Question 19 of 23intermediate🔧 ApplyNumerical3 marks

A wire stretched between two rigid supports vibrates in its fundamental mode with a frequency of 45 Hz. The mass of the wire is 3.5×10−23.5 \times 10^{-2} kg and its linear mass density is 4.0×10−24.0 \times 10^{-2} kg m−1^{-1}. What is (a) the speed of a transverse wave on the string, and (b) the tension in the string?

(a)
Answer

The speed of the transverse wave on the string is 78.75 m/s (approximately 79 m/s).

(b)
Answer

The tension in the string is 248 N.

Explanation

This question tests understanding of standing waves on a string and the relationship between wave speed, tension, and linear mass density. For fundamental mode, the wavelength equals twice the length of the string. The speed can be found using v = fλ, and tension using v = T/μ\sqrt{T/μ}.

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