A sonometer wire supports a 4 kg load and vibrates in fundamental mode with a tuning fork of frequency 416. Hz. The length of the wire between the bridges is now doubled. In order to maintain fundamental mode, the load should be changed to

Question

KollegeApply · Accepted Answer

16 kg According to the relation of the fundamental frequency of a string \nu = $\frac{1}{2}$l$\sqrt$(F/\mu) where l is the length of the string F is the tension μ is the linear mass density of the string We know that ν1 = 416 Hz, l1 = l and l2 = 2l. Also, m1 = 4 kg and m2 = ? \nu_1 = $\frac{1}{2}$ l_1$\sqrt$(m_1 g/\mu).................. (1) \nu_2 = $\frac{1}{2}$ l_2$\sqrt$(m_2 g/\mu) (2) So, in order to maintain the same fundamental mode \nu_1 = \nu_2 squaring both sides of equations (1) and (2) and then equating $\frac{1}{4}$ l^24g/\mu = $\frac{1}{16}$ l^2m_2 g/\mu \Rightarrow m_2 = 16 kg

AChoose Your Answer