Use standing-wave diagrams to track phase and amplitude, calculate allowed frequencies in strings and pipes, and compare resonance and damping responses.
A loudspeaker emits sound of frequency 210 Hz into a pipe with one open and one closed end. The diagram shows a representation of the standing wave established in the pipe.
Outline how the standing wave is formed in the pipe.
Determine the wavelength of the wave.
The solid line represents the standing wave at time t and the dotted line represents the standing wave at an instant later. The dot is the equilibrium position of a particle P in the pipe. The up arrow indicates displacements to the right and the down arrow displacements to the left.
On the diagram, draw
a dot to indicate the approximate position of P at time t,
an arrow to indicate the velocity of P at time t.
The frequency of sound is reduced to 140 Hz . Explain why a standing wave will not be formed in the pipe.