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PHXI15:WAVES

354886 A steel rod $2.5 m$ long is rigidly clamped at its centre $C$ and longitudinal waves are set up on both sides of $C$ by rubbing along the rod.
$Y_{s t e e l} = 2 \times 10^{11} N / M^{2}$
$ρ_{s t e e l} = 8000 k g / m^{3}$
If two antinodes are observed on either side of $C$ , the frequency of the mode in which the rod is vibrating will be:

1

1000 H z

2

3000 H z

3

7000 H z

4

1500 H z

Explanation:

As the rod is clamped at its mid point the midpoint $C$ always behaves like a node.
When both sides of $C$ have two antinodes the wave pattern is
supporting img

$\frac{λ}{4} + \frac{λ}{2} + \frac{λ}{2} + \frac{λ}{4} = l \Rightarrow λ = \frac{2 l}{3}$
$f = \frac{v}{λ} = \sqrt{\frac{Y}{ρ}} (\frac{3}{2 l}) = 3000 H z$
When the rod is in Fundamental mode

$\frac{λ}{4} + \frac{λ}{4} = l \Rightarrow λ = 2 l$
$f = \frac{v}{λ} = \sqrt{\frac{Y}{ρ}} \times \frac{1}{2 l} = 1000 H z$
$v_{max} = A ω = 2 π A f = 1.25 \times 10^{- 2} m / s$
If the rod is clamped at an end and when it has four antinodes then the mode of vibration is
supporting img

$\frac{7 λ}{4} = l \Rightarrow λ = \frac{10}{7} m$
$f = \frac{v}{λ} = 3500 H z$

PHXI15:WAVES

354887 A steel rod $100 c m$ long is clamped at is middle. The fundamental frequency of longitudinal vibrations of the rod are given to be $2.53 k H z$ . What is the speed of sound in steel?

1

6 k m / s

2

5 k m / s

3

7 k m / s

4

4 k m / s

Explanation:

In fundamental mode, $l = 2 (\frac{λ}{4}) = \frac{λ}{2}$
supporting img

$\Rightarrow λ = 2 l$
Given $l = 100 c m, f = 2.53 k H z$
Using $v = f λ$
$\Rightarrow v = 2.53 \times 10^{3} \times 2 \times 100 \times 10^{- 2}$
$v = 5.06 k m / s$

NCERT Exemplar

PHXI15:WAVES

354888 Assertion :
In the case of a stationary wave, a person hear a loud sound at the nodes as compared to the antinodes.
Reason :
In a stationary wave all the particles of the medium vibrate in phase.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

Explanation:

The person hears the loud sound at the nodes, not the antinodes, because sound perception is related to pressure variations. At the nodes, where displacement is zero and strain is maximum, the variation in pressure is also maximum due to the equation $P = - E (d y / d t)$ , causing in the perception of a loud sound. So correct option is (3).

PHXI15:WAVES

354889 Assertion :
In a stationary wave, there is no transfer of energy.
Reason :
There is no motion of the disturbance from one particle to adjoining particle in stationary wave.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

PHXI15:WAVES

354886 A steel rod $2.5 m$ long is rigidly clamped at its centre $C$ and longitudinal waves are set up on both sides of $C$ by rubbing along the rod.
$Y_{s t e e l} = 2 \times 10^{11} N / M^{2}$
$ρ_{s t e e l} = 8000 k g / m^{3}$
If two antinodes are observed on either side of $C$ , the frequency of the mode in which the rod is vibrating will be:

1

1000 H z

2

3000 H z

3

7000 H z

4

1500 H z

Explanation:

As the rod is clamped at its mid point the midpoint $C$ always behaves like a node.
When both sides of $C$ have two antinodes the wave pattern is
supporting img

$\frac{λ}{4} + \frac{λ}{2} + \frac{λ}{2} + \frac{λ}{4} = l \Rightarrow λ = \frac{2 l}{3}$
$f = \frac{v}{λ} = \sqrt{\frac{Y}{ρ}} (\frac{3}{2 l}) = 3000 H z$
When the rod is in Fundamental mode

