there is no sound; just no sound which can be detected by the human ear.
Consequently, a negative value of dB is possible.
s of a sound is often related to a physical measurement of the strength of a sound. However, a psychological assessment can also occur, w
Doppler Effect
This is the apparent change in frequency (or wavelength) of a wave, which occurs because of relative motion between the source and the observer. When the relative speed is greater than the wave speed, the frequency appears to increase.
Conversely, when the relative speed is lower than wave speed, the frequency appears to decrease.
If the source is stationary and the observer moves towards the source, then the speed of the waves relative to the observer will be
.
Consequently, the observed frequency will be:
Where f’ is the observed frequency and v is the velocity of the waves and f is the
frequency of the waves.
Consequently, if the source is stationary and the observer moves away from the source, the observed frequency will be:
If the source is in motion and the observer is at rest, then the distance
between wave fronts will change by
. Hence the distance between wavefronts w ill become . Therefore:
"
"
Most importantly is tha the wave speed remains unchanged. Wave speed is t purely dependent upon the medium and is not affected by any relative motion of the source.
When the source is moving towards the observer:
"
When the source is moving away from the observer:
"
If both the source and observer is moving, then:
ey to for a change in frequency to
occur. If a train approaches at constant velocity, the distance between wave fronts will essentially be the same and therefore, there will be no change in frequency.
K the Doppler Effect is the presence of acceleration
Shock Waves
It is possible for the speed of the source to exceed the speed of the wave. The result is an envelope of these wave fronts in the form of a cone, where the apex half angle is given by
sin . This angle may also be called the Mach angle.
The Mach number is the ratio of the source speed to the wave speed. It is given by
. The relationship between the Mach number and Mach angle is given by:sin . When the mach number is greater than 1, a shock wave will formand the speed is considered supersonic. The shockwave carries a large amount of energy, concentrated in the surface of the cone. Consequently, the pres sure varies greatly according to location.
When an aircraft flies with constant velocity from cold air to warm air, the Mach number will decrease.
Resonance
A system is capable of oscillating in one or more normal modes. Consequently, if a periodic force is applied to a system, the resulting motion is greatest when the frequency of the applied motion is equal to one of the natural frequencies of the system. These natural frequencies are referred to as resonance frequencies, and is symbolised by
. In such systems, the maximum amplitude is only limited by the friction in the system.
Standing Longitudinal Waves in Air Columns
Such waves can e set up in air columns as a result of interference betweenb longitudinal sound waves travelling in the opposite direction to each other. The phase relationship between the incident and reflected waves depend on whether the end of the pipe is open or closed.
If the end of the pipe is closed, then a displacement node is formed at the end of the pipe (and since displacement and pressure are 90° out of phase, it is a pressure antinode). This is because the wall will not allow any further longitudinal motionin the air. Consequently, the reflected wave is 180° out of phase with the incident wave, creating a standing wave. It is worth noting that the open end is a displacement antinode, while the closed end remains a displacement node. The first resonance will given by
, while the first fundamental frequency is given by
. Consequently frequencies of higher modes are given by:
4
2 1 2 1
If the end of the pipe is open, then at the end of the pipe will be a
displacement antinode (or pressure node) because the compressed air is free to expand into the atmosphere (and hence there is no pressure variation). It is worth noting that both ends of the tube are displacement antinodes. The first resonance w ill beof
, while the fundamental frequency will be . Higher
resonances will be equal to
. .
.In practise an antinode forming at the open end of a tube will be slightly beyond the end of the tube. This additional length must be accounted for when considering resonance. For the tube below, the first resonance will be given by
2 .
An example of resonance in air columns can be given by tubes partially filled with water. When a tuning fork is brought near the top of the tube, and the length from the top to the water corresponds to a resonance frequency of the pipe, the sound will be louder. Using these lengths, it is ossible to calculate the lengths wherep resonance occurs.
Standing Longitudinal Waves in Rods
If a rod is clamped in the middle, and strokes are applied the rod (and in the same direction as the rod), longitudinal waves will pass through it, causing the rod to oscillate. The clamp however will force the appearance of a displacement node. The ends of the rod, however, will be free to vibrate and hence will form displacement antinodes.
If the rod is clamped at a point other than the middle, other normal modes of
oscillation can be produced. If the rod is clamped a distance of
from one end of the rod (where
), then the second normal mode will be produced. This concept is utilised on musical instruments such as xylophones and chimes.Standing Wave in Membranes
circular face resulting sound will not be harmonic, since the standing waves have frequencies which are not integer multiples. The fundament
Two dimensional oscillations can be set up in a flexible membrane stretched over a . The
al frequency will
Spatial and Temporal Interference contain one nodal curve.
Spatial interference is when the amplitude of the oscillation in a medium varies with the position in space of the element, such as with standing waves. Temporal
interference is when the waves are periodically in and out of phase. Consequently, een constructive and destructive interference, there is a temporal alternation betw
such as in beats.
Beats
temporal interference will occur when the interfering wave have slightly different equencies. Beating is the periodic variation in amplitude at a given point due to the uperposition of two waves having slightly different frequencies.
A fr
s
.cos .cos 2
.cos .cos 2
2 cos2 2 cos2 2
Consequently, the wave has a mean frequency of:
and is modulated by the time‐varying amplitude of2cos2
.The beat frequency is the number of amplitude maxima per second. It occurs when
cos2 1
. Consequently, it is the ifference between thedfrequencies of two sources, given by
| |
, although the human ear can o nly detect a beat frequency of up to 20beats per second.The wave patterns produced by musical instruments are the result of the
superpositioning of various harmonics. The human perceptive response associated with these mixtures is the quality or timbre of the sound.
For instance, a tuning fork produces a sinusoidal pattern: