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

Question

Philoid · Accepted Answer

(a) Given,

Mass of the wire, m = 3.5 × 10^–2 kg

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

Frequency of vibration, f = 45 Hz

So, Length of the wire, l = m/μ

⇒ l = (3.5 × 10^–² kg)/(4.0 × 10^-2 kg m^-1)

⇒ l = 0.875 m

The wavelength of the stationary wave (λ) and the length of the wire are related as

λ = 2l/m

where, n = Number of nodes in the wire

For fundamental node, n = 1

∴ λ = 2l

⇒ λ = 2 × 0.875 m

⇒ λ = 1.75 m

The speed of the transverse wave in the string is given as

V = fλ= 45 m s^-1 × 1.75 m

⇒ V = 78.75 m s^-1

(b) The tension produced in the string is given as

T = v²μ = (78.75 m s^-1)² × 4.0 × 10^–2 kg m^-1

⇒ T = 248.06 N

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?

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?