355172 Two vibrating strings of the same material but lengths \(L\) and \(2 L\) have radii \(2 r\) 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 \(v_{1}\) and the other with frequency \(v_{2}\). The ratio \(v_{1} / v_{2}\) is
355172 Two vibrating strings of the same material but lengths \(L\) and \(2 L\) have radii \(2 r\) 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 \(v_{1}\) and the other with frequency \(v_{2}\). The ratio \(v_{1} / v_{2}\) is
355172 Two vibrating strings of the same material but lengths \(L\) and \(2 L\) have radii \(2 r\) 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 \(v_{1}\) and the other with frequency \(v_{2}\). The ratio \(v_{1} / v_{2}\) is
355172 Two vibrating strings of the same material but lengths \(L\) and \(2 L\) have radii \(2 r\) 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 \(v_{1}\) and the other with frequency \(v_{2}\). The ratio \(v_{1} / v_{2}\) is