Answer:
B. 0.334 m
Explanation:
Given that fundamental frequency of organ pipe which is closed at one end is, [tex]f_{0}=256Hz[/tex]
And the temperature of air is, [tex]T=18^{\circ} C[/tex]
Now convert temperature in kelvin,
[tex]T=(18+273)K\\T=291 K[/tex]
Now the fundamental frequency formula when the organ pipe is open at one end.
[tex]f_{0} =\frac{v}{2L}[/tex]
Here, v is the velocity of sound, L is the length of organ pipe.
For further solving it for L.
[tex]L=\frac{v}{4f_{0} }[/tex]
And also we know that,
[tex]v=v_{0}\sqrt{\frac{T}{273} }[/tex]
Here, [tex]v_{0}[/tex] is rthe speed of sound at room temperature and the value of this is,
[tex]v_{0}=331 km/s[/tex].
Now,
[tex]v=331\sqrt{\frac{291}{273} } \\v=331\times 1.0324\\v=341.7373 m/s[/tex]
Now put this value in L equation,
[tex]L=\frac{341.7373}{4\times 256} \\L=0.3337 m\\L=0.334 m[/tex]
Therefore, the length of an organ pipe is 0.334 m
