91Ó°ÊÓ

• The wave equation is given as$y=\left(0.021m\right)\sin \left[\left(2.0m^{-1}\right)x+\left(30s^{-1}\right)t\right]$
• Linear density of a string,$\left(\mathrm{μ}\right)=1.6×{10}^{-4}\mathrm{kg}/\mathrm{m}$
• Wavelength,$\left(\mathrm{λ}\right)=0.5\mathrm{m}$
• Frequency,$\left(f\right)=30s^{-1}$

The product of wavelength and frequency of the wave is called speed of the wave. the speed of the wave in a stretched string is directly proportional to the square-root of the tension force and inversely proportional to the square-root of linear density of the string.

Formula:

The wave speed of the wave, $v=n×\mathrm{λ}$ (i)

The velocity of the wave,$v=\sqrt{\frac{T}{\mathrm{μ}}}$ (ii)

Using equation (i), the wave speed is given as:

$$\begin{gathered} \mathrm{v}=30{\mathrm{s}}^{-1}×0.5\mathrm{m} \\ =15\mathrm{m}/\mathrm{s} \end{gathered}$$

Hence, the value of wave speed is 15 m/s

Using equation (ii), the tension in the string is given as:

$$\begin{gathered} T=v^2\mathrm{μ} \\ ={\left(15\mathrm{m}/\mathrm{s}\right)}^2×\left(1.6×{10}^{-4}\mathrm{kg}/\mathrm{m}\right) \\ =3.60×{10}^{-3}\mathrm{N} \end{gathered}$$

Hence, the value of the tension in the string is $3.60×{10}^{-3}\mathrm{N}$.