Question

What are the three longest wavelengths for standing sound waves in a 120-cm-long tube that is (a) open at both ends and (b) open at one end, closed at the other?

Answer 1

Answer

given,

length of tube = 120 cm

a) Open at both ends.

distance between two successive nodes or anti nodes = λ/2

for first possibility =  λ/2 = 120

                          λ  =2 x 120 = 240 cm

for second Possibility, distance between two node or antinode acting symmetrically

                       λ = 120 cm

for three nodes in the tube, distance between them is equal to

$\dfrac{3}{2}\lambda = 120$

$\lambda = 80 cm$

b) Open at one end

 First possibility, The distance between one node or anti node

  $\dfrac{\lambda}{4} = 120$

             λ = 480 cm

 Second Possibility, distance between two node or anti node is equal to

$\dfrac{3}{4}\lambda = 120$

    λ = 160 cm

Third possibility, distance between three nodes and three anti nodes is equal to

$\dfrac{5}{4}\lambda = 120$

   λ = 100 cm