If two waves of length  $80 \mathrm{cm}$ and  $81 \mathrm{cm}$ produced 16 beats per second. Then what is the  velocity of the sound is:

We know that, Number of beats per second (N) is given by: $\mathrm{N}=v_1-v_2=\frac{\mathrm{V}}{{\lambda }_1}-\frac{\mathrm{V}}{{\lambda }_2}\left\{\mathbb{V}v=\frac{\mathrm{V}}{\lambda }\right\}$

Here $v_1=$  Frequency of wave$1,v_2=$ Velocity of sound,  ${\lambda }_1=$ Wavelength of wave $1,{\lambda }_2=$ Wavelength of wave 2 ,

According to question given $\mathrm{N}=16$  beats per second, ${\lambda }_1=81 \mathrm{cm},{\lambda }_2=80 \mathrm{cm}$ Number of beats per second(N) is  $\mathrm{N}=\frac{\mathrm{V}}{{\lambda }_1}-\frac{\mathrm{V}}{{\lambda }_2}$ $16=\mathrm{V}\left(\frac{1}{80}-\frac{1}{81}\right)$ $16=V\left(\frac{1}{80\times 81}\right)$ 

$\mathrm{V}=16\times 80\times 81=103680 \mathrm{cm}/\mathrm{s}=1036.8 \mathrm{m}/\mathrm{s}$