A tuning fork gives 3 beats with $$50 \mathrm{~cm}$$ length of sonometer wire. If the length of the wire is shortened by $$1 \mathrm{~cm}$$, the number of beats is still the same. The frequency of the fork is

A tuning fork of frequency $$220 \mathrm{~Hz}$$ produces sound waves of wavelength $$1.5 \mathrm{~m}$$ in air at N.T.P. The increase in wavelength when the temperature of air is $$27^{\circ} \mathrm{C}$$ is nearly $$\left(\sqrt{\frac{300}{273}}=1.05\right)$$

A uniform string is vibrating with a fundamental frequency '$$n$$'. If radius and length of string both are doubled keeping tension constant then the new frequency of vibration is

The displacement of two sinusoidal waves is given by the equation

$$\begin{aligned} & \mathrm{y}_1=8 \sin (20 \mathrm{x}-30 \mathrm{t}) \\ & \mathrm{y}_2=8 \sin (25 \mathrm{x}-40 \mathrm{t}) \end{aligned}$$

then the phase difference between the waves after time $$t=2 \mathrm{~s}$$ and distance $$x=5 \mathrm{~cm}$$ will be