Question

Two sound waves with wavelength $5.0 \,m$ and $5.5 \,m$ respectively, each propagate in a gas with velocity $330 \,m/s$. We expect the following number of beats per second

• A. 12
• B. zero
• C. 1
• D. 6

Answer 1

Answer: (D)

6

Answer 2

Let $\lambda_{1}=5.0 \,m , v=330\, m / s$ and $\lambda_{2}=5.5\, m$ The relation between frequency, wavelength and velocity is given by $v=n \lambda \Rightarrow n=\frac{v}{\lambda}$...(i) The frequency corresponding to wavelength $\lambda_{1} . n_{1}=\frac{v}{\lambda_{1}}=\frac{330}{5.0}=66\, H z$ The frequency corresponding to wavelength $\lambda_{2}, n_{2}=\frac{v}{\lambda_{2}}=\frac{330}{5.5}=60 \,Hz$ Hence, number of beats per second $=n_{1}-n_{2}=66-60=6$