Mechanical Waves

A mechanical wave is a wave that is an oscillation of matter, and therefore transfers energy through a medium. There are three types of mechanical waves, transverse waves, longitudinal waves, and surface waves.

Transverse wave is the form of wave in which particles of medium vibrates about their mean position perpendicular to the direction of the motion of the wave. Surface waves travel along the surface or interface between two media. Examples of surface waves are waves in a pool, or in an ocean, lake, or any other type of water body. Longitudinal waves cause the medium to vibrate parallel to the direction of the wave. Sound is a longitudinal wave.

Parts of a Wave

When you throw a stone into a pool of water, a ripple wave is created with concentric circles. The equilibrium surface denotes the undisturbed still surface of the water. The Amplitude is the magnitude of the greatest displacement from the equilibrium. The region where the water level is lower than equilibrium is called a Trough while the region where the water level is higher than the equilibrium is called Crest. A complete cycle of a crest followed by a trough is called a wavelength; its symbol is ƛ

A wave front moving out from the point of origin (point source) toward a barrier is called an incident wave. A wave front moving away from the barrier is called a reflected wave, while a series of waves linked together is a wave train.

A ray is a line that originates from the point source of a wave and moves in the direction of the movement of wave. Diverging rays shows a wave spreading out from one point-source.

Transverse and Longitudinal Waves

Using a long spring fixed on one end and free on the other end to demonstrate these two types of waves. If you displace the spring sideways, the sideways oscillations set up a transverse wave. If you displace the spring on its longitudinal axis, making it longer and shorter repeatedly, the displacements that develop along the axis set up a longitudinal wave.

Along the wave, energy is stored as both elastic potential energy and kinetic energy. As a section of the spring moves from the equilibrium position to the top of the crest/trough, that section has both kinetic energy and elastic potential energy. At the point on the pulse where the displacement is greatest the coils are in essence, motionless. Then, the tension in the spring returns the coils to its equilibrium position.

Reflection of Transverse Waves

When a wave reached the fixed end of the spring, the waves is reflected from that end and it travels back towards its origin. The reflected pulse is inverted relative to the original (incident) wave i.e, the crests are reflected as troughs, and vice versa.

Longitudinal Waves

A longitudinal wave (as described previously) is developed when a coil undergoes compression and rarefaction, which correspond to crests and troughs in transverse waves. In longitudinal waves, the spring oscillates back and forth, parallel to the direction of the motion of the wave, once the wave has passed through, the medium returns to its original position. In both cases (transverse and longitudinal) energy is transmitted through the medium without the transmission of matter.

The Universal Wave Equation

The Universal wave equation can be expressed as:

v = f ƛ

Where v is the speed of the wave in m/s, f is the frequency of vibrations in Hz or s^-1 and ƛ is the wavelength in m.

Waves at Boundaries

The speed of a wave is determined by the medium in which the wave is traveling through. When the wave moves into a slower medium, the frequency never changes but the wavelength and amplitude change thereby impacting the speed.

Wave Interference

Multiple waves can occupy the same space at the same time, this is called superposition. The amplitudes of the waves may be added in a condition called Interference. When they amplitudes add together it results in constructive interference, 2 crests form a super-crest and 2 troughs form a super-trough. These points are called antinodes. When a crest and a trough meet, it results in destructive interference. The points where destructive interference occurs such that the amplitude of the wave is equal to 0 are called nodes. A standing wave occurs when a wave reflects off of a barrier and interferes with the incident wave.

Wave Phenomena

Reflection occurs when a wave bounces off of a barrier. The law of reflection indicates that the angle of incidence is equal to the angle of reflection.

Refraction occurs when a wave strikes a boundary to a new medium (in which it travels a different speed), it will bend (refract).

Diffraction occurs when waves appear to bend around corners.

Sound

Sound is a longitudinal wave caused by a vibrating object. Peaks correspond to areas of high pressure and troughs correspond to areas of low pressure. Sound is a mechanical wave, it requires a medium to travel through, which explains why sound cannot be heard in a vacuum. Sound intensity refers to the loudness of sound and is determined by the amplitude of sound. The louder the sound the higher the amplitude. There is an inverse squared relationship between sound intensity and distance from the point-source. The pitch is determined by the frequency of the sound. High frequency sounds are high pitched and low frequency sounds are low pitched.

The Doppler Effect

Sound pitch can change depending on the relative motion of the sound source and the observer. If the source is moving away from the observer, they hear a lower pitch due to a lower frequency. If the source is moving toward the observer, they hear a higher pitch due to a higher frequency. The shift in frequencies is called a Doppler Shift.

Effect of temperature on sound

Temperature affects the speed of sound, as temperature increases, the speed of sound also increases.
v = 331m/s + 0.6 (temperature)

Beats

When two sound waves with two slightly different frequencies interfere with each other to form a wave with oscillating amplitude

Sound Quality

The human ear drum can only detect a single wave composed of all sound waves as a superposition. The quality of a musical note is called timbre.

Resonance

Often the sounds we hear are due to resonance, which is defined as the formation of a standing wave. Resonance describes the phenomenon of increased amplitude that occurs when the frequency of a periodically applied force is equal or close to a natural frequency of the system on which it acts.