A transverse vibration problem in a string under tension refers to the study of how a string behaves when it is stretched between two points and then disturbed by a force perpendicular to the direction of the string. This type of vibration is characterized by the string moving up and down, or side to side, as opposed to vibrating in a longitudinal direction.
The transverse vibration of a string under tension is affected by several factors, including the tension of the string, the length of the string, and the density or thickness of the string. Additionally, the type of material the string is made of and the frequency of the disturbance also play a role in the vibration.
The equation used to calculate the frequency of vibration in a string under tension is known as the wave equation. It is expressed as f = 1/2L * sqrt(T/μ), where f is the frequency, L is the length of the string, T is the tension in the string, and μ is the mass per unit length of the string.
Tension plays a significant role in determining the frequency of vibration in a string. As the tension in the string increases, the frequency of vibration also increases. This means that a tighter string will vibrate at a higher frequency than a looser string, assuming all other factors remain constant.
The wavelength and frequency of vibration in a string under tension are inversely proportional to each other. This means that as the frequency increases, the wavelength decreases, and vice versa. This relationship is expressed as λ = v/f, where λ is the wavelength, v is the velocity of the wave, and f is the frequency of vibration.
