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

A pipe closed at one end vibrating in fifth overtone is in unison with open pipe vibrating in its fifth overtone. The ratio of $l_{\mathrm{c}}: l_{\mathrm{o}}$ is $\left[l_{\mathrm{c}}=\right.$ vibrating length of closed pipe, $l_0=$ vibrating length of open pipe]

Two uniform strings ' $A$ ' and ' $B$ ' made of steel are made to vibrate under same tension. If the first overtone of ' $A$ ' is equal to second overtone of ' B ' and radius of ' A ' is twice that of ' B '. Then the ratio of length of string ' $A$ ' to that of ' $B$ ' is