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PHXI15:WAVES

355165 When a string fixed at both ends vibrates in 1 loop, 2 loops, 3 loops and 4 loops, the frequenices are in the ratio

1

1 : 2 : 3 : 4

2

1 : 1 : 1 : 1

3

1 : 4 : 9 : 16

4

4 : 3 : 2 : 1

Explanation:

When the string vibrates in $n$ loops, its frequency is $f_{n} = \frac{n v}{2 L}$
Where $L$ is the length of the string and $v$ is the velocity of the wave.
$∴$ When the string fixed at its both ends vibrates in 1 loop, 2 loops, 3 loops and 4 loops, the frequencies are in the ratio $1 : 2 : 3 : 4$

PHXI15:WAVES

355166 A $10 c m$ long rubber band obeys Hooke's law. When the rubber band is stretched to a total length of $12 c m$ the lowest resonant frequency is $f_{0}$ . The rubber band is then stretched to a length of $13 c m$ . The lowest resonant frequency will now be

1 Lower than

f_{0}

2 Higher than

f_{0}

3 The same as

f_{0}

4 Changed, but the change (positive or negative) depends on the elastic constant and the original tension

Explanation:

$f_{0} = \frac{1}{2 l} \sqrt{\frac{T}{μ}}$
For elastic wire $T = K x$
$x \to$ elongation from natural length
Hence frequency depends on $K$ and original tension

PHXI15:WAVES

355167 For a stationary wave, $Y = 10 \sin (\frac{π x}{15}) \cos (48 π t) c m$ , the distance between a node and the successive antinode is

1

60 c m

2

30 c m

3

7.5 c m

4

15 c m

Explanation:

On comparing the given equation with a standard stationary wave equation, we get
$k = \frac{π}{15} = \frac{2 π}{λ} \Rightarrow λ = 30 c m$
Distance between node and antinode is,
$\frac{λ}{4} = \frac{30}{4} = 7.5 c m$

MHTCET - 2022

PHXI15:WAVES

355168 The waves formed in stretched strings are

1 Transverse

2 Longitudinal

3 Both longitudinal and transverse

4 Shock waves

PHXI15:WAVES

355165 When a string fixed at both ends vibrates in 1 loop, 2 loops, 3 loops and 4 loops, the frequenices are in the ratio

1

1 : 2 : 3 : 4

2

1 : 1 : 1 : 1

3

1 : 4 : 9 : 16

4

4 : 3 : 2 : 1

Explanation:

When the string vibrates in $n$ loops, its frequency is $f_{n} = \frac{n v}{2 L}$
Where $L$ is the length of the string and $v$ is the velocity of the wave.
$∴$ When the string fixed at its both ends vibrates in 1 loop, 2 loops, 3 loops and 4 loops, the frequencies are in the ratio $1 : 2 : 3 : 4$

PHXI15:WAVES

355166 A $10 c m$ long rubber band obeys Hooke's law. When the rubber band is stretched to a total length of $12 c m$ the lowest resonant frequency is $f_{0}$ . The rubber band is then stretched to a length of $13 c m$ . The lowest resonant frequency will now be

1 Lower than

f_{0}

2 Higher than

f_{0}

3 The same as

f_{0}

4 Changed, but the change (positive or negative) depends on the elastic constant and the original tension

Explanation:

$f_{0} = \frac{1}{2 l} \sqrt{\frac{T}{μ}}$
For elastic wire $T = K x$
$x \to$ elongation from natural length
Hence frequency depends on $K$ and original tension

PHXI15:WAVES

355167 For a stationary wave, $Y = 10 \sin (\frac{π x}{15}) \cos (48 π t) c m$ , the distance between a node and the successive antinode is

1

60 c m

2

30 c m

3

7.5 c m

4

15 c m

Explanation:

On comparing the given equation with a standard stationary wave equation, we get
$k = \frac{π}{15} = \frac{2 π}{λ} \Rightarrow λ = 30 c m$
Distance between node and antinode is,
$\frac{λ}{4} = \frac{30}{4} = 7.5 c m$

MHTCET - 2022

PHXI15:WAVES

355168 The waves formed in stretched strings are

1 Transverse

2 Longitudinal

3 Both longitudinal and transverse

4 Shock waves

PHXI15:WAVES

355165 When a string fixed at both ends vibrates in 1 loop, 2 loops, 3 loops and 4 loops, the frequenices are in the ratio

