Question

A string fixed at both ends is 8.40 m long and has a mass of 0.120 kg. It is subjected to a tension of 96.0 N and set oscillating.
(a) What is the speed of the waves on the string?
(b) What is the longest possible wavelength for a standing wave?
(c) Give the frequency of that wave.

Answer 1

Answer:

81.9756 m/s

16.8 m

4.8795 Hz

Explanation:

m = Mass of string = 0.12 kg

L = Length of string = 8.4 m

T = Tension on string = 96 N

Linear density is given by

$\mu=\dfrac{m}{L}\\\Rightarrow \mu=\dfrac{0.12}{8.4}$

Spee of the wave is given by

$v=\sqrt{\dfrac{T}{\mu}}\\\Rightarrow v=\sqrt{\dfrac{96}{\dfrac{0.12}{8.4}}}\\\Rightarrow v=81.9756\ m/s$

The speed of the waves on the string is 81.9756 m/s

Wavelength is given by

$\lambda=2L\\\Rightarrow \lambda=2\times 8.4\\\Rightarrow \lambda=16.8\ m$

The longest possible wavelength is 16.8 m

Frequency is given by

$f=\dfrac{v}{\lambda}\\\Rightarrow f=\dfrac{81.9756}{16.8}\\\Rightarrow f=4.8795\ Hz$

The frequency of the wave is 4.8795 Hz