Rajasthan BoardEnglish MediumSTD 11 SciencePhysicsWaves3 Marks
Question
Two strings of the same material and length under the same tension may vibrate with different fundamental frequency. Why?
✓
Answer
The frequency of vibration of string is given by $\text{n}=\frac{1}{2\text{l}}\sqrt{\frac{\text{T}}{\text{m}}}$ m (mass per unit length) $=\frac{\text{mass}}{\text{length}}=\frac{\text{volume}\times\text{density}}{\text{l}}$ $=\frac{\pi\text{r}^2\text{l}\times\rho}{\text{l}}=\pi\text{r}^2\rho$ $=\pi\Big(\frac{\text{D}}{2}\Big)^2\rho=\frac{\pi\text{D}^2}{4}\rho$ $\text{n}=\frac{1}{2\text{l}}\sqrt{\frac{4\text{T}}{\pi\text{D}^2\rho}}=\frac{1}{\text{Dl}}\sqrt{\frac{\text{T}}{\pi\rho}}$ $\therefore \text{n}\propto\frac{1}{\text{D}}$ (when l, T, $\rho$ are same) or nD = constant or n1D1 = n2D2 Hence the two strings may vibrate with different frequencies when they have different diameters.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.