QBManager

PHXI15:WAVES

354963 If we study the vibration of a pipe open at both ends, then which of the following statements is not true?

1 All harmonics of the fundamental frequency will be generated

2 Odd harmonics of the fundamental frequency will be generated

3 Antinode will be at open end

4 Pressure change will be maximum at both ends.

PHXI15:WAVES

354964 In the experiment to determine velocity of sound the length of air column in resonance with fork of frequency $450 H z$ in fundamental mode is $40 c m$ . Ignoring end correction, the velocity of sound in air is

1

1020 m s^{- 1}

2

720 m s^{- 1}

3

620 m s^{- 1}

4

820 m s^{- 1}

Explanation:

In the first position of resonance, let length of air column is $l$ ,
$l_{1} = \frac{λ}{4}$
$\Rightarrow λ = 4 l_{1}$
$\Rightarrow λ = 4 \times (0.4)$
$\Rightarrow λ = 1.6 m$
Velocity of sound in air,
$v = f λ$
$= 450 \times 1.6$
$= 720 m s^{- 1}$

AIIMS - 2009

PHXI15:WAVES

354965 An open organ pipe and a closed organ pipe have the frequency of their first overtone identical. The ratio of length of open pipe to that of closed pipe is

1

1 : 2

2

3 : 4

3

4 : 3

4

2 : 1

Explanation:

The frequency higher than the fundamental frequency of sound is known as overtone For open organ pipe, first overtone is
$(v_{0}) = \frac{2 v}{2 L_{0}} = \frac{v}{L_{0}}$
For closed organ pipe, first overtone is
$v_{c} = \frac{3 v}{4 L_{c}}$
It is given that, their first overtone are identical i.e., $v_{o} = v_{c}$
$\frac{v}{L_{o}} = \frac{3 v}{4 L_{c}}$
$\frac{L_{o}}{L_{c}} = \frac{4}{3}$

MHTCET - 2020

PHXI15:WAVES

354966 The closed and open organ pipes have same length. When they are vibrating simultaneously in first overtone, produce three beats. The length of open pipe is made $\frac{1}{3} r d$ and closed pipe is made three times the original, the number of beats produced will be

1 8

2 14

3 17

4 20

Explanation:

For open pipe first overtone
$v_{1} = \frac{v}{L}$
For closed pipe first overtone,
$v_{1} = \frac{3 v}{4 L}$
$∴ v_{1} - v_{1} = \frac{v}{L} - \frac{3 v}{4 L} = 3$
$\Rightarrow \frac{v}{3 L} = 3$
$∴ \frac{v}{L} = 9 (1)$
When length of open pipe is made $\frac{L}{3}$ , then fundamnetal frequency
$v = \frac{v}{2 (\frac{L}{3})} = \frac{3 v}{2 L}$
When length of closed pipe is made 3 times, then fundamental frequency
$v^{'} = \frac{v}{4 (3 L)} = \frac{3 v}{12 L}$
Beats produced $v = v^{'}$ ,
$= \frac{3 v}{2 L} - \frac{v}{12 L} = \frac{17}{12} \frac{v}{L}$
$= \frac{17}{12} \times 12 ∵ [$ from eq. $(1)]$
$= 17$

MHTCET - 2017

PHXI15:WAVES

354963 If we study the vibration of a pipe open at both ends, then which of the following statements is not true?

1 All harmonics of the fundamental frequency will be generated

2 Odd harmonics of the fundamental frequency will be generated

3 Antinode will be at open end

4 Pressure change will be maximum at both ends.

PHXI15:WAVES

354964 In the experiment to determine velocity of sound the length of air column in resonance with fork of frequency $450 H z$ in fundamental mode is $40 c m$ . Ignoring end correction, the velocity of sound in air is

1

1020 m s^{- 1}

2

720 m s^{- 1}

3

620 m s^{- 1}

4

820 m s^{- 1}

Explanation:

In the first position of resonance, let length of air column is $l$ ,
$l_{1} = \frac{λ}{4}$
$\Rightarrow λ = 4 l_{1}$
$\Rightarrow λ = 4 \times (0.4)$
$\Rightarrow λ = 1.6 m$
Velocity of sound in air,
$v = f λ$
$= 450 \times 1.6$
$= 720 m s^{- 1}$

