Two vibrating strings of the same material but lengths $L$ and $2L$ have radii $2r$ and $r$ respectively. They are stretched under the same tension . Both the strings vibrate in their fundamental modes, the one of length $L$ with frequency $f_1$ and the other with frequency $f_2$. The ratio $\frac{f_1}{f_2}$ is given by

Calculate the temperature at which the speed of sound will be two times its   ..... $K$ value at $0\,^oC$

The stationary wave $y = 2a{\mkern 1mu} \,\,sin\,\,{\mkern 1mu} kx{\mkern 1mu} \,\,cos{\mkern 1mu} \,\omega t$ in a stretched string is the result of superposition of $y_1 = a\,sin\,(kx -\omega t)$ and

In a sinusoidal wave, the time required for a particular point to move from maximum displacement to zero displacement is $0.170 \,s$. The frequency of wave is ........ $Hz$

Two identical piano wires, kept under the same tension $T$ have a fundamental frequency of $600\, Hz$. The fractional increase in the tension of one of the wires which will lead to occurrence of $6\, beats/s$ when both the wires oscillate together would be

Fundamental frequency of a sonometer wire is $n$ . If the length and diameter of the wire are doubled keeping the tension same, then the new fundamental frequency is