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

Length of the string, l = 0.486 meters

Step-by-step explanation:

It is given that,

Mass of the string,
`m=2.4* 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{(T)/(\mu)}`........(1)

Where,

`\mu=(m)/(l)`

Also, speed of a wave,
`v=f* \lambda`.........(2)

From equation (1) and (2) :

`l=(f^2\lambda^2m)/(T)`

`l=((260\ Hz)^2* (0.6\ m)^2* 2.4* 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.