AIIMS - 2009

PHXI15:WAVES

354965 An open organ pipe and a closed organ pipe have the frequency of their first overtone identical. The ratio of length of open pipe to that of closed pipe is

1

1 : 2

2

3 : 4

3

4 : 3

4

2 : 1

Explanation:

The frequency higher than the fundamental frequency of sound is known as overtone For open organ pipe, first overtone is
$(v_{0}) = \frac{2 v}{2 L_{0}} = \frac{v}{L_{0}}$
For closed organ pipe, first overtone is
$v_{c} = \frac{3 v}{4 L_{c}}$
It is given that, their first overtone are identical i.e., $v_{o} = v_{c}$
$\frac{v}{L_{o}} = \frac{3 v}{4 L_{c}}$
$\frac{L_{o}}{L_{c}} = \frac{4}{3}$

MHTCET - 2020

PHXI15:WAVES

354966 The closed and open organ pipes have same length. When they are vibrating simultaneously in first overtone, produce three beats. The length of open pipe is made $\frac{1}{3} r d$ and closed pipe is made three times the original, the number of beats produced will be

1 8

2 14

3 17

4 20

Explanation:

For open pipe first overtone
$v_{1} = \frac{v}{L}$
For closed pipe first overtone,
$v_{1} = \frac{3 v}{4 L}$
$∴ v_{1} - v_{1} = \frac{v}{L} - \frac{3 v}{4 L} = 3$
$\Rightarrow \frac{v}{3 L} = 3$
$∴ \frac{v}{L} = 9 (1)$
When length of open pipe is made $\frac{L}{3}$ , then fundamnetal frequency
$v = \frac{v}{2 (\frac{L}{3})} = \frac{3 v}{2 L}$
When length of closed pipe is made 3 times, then fundamental frequency
$v^{'} = \frac{v}{4 (3 L)} = \frac{3 v}{12 L}$
Beats produced $v = v^{'}$ ,
$= \frac{3 v}{2 L} - \frac{v}{12 L} = \frac{17}{12} \frac{v}{L}$
$= \frac{17}{12} \times 12 ∵ [$ from eq. $(1)]$
$= 17$

MHTCET - 2017

PHXI15:WAVES

354963 If we study the vibration of a pipe open at both ends, then which of the following statements is not true?

1 All harmonics of the fundamental frequency will be generated

2 Odd harmonics of the fundamental frequency will be generated

3 Antinode will be at open end

4 Pressure change will be maximum at both ends.

PHXI15:WAVES

354964 In the experiment to determine velocity of sound the length of air column in resonance with fork of frequency $450 H z$ in fundamental mode is $40 c m$ . Ignoring end correction, the velocity of sound in air is

1

1020 m s^{- 1}

2

720 m s^{- 1}

3

620 m s^{- 1}

4

820 m s^{- 1}

Explanation:

In the first position of resonance, let length of air column is $l$ ,
$l_{1} = \frac{λ}{4}$
$\Rightarrow λ = 4 l_{1}$
$\Rightarrow λ = 4 \times (0.4)$
$\Rightarrow λ = 1.6 m$
Velocity of sound in air,
$v = f λ$
$= 450 \times 1.6$
$= 720 m s^{- 1}$

AIIMS - 2009

PHXI15:WAVES

354965 An open organ pipe and a closed organ pipe have the frequency of their first overtone identical. The ratio of length of open pipe to that of closed pipe is

1

1 : 2

2

3 : 4

3

4 : 3

4

2 : 1

Explanation:

The frequency higher than the fundamental frequency of sound is known as overtone For open organ pipe, first overtone is
$(v_{0}) = \frac{2 v}{2 L_{0}} = \frac{v}{L_{0}}$
For closed organ pipe, first overtone is
$v_{c} = \frac{3 v}{4 L_{c}}$
It is given that, their first overtone are identical i.e., $v_{o} = v_{c}$
$\frac{v}{L_{o}} = \frac{3 v}{4 L_{c}}$
$\frac{L_{o}}{L_{c}} = \frac{4}{3}$

MHTCET - 2020

PHXI15:WAVES

354966 The closed and open organ pipes have same length. When they are vibrating simultaneously in first overtone, produce three beats. The length of open pipe is made $\frac{1}{3} r d$ and closed pipe is made three times the original, the number of beats produced will be

