The third overtone of a closed pipe of length ' $\mathrm{L}_{\mathrm{c}}$ ' has the same frequency as the third overtone of an open pipe of length ' $L_0$ '. The ratio ' $\mathrm{L}_{\mathrm{c}}$ ': ' $\mathrm{L}_0$ ' is equal to (Neglecting end correction)

Two sounding sources send waves at certain temperature in air of wavelength 60 cm and 60.6 cm respectively. The frequency of sources differ by 5 Hz . The velocity of sound in air at same temperature is

A simple harmonic progressive wave is given by equation $y=\operatorname{asin} 2 \pi\left(n t-\frac{x}{\lambda}\right)$. If the wave velocity is equal to $\frac{1}{4} \times$ (maximum particle velocity), then the wavelength ' $\lambda$ ' is (Given $\rightarrow \mathrm{a}=$ amplitude, $\mathrm{n}=$ frequency, $\mathrm{t}=$ time, $\mathrm{y}=$ displacement, $\mathrm{x}=$ distance )

Three tuning forks $\mathrm{A}, \mathrm{B}$ and C have respective frequencies $\mathrm{n}_1, \mathrm{n}_2$ and $\mathrm{n}_3$ related as $\mathrm{n}_1=1.03 \mathrm{n}_2$ and $n_3=0.99 n_2$. When $A$ and $C$ are sounded together 4 beats are heard per second. The frequencies of fork B and C are respectively