Stationary waves are produced in a string one meter long producing four loops. To obtain stationary

Question

Stationary waves are produced in a string one meter long producing four loops. To obtain stationary waves producing 6 loops, the tension must be\

Professor PC Thomas Classes · Answer

In the first case, the tension is and there are 4 segments. One segment $=\frac{\lambda}{2}$\ $	herefore 4 \frac{\lambda}{2}=\mathrm{L} \lambda=\frac{\mathrm{L}}{2}$\ In the second case, tension is T'and there are 6 segments each of length $\frac{\lambda^{\prime}}{2}$.\ $6 \frac{\lambda^{\prime}}{2}=\mathrm{L} \quad \lambda^{\prime}=\frac{\mathrm{L}}{3}$ We have $v=n \lambda, v=\sqrt{\frac{T}{m}}$\ $	herefore \sqrt{\frac{\mathrm{T}}{\mathrm{m}}}=\mathrm{n} \lambda$\ $\frac{T}{m}=n^{2} \lambda^{2}$\ $\mathrm{T}=\mathrm{mn}^{2} \lambda^{2}$\ $\mathrm{T}^{\prime}=\min ^{2}\left(\lambda^{\prime}ight)^{2}$\ $\frac{\mathrm{T}^{\prime}}{\mathrm{T}}=\frac{\left(\lambda^{\prime}ight)^{2}}{\lambda^{2}}=\frac{\left(\frac{\mathrm{L}}{3}ight)^{2}}{\left(\frac{\mathrm{~L}}{2}ight)^{2}}$\