Sound Waves Concept Page - 1

Result

Human hearing range

The audible range of sound for human beings extends from about 20 Hz to 20000 Hz. Any sound outside this hearing range is undetected by human ears regardless of its amplitude. 

Example

Audible range of sound in animals

Organism	Audible Range (In Hz)
Human	20 - 20,000
Elephant	16 - 12,000
Cow	16- 40,000
Cat	100 - 32,000
Dog	40 - 46,000
Rabbit	1000 - 1,00,000
Bat	1000 - 1,50,000
Dolphins	70 -1,50,000
Seal	900 2,00,000

Definition

Sound as form of Energy

Sound is the movement of energy through substances in longitudinal (compression/rarefaction) waves.

Sound is produced when a force causes an object or substance to vibrate the energy is transferred through the substance in a wave. Typically, the energy in sound is far less than other forms of energy

Example

Sound as form of Energy

A vibrating drum in a disco transfers energy to the room as sound. Kinetic energy from the moving air molecules transfers the sound energy to the dancers eardrums. Notice that Kinetic (movement) energy in the sticks is being transferred into sound energy.
Sound vibrations create sound waves which move through mediums such as
air and water before reaching our ears

Example

Sound waves are longitudinal waves

Sound waves in air (and any fluid medium) are longitudinal waves. In sound waves, particles of the medium through which the sound is transported vibrates parallel to the direction that the sound wave moves.

Diagram

Compression and Rarefactions by vibrating slinky/speaker

Compression and rarefactions created by the speaker in the air are shown in the image.

Definition

Waveform

Waveform of sound is the shape and form of the sound wave moving in a physical medium. Some examples of waveforms are rectangular, sinusoidal, triangular, etc.

Definition

Amplitude of vibration

The magnitude of the maximum disturbance of particles in the medium on either side of the mean value is called the amplitude of the wave. It is usually represented by the letter A. Its SI unit is metre (m).

Definition

Wavelength of sound waves

The distance traveled by the wave in one time period of vibration is called the wavelength. It is equal to the distance between two consecutive compressions or two consecutive rarefactions at a given instant of time. The wavelength is usually represented by λ$\lambda$. Its SI unit is metre (m).

Example

Calculate amplitude of vibration

Example: A closed organ pipe has length l$l$. The air in it is vibrating in 3rd overtone with a maximum amplitude of A$A$. Find the amplitude of vibration at a distance of l14${\displaystyle \frac{l}{14}}$ from closed end of the pipe.

Solution:
3rd$3^{rd}$ overtone ⇒7λ4=l$\Rightarrow {\displaystyle \frac{7\lambda }{4}}=l$
or, λ=4l7$\lambda ={\displaystyle \frac{4l}{7}}$
or, l14=λ8${\displaystyle \frac{l}{14}}={\displaystyle \frac{\lambda }{8}}$
∴$\therefore$ Amplitude at λ8${\displaystyle \frac{\lambda }{8}}$ is half way between node and antinode, i.e A2${\displaystyle \frac{A}{2}}$

Example

Calculate wavelength of sound waves

Example: A metallic rod of length 2.0 m$2.0m$ is rigidly clamped at its middle point. A longitudinal wave is set up in the rod in such a way that there will be 3$3$ nodes on either side of the clamped point. Find the wavelength of the longitudinal wave so produced.

Solution:
3λ2+λ4=L2${\displaystyle \frac{3\lambda }{2}}+{\displaystyle \frac{\lambda }{4}}={\displaystyle \frac{L}{2}}$
or, 7λ4=L2${\displaystyle \frac{7\lambda }{4}}={\displaystyle \frac{L}{2}}$
or, λ=2L7$\lambda ={\displaystyle \frac{2L}{7}}$
or, λ=47 m$\lambda ={\displaystyle \frac{4}{7}}m$

Diagram

Displacement time graph of sound waves

Displacement-time graph is for an individual particle in the vibrating medium. It shows the displacement of a particle from the rest position at a particular time.Compression, C: highest pressure of sound wave.
Rarefaction, R: lowest pressure of sound wave.
Amplitude, A: the maximum pressure change from surrounding pressure in either direction.
Wavelength: the distance between two consecutive C or R or any two points.C and R are at position of zero displacement, when are at rest position.
Note:
The displacement-time graph is drawn for an instant of time. It changes at every instant of time. The direction of motion of sound wave can be determined by drawing displacement-time graphs at different instances of time.

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