Question

Problem 3 [6 pts] Pictured is a representation of the standing wave exciting a 32 mm tube of air, open at both ends. Take the speed of sound to be 320 m/s. (a) Is this the lowest frequency mode (n = 1), the second lowest frequency mode (n = 2), the third lowest frequency mode (n = 3), or the fourth lowest (n = 4)? Choose one (b) Sketch the mode that is one higher than the one drawn, using the same convention. (c) Are the air molecules oscillating vertically or horizontally? Choose one. (d) At what distances from the left end of the tube do the air molecules oscillate with minimum amplitude? (e) What is the frequency of sound coming from this tube? 32 mm

Answer 1

a) the second lowest frequency mode(n = 2)

b)

c) horizontally

d) from the figure, lamda = 32 mm

the air molecules vibrate with minimum amplitude
at x = lamda/4

= 32/4

= 8 mm

e) f = n*v/(2*L)

= 2*320/(2*32*10^-3)

= 10000 Hz