The fundamental frequency of vibration of a string stretched between two rigid support is 50 Hz. The mass of the string is 18 g and its linear mass density is 20 g / m. The speed of the transverse waves so produced in the string is ___________ ms⁻¹

Solution

Physics sir · 3 steps

The mass and the linear density give you the length, and the length gives you the wavelength.

1. Find the length. Linear mass density is mass per unit length, so L = m/μ = (18 g)/(20 g m⁻¹) = 0.9 m.
2. Fundamental mode. Both ends are fixed, so both ends are nodes. In the fundamental mode the string holds exactly half a wavelength, so λ = 2L = 1.8 m.

   v = fλ = 50 × 1.8 = 90 m s⁻¹

3. So. The transverse waves travel along the string at 90 m s⁻¹.

The common slip: 45. Taking the wavelength equal to the string length (λ = L = 0.9 m) gives 45, not 90. The fundamental is half a wave, so λ = 2L.

The idea to keep. For a string fixed at both ends, the fundamental fits half a wavelength, so λ = 2L. Then v = fλ connects frequency to speed.

Answer from the NTA final answer key. Solution by PrepWiser.