A wire stretched between two rigid supports vibrates in its fundamental mode with a frequency of 45 Hz. The mass of the wire is 3.5 × 10^–2 kg and its linear mass density is 4.0 × 10^–2 kg m^–1. What is (a) the speed of a transverse wave on the string, and (b) the tension in the string?

Solution

(a) Mass of the wire, m = 3.5 × 10^–2 kg
Linear mass density, μ = $straight m over straight l$ = 4.0 × 10^-2 kg m^-1
Frequency of vibration, v = 45 Hz
∴ length of the wire, l =

straight m over straight mu

fraction numerator 3.5 space cross times space 10 to the power of negative 2 end exponent over denominator 4.0 space cross times space 10 to the power of negative 2 end exponent end fraction space equals space 0.875

The wavelength of the stationary wave (λ) is related to the length of the wire by the relation,

straight lambda space equals space fraction numerator 2 space straight l over denominator straight m end fraction

where,
n = Number of nodes in the wire.
For fundamental node, n = 1:
λ = 2l

λ = 2 × 0.875
= 1.75 m
The speed of the transverse wave in the string is given as,
v = νλ
= 45 × 1.75
= 78.75 m/s
(b) The tension produced in the string is given by the relation,
T = v²µ

= (78.75)² × 4.0 × 10^–2 = 248.06 N

Some More Questions From Mechanical Properties of Fluids Chapter

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Mechanical Properties Of Fluids

A wire stretched between two rigid supports vibrates in its fundamental mode with a frequency of 45 Hz. The mass of the wire is 3.5 × 10^–2 kg and its linear mass density is 4.0 × 10^–2 kg m^–1. What is (a) the speed of a transverse wave on the string, and (b) the tension in the string?

Some More Questions From Mechanical Properties of Fluids Chapter

What is common property of all types of waves?

What are different types of wave motions?

Define transverse wave motion.

Define longitudinal wave motion.

Which of the two waves - elastic waves or electromagnetic waves does need any material media for its propagation?

What is sound?

How sound is produced?

Can sound travel in vacuum?

Can two persons hear each other on the moon? Explain.

Can electromagnetic wave propagate in vacuum?

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For Daily Free Study Material Join wiredfaculty

Mechanical Properties Of Fluids

A wire stretched between two rigid supports vibrates in its fundamental mode with a frequency of 45 Hz. The mass of the wire is 3.5 × 10–2 kg and its linear mass density is 4.0 × 10–2 kg m–1. What is (a) the speed of a transverse wave on the string, and (b) the tension in the string?

Some More Questions From Mechanical Properties of Fluids Chapter

What is common property of all types of waves?

What are different types of wave motions?

Define transverse wave motion.

Define longitudinal wave motion.

Which of the two waves - elastic waves or electromagnetic waves does need any material media for its propagation?

What is sound?

How sound is produced?

Can sound travel in vacuum?

Can two persons hear each other on the moon? Explain.

Can electromagnetic wave propagate in vacuum?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

A wire stretched between two rigid supports vibrates in its fundamental mode with a frequency of 45 Hz. The mass of the wire is 3.5 × 10^–2 kg and its linear mass density is 4.0 × 10^–2 kg m^–1. What is (a) the speed of a transverse wave on the string, and (b) the tension in the string?