When two simple harmonic waves having vibrations in mutually perpendicular directions superimpose on each other then the resultant motion of the particle is along a closed path, called the Lissajous Figure. These figures can be of many shapes, depending on:
a) Ratio of frequencies or time periods of two waves.
b) Ratio of amplitudes of two waves.
c) Phase difference between the two waves.
A pipe field with air having rigid walls and diameter less than its length is called an organ pipe. Such pipes are used in producing musical sound by pushing air into the pipe. Flute is best example of an organ pipe. When the pipe is open at both the ends, it is called an open organ pipe. When one end of the pipe is open and other is closed, it is called a closed organ pipe.
1) In longitudinal mode, vibrations of the prongs of tuning fork are along the length of the string. The frequency of vibration of string is half that of tuning fork.
2) In transverse mode, vibrations of the tuning fork are at 90 degree to the length of the string. The frequency of vibration of string is equal to frequency of vibrating tuning fork.
Characteristics of musical sound
Characteristics of musical sound are
1) Intensity or Loudness Intensity of sound at any point is energy emitted/sec. per unit area around that point. Loudness is intensity of sound as perceived by the human ears. Relation between loudness (L) and intensity of sound (I) is given by Weber’s law i.e. L= k loge I. If the sound is just heard, its loudness L = 1 decibel. For whisper, L = 10 . 20 decibel; For ordinary talk, L = 80 . 140 decibel.
2) Pitch or Frequency Pitch is that characteristic of musical sound, which distinguishes between a sharp sound and a dull sound. A sharper sound is said to have higher pitch and vice-versa. Pitch depends on frequency and also on intensity. Higher the frequency, higher will be the pitch. However, lower the intensity, higher will be the pitch. For example, pitch of a roaring lion is low but that of buzzing be is high.
3) Quality or Timber Quality is that characteristic of musical sound, which distinguishes between sounds produced by different source even when they are of same intensity and same pitch. Quality depends on number of harmonics/overtones produced and their relative intensity.
Doppler’s Effect in sound
Whenever there is a relative motion between a source of sound and listener, the apparent frequency of sound heard by the listener is different from the actual frequency of sound produced by the source. Conditions when Doppler’s effect is not observed.
1) When source and listener, both are at rest.
2) When source and listener, both are moving with the same velocity in the same direction.
3) When source and listener are moving at right angles to each other.
4) When motion of source and listener is such that distance between them remains the same.