Practise C.4 by reading standing-wave diagrams, calculating string and pipe harmonics, and interpreting resonance curves and damping responses from experimental data.
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.
The length of the pipe is 1.20 m .
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.
This question is in two parts. Part 1 is about the oscillation of a mass. Part 2 is about the photoelectric effect.
Part 1 Oscillation of a mass
A mass of 0.80 kg rests on a frictionless surface and is connected to two identical springs both of which are fixed at their other ends. A force of 0.030 N is required to extend or compress each spring by 1.0 mm . When the mass is at rest in the centre of the arrangement, the springs are not extended.
Explain how the model in (b) predicts how the lattice will absorb a certain wavelength of electromagnetic infrared radiation.
A mass is attached to a vertical spring. The other end of the spring is attached to the driver of an oscillator.
The mass is performing very lightly damped harmonic oscillations. The frequency of the driver is higher than the natural frequency of the system. At one instant the driver is moving downwards.
The oscillator is switched off. The system has a Q factor of 22. The initial amplitude is 10 cm . Determine the amplitude after one complete period of oscillation.
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.
The length of the pipe is 1.20 m .
Outline how the standing wave is formed in the pipe.
W in (a) is immersed in a beaker of oil. As a result of this immersion the oscillations of W are critically damped. Describe what is meant by critically damped.