QBManager

PHXI15:WAVES

355025 Beats are produced by two waves $y_{1} = a \sin (1000 π t)$ and $y_{2} = a \sin (998 π t)$ The number of beats heard per second is

1 0

2 2

3 1

4 4

Explanation:

Comparing each wave equation with the standard wave equation,
$y = a \sin ω t = a \sin 2 π n t$ ,
the frequencies of the two waves are
$n_{1} = 500 H z$ and $n_{2} = \frac{998}{2} = 499 H z$
$∴$ Beat frequency $= n_{1} - n_{2} = 500 - 499$
$= 1 b e a t / \sec$

PHXI15:WAVES

355026 A closed organ pipe and an open organ pipe of same length produce 2 beats when they are set into vibrations simultaneously in their fundamental mode. The length of the open organ pipe is now halved and of the closed organ pipe is doubled, the number of beats produced will be

1 8

2 7

3 4

4 2

Explanation:

$f_{o} - f_{c} = 2$
or $\frac{v}{2 l} - \frac{v}{4 l} = 2 \Rightarrow \frac{v}{4 l} = 2$
$\Rightarrow \frac{v}{l} = 8 (1)$
When length of open organ pipe is halved and that of closed organ pipe is doubled, the beat frequency will be,
$f_{o}^{'} - f_{c}^{'} = \frac{v}{l} - \frac{v}{8 l} = \frac{7}{8} \frac{v}{l} = \frac{7}{8} \times 8 = 7$

PHXI15:WAVES

355027 There is a set of 4 tuning forks, one with lowest frequency vibrating at $552 H z$ . By using any two forks at time, the beat frequencies heard are 1, $2, 3, 5, 7, 8$ . The possible frequencies of other three forks are :-

1

553, 554 and 560 H z

2

553, 555 and 560 H z

3

553, 556 and 558 H z

4

551, 554 and 560 H z

PHXI15:WAVES

355028 Two identical piano wires kept under the same tension $T$ have a fundamental frequency of $600 H z$ . The dfractional increase in the tension of one of the wires which will lead to occurrence of 6 beats when both the wires ocscillate together would be

1 0.02

2 0.03

3 0.04

4 0.01

Explanation:

According to law of tension, the frequency of the string varies directly as the square root of its tension $f \propto \sqrt{T}$
$\frac{Δ f}{f} = \frac{1}{2} \cdot \frac{Δ T}{T}$ or $\frac{Δ T}{T} = 2 \times \frac{Δ f}{f}$
$\frac{Δ T}{T} = 2 \times \frac{6}{600} = 0.02$

PHXI15:WAVES

355025 Beats are produced by two waves $y_{1} = a \sin (1000 π t)$ and $y_{2} = a \sin (998 π t)$ The number of beats heard per second is

1 0

2 2

3 1

4 4

Explanation:

Comparing each wave equation with the standard wave equation,
$y = a \sin ω t = a \sin 2 π n t$ ,
the frequencies of the two waves are
$n_{1} = 500 H z$ and $n_{2} = \frac{998}{2} = 499 H z$
$∴$ Beat frequency $= n_{1} - n_{2} = 500 - 499$
$= 1 b e a t / \sec$

PHXI15:WAVES

355026 A closed organ pipe and an open organ pipe of same length produce 2 beats when they are set into vibrations simultaneously in their fundamental mode. The length of the open organ pipe is now halved and of the closed organ pipe is doubled, the number of beats produced will be

1 8

2 7

3 4

4 2

Explanation:

$f_{o} - f_{c} = 2$
or $\frac{v}{2 l} - \frac{v}{4 l} = 2 \Rightarrow \frac{v}{4 l} = 2$
$\Rightarrow \frac{v}{l} = 8 (1)$
When length of open organ pipe is halved and that of closed organ pipe is doubled, the beat frequency will be,
$f_{o}^{'} - f_{c}^{'} = \frac{v}{l} - \frac{v}{8 l} = \frac{7}{8} \frac{v}{l} = \frac{7}{8} \times 8 = 7$

PHXI15:WAVES

355027 There is a set of 4 tuning forks, one with lowest frequency vibrating at $552 H z$ . By using any two forks at time, the beat frequencies heard are 1, $2, 3, 5, 7, 8$ . The possible frequencies of other three forks are :-

1

553, 554 and 560 H z

2

553, 555 and 560 H z

3

553, 556 and 558 H z

4

551, 554 and 560 H z

PHXI15:WAVES

355028 Two identical piano wires kept under the same tension $T$ have a fundamental frequency of $600 H z$ . The dfractional increase in the tension of one of the wires which will lead to occurrence of 6 beats when both the wires ocscillate together would be

1 0.02

2 0.03

3 0.04

4 0.01

Explanation:

According to law of tension, the frequency of the string varies directly as the square root of its tension $f \propto \sqrt{T}$
$\frac{Δ f}{f} = \frac{1}{2} \cdot \frac{Δ T}{T}$ or $\frac{Δ T}{T} = 2 \times \frac{Δ f}{f}$
$\frac{Δ T}{T} = 2 \times \frac{6}{600} = 0.02$