$\frac{λ}{4} + \frac{λ}{4} = l \Rightarrow λ = 2 l$
$f = \frac{v}{λ} = \sqrt{\frac{Y}{ρ}} \times \frac{1}{2 l} = 1000 H z$
$v_{max} = A ω = 2 π A f = 1.25 \times 10^{- 2} m / s$
If the rod is clamped at an end and when it has four antinodes then the mode of vibration is
supporting img

$\frac{7 λ}{4} = l \Rightarrow λ = \frac{10}{7} m$
$f = \frac{v}{λ} = 3500 H z$

PHXI15:WAVES

354887 A steel rod $100 c m$ long is clamped at is middle. The fundamental frequency of longitudinal vibrations of the rod are given to be $2.53 k H z$ . What is the speed of sound in steel?

1

6 k m / s

2

5 k m / s

3

7 k m / s

4

4 k m / s

Explanation:

In fundamental mode, $l = 2 (\frac{λ}{4}) = \frac{λ}{2}$
supporting img

$\Rightarrow λ = 2 l$
Given $l = 100 c m, f = 2.53 k H z$
Using $v = f λ$
$\Rightarrow v = 2.53 \times 10^{3} \times 2 \times 100 \times 10^{- 2}$
$v = 5.06 k m / s$

NCERT Exemplar

PHXI15:WAVES

354888 Assertion :
In the case of a stationary wave, a person hear a loud sound at the nodes as compared to the antinodes.
Reason :
In a stationary wave all the particles of the medium vibrate in phase.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

Explanation:

The person hears the loud sound at the nodes, not the antinodes, because sound perception is related to pressure variations. At the nodes, where displacement is zero and strain is maximum, the variation in pressure is also maximum due to the equation $P = - E (d y / d t)$ , causing in the perception of a loud sound. So correct option is (3).

PHXI15:WAVES

354889 Assertion :
In a stationary wave, there is no transfer of energy.
Reason :
There is no motion of the disturbance from one particle to adjoining particle in stationary wave.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

PHXI15:WAVES

354886 A steel rod $2.5 m$ long is rigidly clamped at its centre $C$ and longitudinal waves are set up on both sides of $C$ by rubbing along the rod.
$Y_{s t e e l} = 2 \times 10^{11} N / M^{2}$
$ρ_{s t e e l} = 8000 k g / m^{3}$
If two antinodes are observed on either side of $C$ , the frequency of the mode in which the rod is vibrating will be:

1

1000 H z

2

3000 H z

3

7000 H z

4

1500 H z

Explanation:

As the rod is clamped at its mid point the midpoint $C$ always behaves like a node.
When both sides of $C$ have two antinodes the wave pattern is
supporting img

$\frac{λ}{4} + \frac{λ}{2} + \frac{λ}{2} + \frac{λ}{4} = l \Rightarrow λ = \frac{2 l}{3}$
$f = \frac{v}{λ} = \sqrt{\frac{Y}{ρ}} (\frac{3}{2 l}) = 3000 H z$
When the rod is in Fundamental mode

$\frac{λ}{4} + \frac{λ}{4} = l \Rightarrow λ = 2 l$
$f = \frac{v}{λ} = \sqrt{\frac{Y}{ρ}} \times \frac{1}{2 l} = 1000 H z$
$v_{max} = A ω = 2 π A f = 1.25 \times 10^{- 2} m / s$
If the rod is clamped at an end and when it has four antinodes then the mode of vibration is
supporting img

$\frac{7 λ}{4} = l \Rightarrow λ = \frac{10}{7} m$
$f = \frac{v}{λ} = 3500 H z$

PHXI15:WAVES

354887 A steel rod $100 c m$ long is clamped at is middle. The fundamental frequency of longitudinal vibrations of the rod are given to be $2.53 k H z$ . What is the speed of sound in steel?

