t]

4

y = A sin π [(0.5 c m^{- 1}) x - (200 s^{- 1}) t]

Explanation:

(d) We have
$k = \frac{2 π}{λ} = \frac{2 π}{4} = 0.5 π c m^{- 1}$
$ω = 2 π f = 2 π \times 100 = 200 π s^{- 1}$

NCERT Page-373 / N-284

WAVES (NCERT)

274455 A travelling harmonic wave is represented by the equation $y (x, t) = 10^{- 3} sin (50 t + 2 x)$ , where $x$ and $y$ are in meter and $t$ is in seconds. Which of the following is a correct statement about the wave?

1 The wave is propagating along the negative

x

-axis with speed

25 m s^{- 1}

.

2 The wave is propagating along the positive

x

-axis with speed

100 m s^{- 1}

.

3 The wave is propagating along the positive

x

-axis with speed

25 m s^{- 1}

.

4 The wave is propagating along the negative

x

-axis with speed

100 m s^{- 1}

.

Explanation:

(a) Comparing the given equation
$y = 10^{- 3} sin (50 t + 2 x)$ with standard equation,
$y = asin (ω t - kx)$
$\Rightarrow$ wave is moving along -ve x-axis with speed
$v = \frac{ω}{K} \Rightarrow v = \frac{50}{2} = 25 m / sec$ .

NCERT Page-373 / N-284

WAVES (NCERT)

274436 A progressive wave travelling along the positive $x$ -direction is represented by $y (x, t) = A sin (k x - ω t + ϕ)$ . Its snapshot at $t = 0$ is given in the figure.
For this wave, the phase $ϕ$ is:
12.04.2019 Shift 1 Synergy JEE Mains Nikhil D20

1

- \frac{π}{2}

2

π

3 0

4

\frac{π}{2}

Explanation:

(b) At $t = 0, x = 0, y = 0$
$ϕ = π rad$

NCERT Page-370 / N-282

WAVES (NCERT)

274437 The equation $y = A si n^{2} (k x - ω t)$ represents a wave with

1 amplitude

A

, frequency

ω / 2 π

2 amplitude

A / 2

, frequency

ω / π

3 amplitude

2 A

, frequency

ω / 4 π

4 it does not represent a wave motion

Explanation:

(b) $y = A si n^{2} (k x - ω t)$
$\Rightarrow y = \frac{A}{2} [1 - cos 2 (kx - ω t)]$
$ω^{'} = 2 ω, 2 π v^{'} = 2 ω, v^{'} = \frac{ω}{π}$

NCERT Page-371 / N-283

WAVES (NCERT)

274454 Which of the following equations correctly represents a travelling wave having wavelength $λ = 4.0 cm$ , frequency $v = 100 Hz$ and travelling in positive $x$ -axis direction?

1

y = A sin [(0.50 π c m^{- 1}) x - (100 π s^{- 1}) t]

2

y = A sin 2 π [(0.25 c m^{- 1}) x - (50 s^{- 1}) t]

3

y = A sin [(\frac{2 π}{4} c m^{- 1}) x - (\frac{2 π}{100} s^{- 1}) t]

4

y = A sin π [(0.5 c m^{- 1}) x - (200 s^{- 1}) t]

Explanation:

(d) We have
$k = \frac{2 π}{λ} = \frac{2 π}{4} = 0.5 π c m^{- 1}$
$ω = 2 π f = 2 π \times 100 = 200 π s^{- 1}$

NCERT Page-373 / N-284

WAVES (NCERT)

274455 A travelling harmonic wave is represented by the equation $y (x, t) = 10^{- 3} sin (50 t + 2 x)$ , where $x$ and $y$ are in meter and $t$ is in seconds. Which of the following is a correct statement about the wave?

1 The wave is propagating along the negative

x

-axis with speed

25 m s^{- 1}

.

2 The wave is propagating along the positive

x

-axis with speed

100 m s^{- 1}

.

3 The wave is propagating along the positive

x

-axis with speed

25 m s^{- 1}

.

