A sonometer wire of length 25 cm vibrates in unison with a tuning fork. When its length is decreased by 1 cm, 6 beats are heard per second. What is the frequency of the tuning fork?

The plates of a parallel plate capacitor of capacity '$$\mathrm{C}_1$$' are moved closer together until they ant half their original separation. The new capacitance '$$\mathrm{C}_2$$' is

A p-n junction photodiode is fabricated from a semiconductor with a band gap of $$2.5 \mathrm{~eV}$$. It can detect a signal of wavelength [Planck's constant $$=6.6 \times 10^{-34} \mathrm{Js}, \mathrm{c}=3 \times 10^8 \mathrm{~m} / \mathrm{s}, \mathrm{e}=1.6 \times 10^{-19} \mathrm{C}$$]

Two tuning forks of frequencies $$320 \mathrm{~Hz}$$ and $$480 \mathrm{~Hz}$$ are sounded together to produce sound waves. The velocity of sound in air is $$320 \mathrm{~ms}^{-1}$$. The difference between wavelengths of these waves is nearly