(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.
Explanation
(a) A wave motion is succession of pulses propagated with time from one region of space to another. Energy is transmitted in the process.
A is the amplitude. It is the maximum displacement from equilibrium position of the wave particle. \(\lambda\) - the wavelength, is the distance between two successive points on the wave that is in phase.
(b) Experiment to determine the frequency of a note emitted by a source of sound
Assuming that the source of sound is a turning fork. The vibrating tube turning fork is held close to the top of a moveable tube as shown. The tube is deeped in a cylinder that is 3/4 filled with water. Starting with the air column of length, I, with the turning fork sounding gently close to the top, the length I is gradually increased; The, sound coming from the air column is heard to increase. When the sound is loudest the air has been set into resonance by the fork. The length of I of the air column is measured and recorded. The length of the air column can be shown to be \(\frac{\lambda}{4}\) neglecting end correction. Thus using the equation:
\(f = \frac{V}{\lambda} = \frac{V}{4l}\)
where V is the velocity of sound in air, f the frequency of the turning-fork the source of sound, the frequency is then determined.
(ii) Using \(f = \frac{V}{\lambda} = \frac{V}{4l}\)
= \(\frac{340}{4 \times 1} = 85 Hz\)
(c) A sound wave :
(i) requires material medium for propagation. (ii) is a longitudinal wave motion. While radio wave (i) does not require material medium for propagation. (ii) is a transverse wave motion.