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 × 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?

Answer 1

see the figure .
In fundamental mode ,
wavelength = 2 × Length of wire
Given,
Mass density = Mass of wire/length of wire = 3.5 × 10^-2/length of wire = 4 × 10^-2
Length of wire = 4/3.5 = 0.875 m

wavelength = 2 × length of wire
= 2 × 0.875 m
= 1.75 m
speed of wave = frequency × wavelength
= 45 × 1.75
= 78.75 m/s

Use formula,
Tension =( speed of wave)² × mass density
= (78.75)² × 4 × 10^-2
= 248.06 N