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IMPORTANT

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A steel wire of length $50 \sqrt{3} cm$ is connected to an aluminium wire of length $60 cm$ and stretched between two fixed supports. The tension produced is $104 N$ , if the cross-section area of each wire is $1 {mm}^{2}$ . If a transverse wave is set up in the wire, find the lowest frequency for which standing waves with nodes at the joint are produced. (Density of aluminium $= 2.6 gm {cm}^{- 3}$ and density of steel $= 7.8 gm {cm}^{- 3}$ )

Important Questions on Wave Motion on a String

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IMPORTANT

Alpha Question Bank for Engineering: Physics>Chapter 20 - Wave Motion on a String>Exercise - 4>Q 6

An aluminium wire of cross-sectional area

1 \times 10^{- 6} m^{2}

is joined to a steel wire of same cross-sectional area. This compound wire is stretched on a sonometer, pulled by weight of

10 kg

. The total length of the compound wire between the bridges is

1.5 m

, of which the aluminium is

0.6 m

and the rest is steel wire. Transverse vibrations are set up in the wire by using an external force of variable frequency. Find the lowest frequency of excitation for which standing waves are formed such that the joint in the wire is a node. What is the total number of nodes observed at this frequency, excluding the two at the ends of the wire? The density of aluminium is

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

and that of steel is

1.04 \times 10^{4} kg m^{- 3}

. (Take

g = 10 m s^{- 2}

)

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IMPORTANT

Alpha Question Bank for Engineering: Physics>Chapter 20 - Wave Motion on a String>Exercise - 4>Q 7

The fundamental frequency of a sonometer wire increases by

6 Hz

if its tension is increased by

44 %

keeping the length constant. Find the change in the fundamental frequency of the sonometer when the length of the wire is increased by

20 %

keeping the original tension in the wire.

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IMPORTANT

Alpha Question Bank for Engineering: Physics>Chapter 20 - Wave Motion on a String>Exercise - 4>Q 8

A metal wire with volume density

ρ

and young's modulus

Y

is stretched between rigid supports. At temperature

T

, the speed of a transverse wave is found to be

v_{1}

. When the temperature decreases

T - ∆ T

, the speed increases to

v_{2}

. Determine the coefficient of linear expansion of wire.

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IMPORTANT

Alpha Question Bank for Engineering: Physics>Chapter 20 - Wave Motion on a String>Exercise - 4>Q 9

Find velocity of wave in $(m s^{- 1})$ in string $A$ and $B$ .

Question Image

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IMPORTANT

Alpha Question Bank for Engineering: Physics>Chapter 20 - Wave Motion on a String>Exercise - 4>Q 10

A string of length

50 cm

is vibrating with a fundamental frequency of

400 Hz

in horizontal position. In the fundamental mode, the maximum displacement at the middle is

2 cm

from equilibrium position and the tension in the string is

10 N

. Determine the maximum value of the vertical component of force on the end supporting.

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IMPORTANT

Alpha Question Bank for Engineering: Physics>Chapter 20 - Wave Motion on a String>Exercise - 4>Q 11

A string fixed at both ends is vibrating in the lowest mode of vibration for which a point at quarter of its length from one end is a point of maximum displacement. The frequency of vibration in this mode is

100 Hz

. What will be the frequency (in Hertz) emitted when it vibrates in the next higher mode such that this point is again a point of maximum displacement.

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IMPORTANT

Alpha Question Bank for Engineering: Physics>Chapter 20 - Wave Motion on a String>Exercise - 4>Q 12

A guitar string is

180 cm

long and has a fundamental frequency of

90 Hz

. Where should it be pressed to produce a fundamental frequency of

135 Hz

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IMPORTANT

Alpha Question Bank for Engineering: Physics>Chapter 20 - Wave Motion on a String>Exercise - 4>Q 13

A piano wire weighing

4 g

and having a length of

90.0 cm

emits a fundamental frequency corresponding to the “Middle

C

”

(ν = 125 Hz)

. Find the tension in the wire.

Important Questions on Wave Motion on a String

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