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PHXI15:WAVES

354524 The equation of the progressive wave is $y = 3 \sin [π (\frac{t}{3} - \frac{x}{5}) + \frac{π}{4}]$ , where $x$ and $y$ are in metre and time in second. Which of the following is correct?

1 Velocity

v = 1.5 m / s

2 Amplitude

A = 3 c m

3 Frequency

f = 0.2 H z

4 Wavelength

λ = 10 m

Explanation:

Compare the given equation with the standard equation of wave motion, $Y = A \sin [2 π (\frac{t}{T} - \frac{x}{λ}) + \frac{π}{4}]$
Where, $A$ and $λ$ are amplitude and wavelength, respectively
Amplitude A $= 3 m$
Wavelength $λ = 10 m$ .

MHTCET - 2017

PHXI15:WAVES

354525 $y = (x, t) = \frac{0.8}{(4 x + 5 t)^{2} + 5}$ represents a moving pulse, where $x$ and $y$ are in metre and $t$ is in second, then incorrect statement of the following

1 Pulse is moving in

+ x

direction

2 In

2 s

it will travel a distance of

2.5 m

3 Its maximum displacement is

0.16 m

4 It is a symmetric pulse

Explanation:

$y = \frac{0.8}{(4 x + 5 t)^{2} + 5} = \frac{0.8}{4^{2} {(x + \frac{5}{4} t)}^{2} + 5}$
$y = f (n \pm v t)$
$v = \frac{5}{4} m / s$
$∴ x = v t = \frac{5}{4} \times 2 = 2.5 m / s$
wave is moving -ve $x$ -direction
$∴$ Distance traversed in $2 \sec = \frac{5}{4} \times 2 m = 2.5 m$ At $t = 0, x = 0, y_{max} (x, t) = \frac{0.8}{5} m = 0.16 m$
At $t = 0$ and $x = \pm a (a = a + v e$ constant ) . $y$ will have same value. So the pulse is symmetric.

PHXI15:WAVES

354526 A wave equation which gives the displacement along the $y$ -direction is given by
$y = 10^{- 4} \sin (60 t + 2 x)$ where $x$ and $y$ are in metre and $t$ is time in second. This represents a wave

1 Travelling with a velocity of

30 m / s

in the positive

x

-direction

2 Of wavelength

2 π m

3 Of frequency

\frac{30}{π}

hertz

4 Of amplitude

2 \times 10^{- 4} m

Explanation:

$y = 10^{- 4} \sin (60 t + 2 x)$
$A = 10^{- 4} m, ω = 60 r a d / \sec, k = 2 m^{- 1}$
Speed of wave $v = \frac{ω}{k} = 30 m / \sec$
$f = \frac{ω}{2 π} = \frac{60}{2 π} = \frac{30}{π} H z$
$λ = \frac{2 π}{k} = π m$

PHXI15:WAVES

354527 Which of the following does not represent a travelling wave?

1

y = y_{m} \sin k (x + v t)

2

y = \sin (x - v t)

3

y = f (x^{2} - v t^{2})

4

y = y_{m} \log (x - v t)

Explanation:

$y = f (x^{2} - v t^{2})$ doesn't follow the standard wave equation $f (x \pm t)$ .

PHXI15:WAVES

354524 The equation of the progressive wave is $y = 3 \sin [π (\frac{t}{3} - \frac{x}{5}) + \frac{π}{4}]$ , where $x$ and $y$ are in metre and time in second. Which of the following is correct?

1 Velocity

v = 1.5 m / s

2 Amplitude

A = 3 c m

3 Frequency

f = 0.2 H z

4 Wavelength

λ = 10 m

Explanation:

Compare the given equation with the standard equation of wave motion, $Y = A \sin [2 π (\frac{t}{T} - \frac{x}{λ}) + \frac{π}{4}]$
Where, $A$ and $λ$ are amplitude and wavelength, respectively
Amplitude A $= 3 m$
Wavelength $λ = 10 m$ .

