A steel wire with a length of 64 cm weighs 5 g . If it is stretched by an 8 N force, determine the speed of a transverse wave travelling on it.

Correct answer: A. 32 m/s Given, length of the wire L = 64 cm = 0.64 m Mass of the wire m = 5 g = 5 × 10^ -3 kg Tension in the wire T = 8 N The linear mass density of the wire is given by: μ = (m)/(L) = 5 × 10^ -3 0.64 = (5)/(640) = (1)/(128) kg/m The speed of a transverse wave on a stretched string is: v = (T)/(μ) Substituting the values: v = (8)/(1/128) = 8 × 128 = 1024 = 32 m/s

Concepts Of Physics MCQ Edition [Volume 1]

Exam: Concepts Of Physics MCQ Edition [Volume 1]
Subject: Physics
Chapter: Wave Motion and Waves on a String

Concepts Of Physics MCQ Edition [Volume 1] · Physics · Wave Motion and Waves on a String

A steel wire with a length of 64 cm weighs 5 g . If it is stretched...

A steel wire with a length of

64 \text{ cm}

weighs

5 \text{ g}

. If it is stretched by an

8 \text{ N}

force, determine the speed of a transverse wave travelling on it.

Options

A $32 \text{ m/s}$
B $40 \text{ m/s}$
C $64 \text{ m/s}$
D $16 \text{ m/s}$

Correct answer

A. $32 \text{ m/s}$

Step-by-step solution

Given, length of the wire

L = 64 \text{ cm} = 0.64 \text{ m}

Mass of the wire

m = 5 \text{ g} = 5 \times 10^{-3} \text{ kg}

Tension in the wire

T = 8 \text{ N}

The linear mass density of the wire is given by:

\mu = \dfrac{m}{L} = \dfrac{5 \times 10^{-3}}{0.64} = \dfrac{5}{640} = \dfrac{1}{128} \text{ kg/m}

The speed of a transverse wave on a stretched string is:

v = \sqrt{\dfrac{T}{\mu}}

Substituting the values:

v = \sqrt{\dfrac{8}{1/128}} = \sqrt{8 \times 128} = \sqrt{1024} = 32 \text{ m/s}

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