SP$3$

A pipe that is open at both ends will form standing waves, if properly excited, with antinodes near both ends of the pipe. Suppose we have an open pipe $40$ cm in length.

a$.$ Sketch the standing$-$wave pattern for the fundamental standing wave for this pipe. $($There will be a node in the middle and antinodes at either end.$)$

b$.$ What is the wavelength of the sound waves that interfere to form the fundamental wave?

c$.$ If the speed of sound in air is $340\frac{m}{s},$ what is the frequency of this sound wave?

d$.$ If the air temperature increases so that the speed of sound is now $350\frac{m}{s},$ by how much does the frequency change?

e$.$ Sketch the standing$-$wave pattern and find the wavelength and frequency for the next harmonic in this pipe.