PHXI15:WAVES

355025 Beats are produced by two waves $y_{1} = a \sin (1000 π t)$ and $y_{2} = a \sin (998 π t)$ The number of beats heard per second is

1 0

2 2

3 1

4 4

Explanation:

Comparing each wave equation with the standard wave equation,
$y = a \sin ω t = a \sin 2 π n t$ ,
the frequencies of the two waves are
$n_{1} = 500 H z$ and $n_{2} = \frac{998}{2} = 499 H z$
$∴$ Beat frequency $= n_{1} - n_{2} = 500 - 499$
$= 1 b e a t / \sec$

PHXI15:WAVES

355026 A closed organ pipe and an open organ pipe of same length produce 2 beats when they are set into vibrations simultaneously in their fundamental mode. The length of the open organ pipe is now halved and of the closed organ pipe is doubled, the number of beats produced will be

1 8

2 7

3 4

4 2

Explanation:

$f_{o} - f_{c} = 2$
or $\frac{v}{2 l} - \frac{v}{4 l} = 2 \Rightarrow \frac{v}{4 l} = 2$
$\Rightarrow \frac{v}{l} = 8 (1)$
When length of open organ pipe is halved and that of closed organ pipe is doubled, the beat frequency will be,
$f_{o}^{'} - f_{c}^{'} = \frac{v}{l} - \frac{v}{8 l} = \frac{7}{8} \frac{v}{l} = \frac{7}{8} \times 8 = 7$

PHXI15:WAVES

355027 There is a set of 4 tuning forks, one with lowest frequency vibrating at $552 H z$ . By using any two forks at time, the beat frequencies heard are 1, $2, 3, 5, 7, 8$ . The possible frequencies of other three forks are :-

1

553, 554 and 560 H z

2

553, 555 and 560 H z

3

553, 556 and 558 H z

4

551, 554 and 560 H z

PHXI15:WAVES

355028 Two identical piano wires kept under the same tension $T$ have a fundamental frequency of $600 H z$ . The dfractional increase in the tension of one of the wires which will lead to occurrence of 6 beats when both the wires ocscillate together would be

1 0.02

2 0.03

3 0.04

4 0.01

Explanation:

According to law of tension, the frequency of the string varies directly as the square root of its tension $f \propto \sqrt{T}$
$\frac{Δ f}{f} = \frac{1}{2} \cdot \frac{Δ T}{T}$ or $\frac{Δ T}{T} = 2 \times \frac{Δ f}{f}$
$\frac{Δ T}{T} = 2 \times \frac{6}{600} = 0.02$

PHXI15:WAVES

355025 Beats are produced by two waves $y_{1} = a \sin (1000 π t)$ and $y_{2} = a \sin (998 π t)$ The number of beats heard per second is

1 0

2 2

3 1

4 4

Explanation:

Comparing each wave equation with the standard wave equation,
$y = a \sin ω t = a \sin 2 π n t$ ,
the frequencies of the two waves are
$n_{1} = 500 H z$ and $n_{2} = \frac{998}{2} = 499 H z$
$∴$ Beat frequency $= n_{1} - n_{2} = 500 - 499$
$= 1 b e a t / \sec$

PHXI15:WAVES

355026 A closed organ pipe and an open organ pipe of same length produce 2 beats when they are set into vibrations simultaneously in their fundamental mode. The length of the open organ pipe is now halved and of the closed organ pipe is doubled, the number of beats produced will be

1 8

2 7

3 4

4 2

Explanation:

$f_{o} - f_{c} = 2$
or $\frac{v}{2 l} - \frac{v}{4 l} = 2 \Rightarrow \frac{v}{4 l} = 2$
$\Rightarrow \frac{v}{l} = 8 (1)$
When length of open organ pipe is halved and that of closed organ pipe is doubled, the beat frequency will be,
$f_{o}^{'} - f_{c}^{'} = \frac{v}{l} - \frac{v}{8 l} = \frac{7}{8} \frac{v}{l} = \frac{7}{8} \times 8 = 7$

PHXI15:WAVES

355027 There is a set of 4 tuning forks, one with lowest frequency vibrating at $552 H z$ . By using any two forks at time, the beat frequencies heard are 1, $2, 3, 5, 7, 8$ . The possible frequencies of other three forks are :-

1

553, 554 and 560 H z

2

553, 555 and 560 H z

3

553, 556 and 558 H z

4

551, 554 and 560 H z

PHXI15:WAVES

355028 Two identical piano wires kept under the same tension $T$ have a fundamental frequency of $600 H z$ . The dfractional increase in the tension of one of the wires which will lead to occurrence of 6 beats when both the wires ocscillate together would be

1 0.02

2 0.03

3 0.04

4 0.01

Explanation:

According to law of tension, the frequency of the string varies directly as the square root of its tension $f \propto \sqrt{T}$
$\frac{Δ f}{f} = \frac{1}{2} \cdot \frac{Δ T}{T}$ or $\frac{Δ T}{T} = 2 \times \frac{Δ f}{f}$
$\frac{Δ T}{T} = 2 \times \frac{6}{600} = 0.02$

Question Bank Series

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation: