15 A closed organ pipe has length L The air in it is vibrating in 3rd overtone with a maximum - Physics - Electromagnetic Waves

Question

15 A closed organ pipe has length L The air in it is vibrating in
3rd overtone with a maximum amplitude of A Find the amplitude at a
distance of L/14 from closed end of the pipe ---------

Somnath physics · Accepted Answer

From theory of standing waves we have y=Acos2πxλsin2πvtλAmplitude at x=L14 is given bya=Acos2πλL14=AcosπλL7Again we have λ=vf∴a=AcosπfvL7−−−1
For closed organ pipe, (open at one end and closed at the other) the permissible modes of vibration is given by f=(2n−1)v4LFor third overtone n = 4f=7v4Lby eqn
 1a=AcosπvL7(7v4L)=Acosπ4=>a=A2

15.A closed organ pipe has length L.The air in it is vibrating in 3rd overtone with a maximum amplitude of A.Find the amplitude at a distance of L/14 from closed end of the pipe ---------