4 The wave is propagating along the negative

x

-axis with speed

100 m s^{- 1}

.

Explanation:

(a) Comparing the given equation
$y = 10^{- 3} sin (50 t + 2 x)$ with standard equation,
$y = asin (ω t - kx)$
$\Rightarrow$ wave is moving along -ve x-axis with speed
$v = \frac{ω}{K} \Rightarrow v = \frac{50}{2} = 25 m / sec$ .

NCERT Page-373 / N-284

WAVES (NCERT)

274436 A progressive wave travelling along the positive $x$ -direction is represented by $y (x, t) = A sin (k x - ω t + ϕ)$ . Its snapshot at $t = 0$ is given in the figure.
For this wave, the phase $ϕ$ is:
12.04.2019 Shift 1 Synergy JEE Mains Nikhil D20

1

- \frac{π}{2}

2

π

3 0

4

\frac{π}{2}

Explanation:

(b) At $t = 0, x = 0, y = 0$
$ϕ = π rad$

NCERT Page-370 / N-282

WAVES (NCERT)

274437 The equation $y = A si n^{2} (k x - ω t)$ represents a wave with

1 amplitude

A

, frequency

ω / 2 π

2 amplitude

A / 2

, frequency

ω / π

3 amplitude

2 A

, frequency

ω / 4 π

4 it does not represent a wave motion

Explanation:

(b) $y = A si n^{2} (k x - ω t)$
$\Rightarrow y = \frac{A}{2} [1 - cos 2 (kx - ω t)]$
$ω^{'} = 2 ω, 2 π v^{'} = 2 ω, v^{'} = \frac{ω}{π}$

NCERT Page-371 / N-283

WAVES (NCERT)

274454 Which of the following equations correctly represents a travelling wave having wavelength $λ = 4.0 cm$ , frequency $v = 100 Hz$ and travelling in positive $x$ -axis direction?

1

y = A sin [(0.50 π c m^{- 1}) x - (100 π s^{- 1}) t]

2

y = A sin 2 π [(0.25 c m^{- 1}) x - (50 s^{- 1}) t]

3

y = A sin [(\frac{2 π}{4} c m^{- 1}) x - (\frac{2 π}{100} s^{- 1}) t]

4

y = A sin π [(0.5 c m^{- 1}) x - (200 s^{- 1}) t]

Explanation:

(d) We have
$k = \frac{2 π}{λ} = \frac{2 π}{4} = 0.5 π c m^{- 1}$
$ω = 2 π f = 2 π \times 100 = 200 π s^{- 1}$

NCERT Page-373 / N-284

WAVES (NCERT)

274455 A travelling harmonic wave is represented by the equation $y (x, t) = 10^{- 3} sin (50 t + 2 x)$ , where $x$ and $y$ are in meter and $t$ is in seconds. Which of the following is a correct statement about the wave?

1 The wave is propagating along the negative

x

-axis with speed

25 m s^{- 1}

.

2 The wave is propagating along the positive

x

-axis with speed

100 m s^{- 1}

.

3 The wave is propagating along the positive

x

-axis with speed

25 m s^{- 1}

.

4 The wave is propagating along the negative

x

-axis with speed

100 m s^{- 1}

.

Explanation:

(a) Comparing the given equation
$y = 10^{- 3} sin (50 t + 2 x)$ with standard equation,
$y = asin (ω t - kx)$
$\Rightarrow$ wave is moving along -ve x-axis with speed
$v = \frac{ω}{K} \Rightarrow v = \frac{50}{2} = 25 m / sec$ .

