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a wire stretched between two rigid supports vibrat...

Question:
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 x 10^-2 kg and its linear mass density is 4.0 x 10^-2 kg m^-1. What is

(a) the speed of a transverse wave on the string, and

(b) the tension in the string?

Answer:

(a) Mass of the wire, m = 3.5 × 10^-2 kg

Linear mass density, μ = m / l = 4.0 x 10^-2 kg m^-1

Frequency of vibration, V = 45 Hz

∴Length of the wire, l = m / μ = 3.5 × 10^-2/ 4.0 x 10^-2

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

λ = 2l / n

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 = V λ = 45 × 1.75 = 78.75 m/s

(b) The tension produced in the string is given by the relation:

T = v² µ

= (78.75)² × 4.0 × 10^-2 = 248.06 N

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Question:
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 x 10^-2 kg and its linear mass density is 4.0 x 10^-2 kg m^-1. What is

(a) the speed of a transverse wave on the string, and

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Question: 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 x 10-2 kg and its linear mass density is 4.0 x 10-2 kg m-1. What is (a) the speed of a transverse wave on the string, and (b) the tension in the string?

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Question:
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 x 10^-2 kg and its linear mass density is 4.0 x 10^-2 kg m^-1. What is

(a) the speed of a transverse wave on the string, and

(b) the tension in the string?