1

6 k m / s

2

5 k m / s

3

7 k m / s

4

4 k m / s

Explanation:

In fundamental mode, $l = 2 (\frac{λ}{4}) = \frac{λ}{2}$
supporting img

$\Rightarrow λ = 2 l$
Given $l = 100 c m, f = 2.53 k H z$
Using $v = f λ$
$\Rightarrow v = 2.53 \times 10^{3} \times 2 \times 100 \times 10^{- 2}$
$v = 5.06 k m / s$

NCERT Exemplar

PHXI15:WAVES

354888 Assertion :
In the case of a stationary wave, a person hear a loud sound at the nodes as compared to the antinodes.
Reason :
In a stationary wave all the particles of the medium vibrate in phase.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

Explanation:

The person hears the loud sound at the nodes, not the antinodes, because sound perception is related to pressure variations. At the nodes, where displacement is zero and strain is maximum, the variation in pressure is also maximum due to the equation $P = - E (d y / d t)$ , causing in the perception of a loud sound. So correct option is (3).

PHXI15:WAVES

354889 Assertion :
In a stationary wave, there is no transfer of energy.
Reason :
There is no motion of the disturbance from one particle to adjoining particle in stationary wave.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

PHXI15:WAVES

354886 A steel rod $2.5 m$ long is rigidly clamped at its centre $C$ and longitudinal waves are set up on both sides of $C$ by rubbing along the rod.
$Y_{s t e e l} = 2 \times 10^{11} N / M^{2}$
$ρ_{s t e e l} = 8000 k g / m^{3}$
If two antinodes are observed on either side of $C$ , the frequency of the mode in which the rod is vibrating will be:

1

1000 H z

2

3000 H z

3

7000 H z

4

1500 H z

Explanation:

As the rod is clamped at its mid point the midpoint $C$ always behaves like a node.
When both sides of $C$ have two antinodes the wave pattern is
supporting img

$\frac{λ}{4} + \frac{λ}{2} + \frac{λ}{2} + \frac{λ}{4} = l \Rightarrow λ = \frac{2 l}{3}$
$f = \frac{v}{λ} = \sqrt{\frac{Y}{ρ}} (\frac{3}{2 l}) = 3000 H z$
When the rod is in Fundamental mode

$\frac{λ}{4} + \frac{λ}{4} = l \Rightarrow λ = 2 l$
$f = \frac{v}{λ} = \sqrt{\frac{Y}{ρ}} \times \frac{1}{2 l} = 1000 H z$
$v_{max} = A ω = 2 π A f = 1.25 \times 10^{- 2} m / s$
If the rod is clamped at an end and when it has four antinodes then the mode of vibration is
supporting img

$\frac{7 λ}{4} = l \Rightarrow λ = \frac{10}{7} m$
$f = \frac{v}{λ} = 3500 H z$

PHXI15:WAVES

354887 A steel rod $100 c m$ long is clamped at is middle. The fundamental frequency of longitudinal vibrations of the rod are given to be $2.53 k H z$ . What is the speed of sound in steel?

1

6 k m / s

2

5 k m / s

3

7 k m / s

4

4 k m / s

Explanation:

In fundamental mode, $l = 2 (\frac{λ}{4}) = \frac{λ}{2}$
supporting img

$\Rightarrow λ = 2 l$
Given $l = 100 c m, f = 2.53 k H z$
Using $v = f λ$
$\Rightarrow v = 2.53 \times 10^{3} \times 2 \times 100 \times 10^{- 2}$
$v = 5.06 k m / s$

NCERT Exemplar

PHXI15:WAVES

354888 Assertion :
In the case of a stationary wave, a person hear a loud sound at the nodes as compared to the antinodes.
Reason :
In a stationary wave all the particles of the medium vibrate in phase.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

Explanation:

The person hears the loud sound at the nodes, not the antinodes, because sound perception is related to pressure variations. At the nodes, where displacement is zero and strain is maximum, the variation in pressure is also maximum due to the equation $P = - E (d y / d t)$ , causing in the perception of a loud sound. So correct option is (3).

PHXI15:WAVES

354889 Assertion :
In a stationary wave, there is no transfer of energy.
Reason :
There is no motion of the disturbance from one particle to adjoining particle in stationary wave.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

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