(a) What is a wave motion?
The equation \(y = A \sin \frac{2\pi}{\lambda} (Vt-X)\) represents a wavetrain in which y is the vertical displacement of a particle at distance X from the origin in the medium through which the wave is travelling. Explain, with the aid of a diagram, what A and \(\lambda\) represent.
(b) (i) Describe an experiment to determine the frequency of a note emitted by a source of sound
(ii) A pipe closed at one end is 1 m long. The air in the pipe is set into vibration and a fundamental note is produced. If the velocity of sound in air is 340ms\(^{-1}\), calculate the frequency of the note
(c) State two differences between a sound wave and a radio wave.
(a) Wave motion
A wave motion is a disturbance that travels through a medium (or space), transferring energy from one point to another without any permanent transfer of the particles of the medium.
In the equation \( y = A \sin \dfrac{2\pi}{\lambda}(Vt - X) \):
- A is the amplitude, the maximum displacement of a particle from its rest (equilibrium) position. On a displacement graph it is the height of a crest (or depth of a trough) measured from the axis.
- \( \lambda \) is the wavelength, the distance between two successive particles that are in the same phase (for example crest to crest or trough to trough).
(b)(i) Experiment to determine the frequency of a note
Use a resonance tube: a tuning fork of known frequency is not used here; instead a sonometer/resonance-tube method with a signal source can be used. In the resonance-tube method, a vibrating source is held over the open end of a tube whose air-column length is varied until resonance (loudest sound) occurs at length \( l_1 \) (first resonance). Then \( f = \dfrac{v}{4(l_1 + c)} \), where v is the speed of sound and c the end correction; measuring the resonance lengths and the speed of sound gives the frequency of the note.
(b)(ii) Fundamental note of a closed pipe
For a pipe closed at one end, the fundamental has a node at the closed end and an antinode at the open end, so \( l = \dfrac{\lambda}{4} \), giving \( \lambda = 4l = 4 \times 1 = 4\,\text{m} \).
\[ f = \frac{v}{\lambda} = \frac{340}{4} = 85\,\text{Hz} \]
(c) Two differences between a sound wave and a radio wave
- A sound wave is a mechanical, longitudinal wave and needs a material medium to travel; a radio wave is an electromagnetic, transverse wave that can travel through a vacuum.
- Sound travels much more slowly (about \( 340\,\text{m s}^{-1} \) in air) than a radio wave (about \( 3.0 \times 10^{8}\,\text{m s}^{-1} \)).
(a) Wave motion
A wave motion is a disturbance that travels through a medium (or space), transferring energy from one point to another without any permanent transfer of the particles of the medium.
In the equation \( y = A \sin \dfrac{2\pi}{\lambda}(Vt - X) \):
- A is the amplitude, the maximum displacement of a particle from its rest (equilibrium) position. On a displacement graph it is the height of a crest (or depth of a trough) measured from the axis.
- \( \lambda \) is the wavelength, the distance between two successive particles that are in the same phase (for example crest to crest or trough to trough).
(b)(i) Experiment to determine the frequency of a note
Use a resonance tube: a tuning fork of known frequency is not used here; instead a sonometer/resonance-tube method with a signal source can be used. In the resonance-tube method, a vibrating source is held over the open end of a tube whose air-column length is varied until resonance (loudest sound) occurs at length \( l_1 \) (first resonance). Then \( f = \dfrac{v}{4(l_1 + c)} \), where v is the speed of sound and c the end correction; measuring the resonance lengths and the speed of sound gives the frequency of the note.
(b)(ii) Fundamental note of a closed pipe
For a pipe closed at one end, the fundamental has a node at the closed end and an antinode at the open end, so \( l = \dfrac{\lambda}{4} \), giving \( \lambda = 4l = 4 \times 1 = 4\,\text{m} \).
\[ f = \frac{v}{\lambda} = \frac{340}{4} = 85\,\text{Hz} \]
(c) Two differences between a sound wave and a radio wave
- A sound wave is a mechanical, longitudinal wave and needs a material medium to travel; a radio wave is an electromagnetic, transverse wave that can travel through a vacuum.
- Sound travels much more slowly (about \( 340\,\text{m s}^{-1} \) in air) than a radio wave (about \( 3.0 \times 10^{8}\,\text{m s}^{-1} \)).
