Answer:
The beat frequency is 33.33 Hz.
Explanation:
Given that,
Length of first pipe =60 cm
Length of other pipe = 68 cm
Speed of sound = 340 m/s
We need to calculate the frequency
We know that,
When they operate at fundamental frequency then the length is given by,
[tex]L=\dfrac{\lambda}{2}[/tex]
The wavelength is given by
[tex]\lambda=2L[/tex]
For first organ pipe,
Using formula of frequency
[tex]f=\dfrac{v}{\lambda}[/tex]
[tex]f_{1}=\dfrac{v}{2L_{1}}[/tex]...(I)
Put the value into the formula
[tex]f_{1}=\dfrac{340}{2\times60\times10^{-2}}[/tex]
[tex]f_{1}=283.33\ Hz[/tex]
For second organ pipe,
[tex]f_{2}=\dfrac{v}{2L_{2}}[/tex]...(II)
Put the value in the equation (II)
[tex]f_{2}=\dfrac{340}{2\times68\times10^{-2}}[/tex]
[tex]f_{2}=250\ Hz[/tex]
Therefore the beat frequency
[tex]\Delta f=f_{1}-f_{2}[/tex]
[tex]\Delta f=283.33-250[/tex]
[tex]\Delta f=33.33\ Hz[/tex]
Hence, The beat frequency is 33.33 Hz.