MHTCET - 2017

PHXI15:WAVES

354525 $y = (x, t) = \frac{0.8}{(4 x + 5 t)^{2} + 5}$ represents a moving pulse, where $x$ and $y$ are in metre and $t$ is in second, then incorrect statement of the following

1 Pulse is moving in

+ x

direction

2 In

2 s

it will travel a distance of

2.5 m

3 Its maximum displacement is

0.16 m

4 It is a symmetric pulse

Explanation:

$y = \frac{0.8}{(4 x + 5 t)^{2} + 5} = \frac{0.8}{4^{2} {(x + \frac{5}{4} t)}^{2} + 5}$
$y = f (n \pm v t)$
$v = \frac{5}{4} m / s$
$∴ x = v t = \frac{5}{4} \times 2 = 2.5 m / s$
wave is moving -ve $x$ -direction
$∴$ Distance traversed in $2 \sec = \frac{5}{4} \times 2 m = 2.5 m$ At $t = 0, x = 0, y_{max} (x, t) = \frac{0.8}{5} m = 0.16 m$
At $t = 0$ and $x = \pm a (a = a + v e$ constant ) . $y$ will have same value. So the pulse is symmetric.

PHXI15:WAVES

354526 A wave equation which gives the displacement along the $y$ -direction is given by
$y = 10^{- 4} \sin (60 t + 2 x)$ where $x$ and $y$ are in metre and $t$ is time in second. This represents a wave

1 Travelling with a velocity of

30 m / s

in the positive

x

-direction

2 Of wavelength

2 π m

3 Of frequency

\frac{30}{π}

hertz

4 Of amplitude

2 \times 10^{- 4} m

Explanation:

$y = 10^{- 4} \sin (60 t + 2 x)$
$A = 10^{- 4} m, ω = 60 r a d / \sec, k = 2 m^{- 1}$
Speed of wave $v = \frac{ω}{k} = 30 m / \sec$
$f = \frac{ω}{2 π} = \frac{60}{2 π} = \frac{30}{π} H z$
$λ = \frac{2 π}{k} = π m$

PHXI15:WAVES

354527 Which of the following does not represent a travelling wave?

1

y = y_{m} \sin k (x + v t)

2

y = \sin (x - v t)

3

y = f (x^{2} - v t^{2})

4

y = y_{m} \log (x - v t)

Explanation:

$y = f (x^{2} - v t^{2})$ doesn't follow the standard wave equation $f (x \pm t)$ .

PHXI15:WAVES

354524 The equation of the progressive wave is $y = 3 \sin [π (\frac{t}{3} - \frac{x}{5}) + \frac{π}{4}]$ , where $x$ and $y$ are in metre and time in second. Which of the following is correct?

1 Velocity

v = 1.5 m / s

2 Amplitude

A = 3 c m

3 Frequency

f = 0.2 H z

4 Wavelength

λ = 10 m

Explanation:

Compare the given equation with the standard equation of wave motion, $Y = A \sin [2 π (\frac{t}{T} - \frac{x}{λ}) + \frac{π}{4}]$
Where, $A$ and $λ$ are amplitude and wavelength, respectively
Amplitude A $= 3 m$
Wavelength $λ = 10 m$ .

MHTCET - 2017

PHXI15:WAVES

354525 $y = (x, t) = \frac{0.8}{(4 x + 5 t)^{2} + 5}$ represents a moving pulse, where $x$ and $y$ are in metre and $t$ is in second, then incorrect statement of the following

1 Pulse is moving in

+ x

direction

2 In

2 s

it will travel a distance of

2.5 m

3 Its maximum displacement is

0.16 m

4 It is a symmetric pulse

Explanation:

$y = \frac{0.8}{(4 x + 5 t)^{2} + 5} = \frac{0.8}{4^{2} {(x + \frac{5}{4} t)}^{2} + 5}$
$y = f (n \pm v t)$
$v = \frac{5}{4} m / s$
$∴ x = v t = \frac{5}{4} \times 2 = 2.5 m / s$
wave is moving -ve $x$ -direction
$∴$ Distance traversed in $2 \sec = \frac{5}{4} \times 2 m = 2.5 m$ At $t = 0, x = 0, y_{max} (x, t) = \frac{0.8}{5} m = 0.16 m$
At $t = 0$ and $x = \pm a (a = a + v e$ constant ) . $y$ will have same value. So the pulse is symmetric.

