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
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
Updated On: Aug 1, 2022
- 12
- zero
- 1
- 6
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The Correct Option is D
Solution and Explanation
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
$=n_{1}-n_{2}=66-60=6$
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Concepts Used:
Beats
What is Beat Frequency?
Let’s see from fig.m, the frequency of a pink-colored wave is f1, and that of a green-colored wave is f2. So, the frequency of the beat is the difference between these two, which is:
fBEATS = |f1 - f2|
Interference and Beats
When two or more waves travelling in a medium meet, the resulting phenomenon is called interference and beats are an excellent example of the phenomenon of interference.
What is Interference?
When two or more waves travelling in a medium meet, the resulting phenomenon is called interference and beats are an excellent example of the phenomenon of interference.
The Application of Beats:
- Beats are used in determining the unknown frequency
- Beats are used in determining the existence of poisonous gases in mines.