Question

The mass of a string is 2.40×10-3 kg, and it is stretched so the tension in it is 120 N. A transverse wave traveling on this string has a frequency of 260 Hz and a wavelength of 0.60 m. What is the length of the string?

Answer 1

Answer:

Length of the string, l = 0.486 meters

Explanation:

It is given that,

Mass of the string, $m=2.4\times 10^{-3}\ kg$

Tension in the string, T = 120 N

Frequency of transverse wave, f = 260 Hz

Wavelength of the wave, $\lambda=0.6\ m$

The speed of a transverse wave (v) is given by :

$v=\sqrt{\dfrac{T}{\mu}}$........(1)

Where,

$\mu=\dfrac{m}{l}$

Also, speed of a wave, $v=f\times \lambda$.........(2)

From equation (1) and (2) :

$l=\dfrac{f^2\lambda^2m}{T}$

$l=\dfrac{(260\ Hz)^2\times (0.6\ m)^2\times 2.4\times 10^{-3}\ kg}{120\ N}$

l = 0.486 m

So, the length of the string is 0.486 meters. Hence, this is the required solution.