Mechanical Waves and Sounds
Waves refer to disturbances that travel outwards or propagate from a source. Waves are a way to transfer energy thus will always involve energy, but it is important to note that waves do not necessarily transfer mass. Examples of waves that have no transfer of mass involved are light and sound.
Now onto the main focus, MECHANICAL WAVES. Mechanical waves are waves that require a medium for them to be able to travel; mediums can be solid liquid, or gas and the speed of the wave will depend on the physical properties of the medium. Examples of mechanical waves are sound and water.
To make waves easier to understand and visualize, imagine a water wave where the disturbance occurs on the water's surface.
There are many things that can cause a disturbance. For water, something as simple as a rock being thrown into a pond can cause a disturbance. For soundwaves, one cause will be a change in the air pressure where it is traveling.
OBJECTIVES
- Apply the inverse-square relation between the intensity of waves and the distance from the source
- Describe qualitatively and quantitatively the superposition of waves
- Apply the condition for standing waves on a string
- Relate the frequency (source dependent) and wavelength of sound with the motion of the source and the listener
- Solve problems involving sound and mechanical waves in contexts such as, but not limited to, echolocation, musical instruments, ambulance sound
TYPES ACCORDING TO MOTION
Mechanical waves can be categorized according to how they move. These two categories being transverse and longitudinal waves.
A transverse wave (shear) propagates so that the disturbance is perpendicular to the direction of propagation; shear or S-waves
In a longitudinal wave (compression), the disturbance is parallel to the direction of propagation; pressure or P-waves
Of course, there are also cases where waves are a combination of the two.
Sound in solids can be both longitudinal and transverse.
SUPERPOSITION
Dictionary definition: the action of placing one thing on or above another, especially so that they coincide
Definition according to physics: they result from two or more simple waves that combine as they come together at the same place at the same time
SUPERPOSITION WITH SIMPLEST RESULTS
Constructive Interference
- Two identical waves arrive at the same point exactly in phase.
- The crests and troughs of the two waves are precisely aligned.
- The resultant is twice the amplitude of the two individual waves, hence the
2Xand-2X.
Destructive Interference
- Two identical waves arrive exactly out of phase—complete opposites of crests and troughs at precisely the same locations—producing pure destructive interference.
- The resulting amplitude of resultant is zero for pure destructive interference; they cancel each other out due to having opposite directions.
HOWEVER, combinations of constructive destructive interferences are naturally more common than pure ones.
Waves that are not results of pure constructive or destructive interference can vary from different places at different times.
What happens when two waves that are not similar and have different amplitudes and wavelengths are superimposed?
ANSWER: The resultant wave from the combined disturbances of two dissimilar waves looks much different than the idealized sinusoidal shape of a periodic wave.
INTERFERENCE SIMULATION
STANDING WAVES are waves that appear to be still as they vibrate; formed by the superposition of two or more waves with different directions
If the two waves have the same amplitude and wavelength with its waves moving in different or opposite directions, then they alternate between constructive and destructive interference.
The nodes are the points where the string does not move; more generally, the nodes are the points where the wave disturbance is zero in a standing wave. The fixed ends of strings must be nodes, too, because the string cannot move there.
Inverse-square relation
Inverse square law
d - distance
I - radiation intensityThe intensity of the radiation is inversely proportional to the square of the distance.
In relation to intensity of waves and distance from the source:
Inverse square law
r - distance from the source
I - intensity of the waveThe intensity of a wave decreases in proportion to the square of the distance from the source.
When moving away from the source of the wave, the intensity diminishes rapidly.
Ex: Doubling the distance from the source, intensity decreases by four.
- Sound Waves
When moving twice as far away from the sound source, the intensity of the sound decreases to one-fourth of its original value. This illustrates how sound spreads out in all directions from its source. - Mechanical Waves
As one moves away from the epicenter, the intensity of shaking caused by seismic waves diminishes.
DOPPLER EFFECT
The doppler effect or doppler shift is a phenomena that says relative motion between a sound source and listener affects the perceived frequency and wavelength of sound.
It is also defined as the increase or decrease of frequency in waves as the source and listener moves towards or away from each other.
When moving closer, the listener experiences higher frequency and shorter wavelength due to encountering sound waves more frequently.
Moving away results in lower frequency and longer wavelength for the listener as sound waves are encountered less frequently.
References:
BYJU’S (2021, April 27). Inverse Square Law - Statement, Formula and Applications. BYJU’S. https://byjus.com/physics/inverse-square-law/
BYJU’S (2019, February 19). Doppler Effect - Definition, Formula, Examples, Uses, FAQs. BYJU’S. https://byjus.com/physics/doppler-effect/
n. d. (2023). The Doppler Effect. the Physics Classroom. https://www.physicsclassroom.com/class/waves/Lesson-3/The-Doppler-Effect
Paul Peter Urone, & Hinrichs, R. (2015). 13.3 Wave Interaction: Superposition and Interference - Physics | OpenStax. Openstax.org; OpenStax. https://openstax.org/books/physics/pages/13-3-wave-interaction-superposition-and-interference