1 8

2 14

3 17

4 20

Explanation:

For open pipe first overtone
$v_{1} = \frac{v}{L}$
For closed pipe first overtone,
$v_{1} = \frac{3 v}{4 L}$
$∴ v_{1} - v_{1} = \frac{v}{L} - \frac{3 v}{4 L} = 3$
$\Rightarrow \frac{v}{3 L} = 3$
$∴ \frac{v}{L} = 9 (1)$
When length of open pipe is made $\frac{L}{3}$ , then fundamnetal frequency
$v = \frac{v}{2 (\frac{L}{3})} = \frac{3 v}{2 L}$
When length of closed pipe is made 3 times, then fundamental frequency
$v^{'} = \frac{v}{4 (3 L)} = \frac{3 v}{12 L}$
Beats produced $v = v^{'}$ ,
$= \frac{3 v}{2 L} - \frac{v}{12 L} = \frac{17}{12} \frac{v}{L}$
$= \frac{17}{12} \times 12 ∵ [$ from eq. $(1)]$
$= 17$

MHTCET - 2017

PHXI15:WAVES

354963 If we study the vibration of a pipe open at both ends, then which of the following statements is not true?

1 All harmonics of the fundamental frequency will be generated

2 Odd harmonics of the fundamental frequency will be generated

3 Antinode will be at open end

4 Pressure change will be maximum at both ends.

PHXI15:WAVES

354964 In the experiment to determine velocity of sound the length of air column in resonance with fork of frequency $450 H z$ in fundamental mode is $40 c m$ . Ignoring end correction, the velocity of sound in air is

1

1020 m s^{- 1}

2

720 m s^{- 1}

3

620 m s^{- 1}

4

820 m s^{- 1}

Explanation:

In the first position of resonance, let length of air column is $l$ ,
$l_{1} = \frac{λ}{4}$
$\Rightarrow λ = 4 l_{1}$
$\Rightarrow λ = 4 \times (0.4)$
$\Rightarrow λ = 1.6 m$
Velocity of sound in air,
$v = f λ$
$= 450 \times 1.6$
$= 720 m s^{- 1}$

AIIMS - 2009

PHXI15:WAVES

354965 An open organ pipe and a closed organ pipe have the frequency of their first overtone identical. The ratio of length of open pipe to that of closed pipe is

1

1 : 2

2

3 : 4

3

4 : 3

4

2 : 1

Explanation:

The frequency higher than the fundamental frequency of sound is known as overtone For open organ pipe, first overtone is
$(v_{0}) = \frac{2 v}{2 L_{0}} = \frac{v}{L_{0}}$
For closed organ pipe, first overtone is
$v_{c} = \frac{3 v}{4 L_{c}}$
It is given that, their first overtone are identical i.e., $v_{o} = v_{c}$
$\frac{v}{L_{o}} = \frac{3 v}{4 L_{c}}$
$\frac{L_{o}}{L_{c}} = \frac{4}{3}$

MHTCET - 2020

PHXI15:WAVES

354966 The closed and open organ pipes have same length. When they are vibrating simultaneously in first overtone, produce three beats. The length of open pipe is made $\frac{1}{3} r d$ and closed pipe is made three times the original, the number of beats produced will be

1 8

2 14

3 17

4 20

Explanation:

For open pipe first overtone
$v_{1} = \frac{v}{L}$
For closed pipe first overtone,
$v_{1} = \frac{3 v}{4 L}$
$∴ v_{1} - v_{1} = \frac{v}{L} - \frac{3 v}{4 L} = 3$
$\Rightarrow \frac{v}{3 L} = 3$
$∴ \frac{v}{L} = 9 (1)$
When length of open pipe is made $\frac{L}{3}$ , then fundamnetal frequency
$v = \frac{v}{2 (\frac{L}{3})} = \frac{3 v}{2 L}$
When length of closed pipe is made 3 times, then fundamental frequency
$v^{'} = \frac{v}{4 (3 L)} = \frac{3 v}{12 L}$
Beats produced $v = v^{'}$ ,
$= \frac{3 v}{2 L} - \frac{v}{12 L} = \frac{17}{12} \frac{v}{L}$
$= \frac{17}{12} \times 12 ∵ [$ from eq. $(1)]$
$= 17$

MHTCET - 2017

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Question Bank Series