Question

A 125 cm length of string has mass 2.00 g and tension 7.00 N. (a) What is the wave speed for this string? (b) What is the lowest resonant frequency of this string?

Answer 1

Answer on Question #39568, Physics, Mechanics | Kinematics | Dynamics

Question:

A 125 cm length of string has mass 2.00 g and tension 7.00 N. (a) What is the wave speed for this string? (b) What is the lowest resonant frequency of this string?

Answer:

a) The speed of the waves on the string is given by:

$$v = \sqrt {\frac {T}{m / L}} = \sqrt {\frac {7 N}{0 . 0 0 2 k g / 1 . 2 5 m}} = 6 6. 1 \frac {m}{s}$$

where $T$ is tension, $m$ is mass, $L$ is length.

b) The lowest resonance frequency is known as the fundamental frequency for the string. The fundamental vibrational mode of a stretched string is such that the wavelength is twice the length of the string:

$$\lambda = 2 L$$

Therefore the lowest resonant frequency equals:

$$f = \frac {v}{\lambda} = \frac {\sqrt {\frac {T}{m / L}}}{2 L} = 2 6. 5 H z$$