1

1 : 2 : 3 : 4

2

1 : 1 : 1 : 1

3

1 : 4 : 9 : 16

4

4 : 3 : 2 : 1

Explanation:

When the string vibrates in $n$ loops, its frequency is $f_{n} = \frac{n v}{2 L}$
Where $L$ is the length of the string and $v$ is the velocity of the wave.
$∴$ When the string fixed at its both ends vibrates in 1 loop, 2 loops, 3 loops and 4 loops, the frequencies are in the ratio $1 : 2 : 3 : 4$

PHXI15:WAVES

355166 A $10 c m$ long rubber band obeys Hooke's law. When the rubber band is stretched to a total length of $12 c m$ the lowest resonant frequency is $f_{0}$ . The rubber band is then stretched to a length of $13 c m$ . The lowest resonant frequency will now be

1 Lower than

f_{0}

2 Higher than

f_{0}

3 The same as

f_{0}

4 Changed, but the change (positive or negative) depends on the elastic constant and the original tension

Explanation:

$f_{0} = \frac{1}{2 l} \sqrt{\frac{T}{μ}}$
For elastic wire $T = K x$
$x \to$ elongation from natural length
Hence frequency depends on $K$ and original tension

PHXI15:WAVES

355167 For a stationary wave, $Y = 10 \sin (\frac{π x}{15}) \cos (48 π t) c m$ , the distance between a node and the successive antinode is

1

60 c m

2

30 c m

3

7.5 c m

4

15 c m

Explanation:

On comparing the given equation with a standard stationary wave equation, we get
$k = \frac{π}{15} = \frac{2 π}{λ} \Rightarrow λ = 30 c m$
Distance between node and antinode is,
$\frac{λ}{4} = \frac{30}{4} = 7.5 c m$

MHTCET - 2022

PHXI15:WAVES

355168 The waves formed in stretched strings are

1 Transverse

2 Longitudinal

3 Both longitudinal and transverse

4 Shock waves

PHXI15:WAVES

355165 When a string fixed at both ends vibrates in 1 loop, 2 loops, 3 loops and 4 loops, the frequenices are in the ratio

1

1 : 2 : 3 : 4

2

1 : 1 : 1 : 1

3

1 : 4 : 9 : 16

4

4 : 3 : 2 : 1

Explanation:

When the string vibrates in $n$ loops, its frequency is $f_{n} = \frac{n v}{2 L}$
Where $L$ is the length of the string and $v$ is the velocity of the wave.
$∴$ When the string fixed at its both ends vibrates in 1 loop, 2 loops, 3 loops and 4 loops, the frequencies are in the ratio $1 : 2 : 3 : 4$

PHXI15:WAVES

355166 A $10 c m$ long rubber band obeys Hooke's law. When the rubber band is stretched to a total length of $12 c m$ the lowest resonant frequency is $f_{0}$ . The rubber band is then stretched to a length of $13 c m$ . The lowest resonant frequency will now be

1 Lower than

f_{0}

2 Higher than

f_{0}

3 The same as

f_{0}

4 Changed, but the change (positive or negative) depends on the elastic constant and the original tension

Explanation:

$f_{0} = \frac{1}{2 l} \sqrt{\frac{T}{μ}}$
For elastic wire $T = K x$
$x \to$ elongation from natural length
Hence frequency depends on $K$ and original tension

PHXI15:WAVES

355167 For a stationary wave, $Y = 10 \sin (\frac{π x}{15}) \cos (48 π t) c m$ , the distance between a node and the successive antinode is

1

60 c m

2

30 c m

3

7.5 c m

4

15 c m

Explanation:

On comparing the given equation with a standard stationary wave equation, we get
$k = \frac{π}{15} = \frac{2 π}{λ} \Rightarrow λ = 30 c m$
Distance between node and antinode is,
$\frac{λ}{4} = \frac{30}{4} = 7.5 c m$

MHTCET - 2022

PHXI15:WAVES

355168 The waves formed in stretched strings are

1 Transverse

2 Longitudinal

3 Both longitudinal and transverse

4 Shock waves

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