NCERT Page-373 / N-284

WAVES (NCERT)

274436 A progressive wave travelling along the positive $x$ -direction is represented by $y (x, t) = A sin (k x - ω t + ϕ)$ . Its snapshot at $t = 0$ is given in the figure.
For this wave, the phase $ϕ$ is:
12.04.2019 Shift 1 Synergy JEE Mains Nikhil D20

1

- \frac{π}{2}

2

π

3 0

4

\frac{π}{2}

Explanation:

(b) At $t = 0, x = 0, y = 0$
$ϕ = π rad$

NCERT Page-370 / N-282

WAVES (NCERT)

274437 The equation $y = A si n^{2} (k x - ω t)$ represents a wave with

1 amplitude

A

, frequency

ω / 2 π

2 amplitude

A / 2

, frequency

ω / π

3 amplitude

2 A

, frequency

ω / 4 π

4 it does not represent a wave motion

Explanation:

(b) $y = A si n^{2} (k x - ω t)$
$\Rightarrow y = \frac{A}{2} [1 - cos 2 (kx - ω t)]$
$ω^{'} = 2 ω, 2 π v^{'} = 2 ω, v^{'} = \frac{ω}{π}$

NCERT Page-371 / N-283

WAVES (NCERT)

274454 Which of the following equations correctly represents a travelling wave having wavelength $λ = 4.0 cm$ , frequency $v = 100 Hz$ and travelling in positive $x$ -axis direction?

1

y = A sin [(0.50 π c m^{- 1}) x - (100 π s^{- 1}) t]

2

y = A sin 2 π [(0.25 c m^{- 1}) x - (50 s^{- 1}) t]

3

y = A sin [(\frac{2 π}{4} c m^{- 1}) x - (\frac{2 π}{100} s^{- 1}) t]

4

y = A sin π [(0.5 c m^{- 1}) x - (200 s^{- 1}) t]

Explanation:

(d) We have
$k = \frac{2 π}{λ} = \frac{2 π}{4} = 0.5 π c m^{- 1}$
$ω = 2 π f = 2 π \times 100 = 200 π s^{- 1}$

NCERT Page-373 / N-284

WAVES (NCERT)

274455 A travelling harmonic wave is represented by the equation $y (x, t) = 10^{- 3} sin (50 t + 2 x)$ , where $x$ and $y$ are in meter and $t$ is in seconds. Which of the following is a correct statement about the wave?

1 The wave is propagating along the negative

x

-axis with speed

25 m s^{- 1}

.

2 The wave is propagating along the positive

x

-axis with speed

100 m s^{- 1}

.

3 The wave is propagating along the positive

x

-axis with speed

25 m s^{- 1}

.

4 The wave is propagating along the negative

x

-axis with speed

100 m s^{- 1}

.

Explanation:

(a) Comparing the given equation
$y = 10^{- 3} sin (50 t + 2 x)$ with standard equation,
$y = asin (ω t - kx)$
$\Rightarrow$ wave is moving along -ve x-axis with speed
$v = \frac{ω}{K} \Rightarrow v = \frac{50}{2} = 25 m / sec$ .

NCERT Page-373 / N-284

WAVES (NCERT)

274436 A progressive wave travelling along the positive $x$ -direction is represented by $y (x, t) = A sin (k x - ω t + ϕ)$ . Its snapshot at $t = 0$ is given in the figure.
For this wave, the phase $ϕ$ is:
12.04.2019 Shift 1 Synergy JEE Mains Nikhil D20

1

- \frac{π}{2}

2

π

3 0

4

\frac{π}{2}

Explanation:

(b) At $t = 0, x = 0, y = 0$
$ϕ = π rad$

NCERT Page-370 / N-282

WAVES (NCERT)

274437 The equation $y = A si n^{2} (k x - ω t)$ represents a wave with

1 amplitude

A

, frequency

ω / 2 π

2 amplitude

A / 2

, frequency

ω / π

3 amplitude

2 A

, frequency

ω / 4 π

4 it does not represent a wave motion

Explanation:

(b) $y = A si n^{2} (k x - ω t)$
$\Rightarrow y = \frac{A}{2} [1 - cos 2 (kx - ω t)]$
$ω^{'} = 2 ω, 2 π v^{'} = 2 ω, v^{'} = \frac{ω}{π}$

NCERT Page-371 / N-283

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