A wire of density 9 × 10 3 kg m - 3 is stretched between two clamps 1 m apart and is subjected to an extension of 4 . 9 × 10 - 4 m . What will be the lowest frequency of the transverse vibrations in the wire? Y = 9 × 10 10 N m - 2

Given: A wire of density ρ = 9 × 10 3 kg m - 3 Length l = 1 m y = 9 × 10 10 N m - 2 μ = m l = ρ A × l l = A . ρ T = γ ∆ l l × A Lowest frequency of the vibration n = 1 2 l T μ n = 1 2 l γ ∆ l l × A A . ρ n = 1 2 1 9 × 10 10 × 4 . 9 × 10 - 4 9 × 10 3 n = 35 Hz The lowest frequency of the transverse vibration in the wire n = 35 Hz .

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If the tension in a stretched string is increased by $5 kg$ wt, the frequency of its fundamental tone increases in the ratio $2 : 3$ . What was the initial tension in the string?

Important Questions on Vibrations of Stretched Strings

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IMPORTANT

ISC Physics Class XI Part 1>Chapter 32 - Vibrations of Stretched Strings>NUMERICALS>Q 10

The length of a wire between two ends of a sonometer is

105 cm

. Where should the bridges be placed so that the fundamental frequencies of the three segments are in the ratio of

1 : 3 : 15

EASY

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IMPORTANT

ISC Physics Class XI Part 1>Chapter 32 - Vibrations of Stretched Strings>NUMERICALS>Q 11

Two wires whose lengths are in the ratio

3 : 2

, when stretched by equal weights, produce the same note. If the wires are made of different metals and their radii are in the ratio

1 : 2

, then determine the ratio of the densities of the two metals.

EASY

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IMPORTANT

ISC Physics Class XI Part 1>Chapter 32 - Vibrations of Stretched Strings>NUMERICALS>Q 12

A wire of density

9 \times 10^{3} kg m^{- 3}

is stretched between two clamps

1 m

apart and is subjected to an extension of

4.9 \times 10^{- 4} m

. What will be the lowest frequency of the transverse vibrations in the wire?

(Y = 9 \times 10^{10} N m^{- 2})

EASY

11th ICSE

IMPORTANT

ISC Physics Class XI Part 1>Chapter 32 - Vibrations of Stretched Strings>NUMERICALS>Q 13

Two wires A and B are stretched between two points. The diameter, tension and density of B are twice the diameter, tension and density of A. What will be the ratio of frequencies of A and B?

EASY

11th ICSE

IMPORTANT

ISC Physics Class XI Part 1>Chapter 32 - Vibrations of Stretched Strings>NUMERICALS>Q 14

A and B are two wires stretched under the same tension. The length of A is twice the length of B and the diameter of A is half the diameter of B. If the density of A is

0.09

times the density of B, then compare the frequencies of A and B.

EASY

11th ICSE

IMPORTANT

ISC Physics Class XI Part 1>Chapter 32 - Vibrations of Stretched Strings>NUMERICALS>Q 15

A wire has a length of

100 cm

and a mass of

0.4 g

. If a

5 kg

weight has been suspended from the wire and the wire is vibrating in two segments, then determine the frequency of the note emitted by the wire.

EASY

11th ICSE

IMPORTANT

ISC Physics Class XI Part 1>Chapter 32 - Vibrations of Stretched Strings>NUMERICALS>Q 16

The frequency of the fundamental note of a

66 cm

long open tube is the same as that of a

20 cm

long stretched wire whose mass is

0.1 g {cm}^{- 1}

. If the speed of sound in air is

330 m s^{- 1}

, then determine the tension in the wire.

EASY

11th ICSE

IMPORTANT

ISC Physics Class XI Part 1>Chapter 32 - Vibrations of Stretched Strings>NUMERICALS>Q 17

A tuning fork of frequency

256 Hz

is in unison with a certain length of a sonometer wire. On increasing the length of the wire,

10

beats/s are produced. Calculate the frequency of the wire of increased length.

If the tension in a stretched string is increased by 5 kg wt, the frequency of its fundamental tone increases in the ratio 2 : 3. What was the initial tension in the string?

Important Questions on Vibrations of Stretched Strings

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If the tension in a stretched string is increased by $5 kg$ wt, the frequency of its fundamental tone increases in the ratio $2 : 3$ . What was the initial tension in the string?