PHXI15:WAVES

354526 A wave equation which gives the displacement along the $y$ -direction is given by
$y = 10^{- 4} \sin (60 t + 2 x)$ where $x$ and $y$ are in metre and $t$ is time in second. This represents a wave

1 Travelling with a velocity of

30 m / s

in the positive

x

-direction

2 Of wavelength

2 π m

3 Of frequency

\frac{30}{π}

hertz

4 Of amplitude

2 \times 10^{- 4} m

Explanation:

$y = 10^{- 4} \sin (60 t + 2 x)$
$A = 10^{- 4} m, ω = 60 r a d / \sec, k = 2 m^{- 1}$
Speed of wave $v = \frac{ω}{k} = 30 m / \sec$
$f = \frac{ω}{2 π} = \frac{60}{2 π} = \frac{30}{π} H z$
$λ = \frac{2 π}{k} = π m$

PHXI15:WAVES

354527 Which of the following does not represent a travelling wave?

1

y = y_{m} \sin k (x + v t)

2

y = \sin (x - v t)

3

y = f (x^{2} - v t^{2})

4

y = y_{m} \log (x - v t)

Explanation:

$y = f (x^{2} - v t^{2})$ doesn't follow the standard wave equation $f (x \pm t)$ .

PHXI15:WAVES

354524 The equation of the progressive wave is $y = 3 \sin [π (\frac{t}{3} - \frac{x}{5}) + \frac{π}{4}]$ , where $x$ and $y$ are in metre and time in second. Which of the following is correct?

1 Velocity

v = 1.5 m / s

2 Amplitude

A = 3 c m

3 Frequency

f = 0.2 H z

4 Wavelength

λ = 10 m

Explanation:

Compare the given equation with the standard equation of wave motion, $Y = A \sin [2 π (\frac{t}{T} - \frac{x}{λ}) + \frac{π}{4}]$
Where, $A$ and $λ$ are amplitude and wavelength, respectively
Amplitude A $= 3 m$
Wavelength $λ = 10 m$ .

MHTCET - 2017

PHXI15:WAVES

354525 $y = (x, t) = \frac{0.8}{(4 x + 5 t)^{2} + 5}$ represents a moving pulse, where $x$ and $y$ are in metre and $t$ is in second, then incorrect statement of the following

1 Pulse is moving in

+ x

direction

2 In

2 s

it will travel a distance of

2.5 m

3 Its maximum displacement is

0.16 m

4 It is a symmetric pulse

Explanation:

$y = \frac{0.8}{(4 x + 5 t)^{2} + 5} = \frac{0.8}{4^{2} {(x + \frac{5}{4} t)}^{2} + 5}$
$y = f (n \pm v t)$
$v = \frac{5}{4} m / s$
$∴ x = v t = \frac{5}{4} \times 2 = 2.5 m / s$
wave is moving -ve $x$ -direction
$∴$ Distance traversed in $2 \sec = \frac{5}{4} \times 2 m = 2.5 m$ At $t = 0, x = 0, y_{max} (x, t) = \frac{0.8}{5} m = 0.16 m$
At $t = 0$ and $x = \pm a (a = a + v e$ constant ) . $y$ will have same value. So the pulse is symmetric.

PHXI15:WAVES

354526 A wave equation which gives the displacement along the $y$ -direction is given by
$y = 10^{- 4} \sin (60 t + 2 x)$ where $x$ and $y$ are in metre and $t$ is time in second. This represents a wave

1 Travelling with a velocity of

30 m / s

in the positive

x

-direction

2 Of wavelength

2 π m

3 Of frequency

\frac{30}{π}

hertz

4 Of amplitude

2 \times 10^{- 4} m

Explanation:

$y = 10^{- 4} \sin (60 t + 2 x)$
$A = 10^{- 4} m, ω = 60 r a d / \sec, k = 2 m^{- 1}$
Speed of wave $v = \frac{ω}{k} = 30 m / \sec$
$f = \frac{ω}{2 π} = \frac{60}{2 π} = \frac{30}{π} H z$
$λ = \frac{2 π}{k} = π m$

PHXI15:WAVES

354527 Which of the following does not represent a travelling wave?

1

y = y_{m} \sin k (x + v t)

2

y = \sin (x - v t)

3

y = f (x^{2} - v t^{2})

4

y = y_{m} \log (x - v t)

Explanation:

$y = f (x^{2} - v t^{2})$ doesn't follow the standard wave equation $f (x \pm t)$ .