What are the basic sound interference phenomena?

In any mechanical media, two traveling waves interact with others. Constructive interference occurs when their peaks add, while interference pattern occurs once they are "out of phase" and destruct. Throughout theater sound quality, trends of destructive and constructive interference can result in "dead zones" and "real-time locations." The phenomenon of standing waves requires the interaction of transmitted and reflected waves. Due to the generation of "beats" among two frequencies that interact with each other, interference has far-reaching repercussions.

Interference and sounds related terminologies

Wave interference

Compressions and rarefactions make up the sound waves, which are pressure waves. Compression usually brings particles together like a tiny area of space as it travels through a segment of a material, leading to a high-pressure region. A rarefaction helps push particles apart when it passes across a segment of a medium, resulting in a low-pressure area. Sound waves collide, causing the medium's atoms to act in a way that reflects the net influence of the two separate waves upon that particles.

Superposition

If two waves collide at the same time, it is known as superposition. Superposition happens when two waves are in the same location. The amplitudes of these two waves add together as a consequence of superposition. If two waves superimpose and the resulting wave has a larger amplitude than that of the prior waves, it is known as constructive interference. If two waves superimpose and the resulting wave has a smaller amplitude than that of the prior waves, destructive interference occurs, resulting in a reduced amplitude of the resulting wave. Because the waves are not completely identical, most wave superposition’s feature a combination of constructive and destructive interference. The term "superimpose" refers to the act of placing one object on top of another.

Constructive interference

As two waves collide while traveling through the same medium, it is known as wave interference. For instance, when a compression (highly pressurized) of one wave encounters a compression (highly pressurized) of a second another at the same position in the media. The consequence is that the pressure at a certain location is higher. Constructive interference is a term that refers to the act of interfering positively. When two rarefactions (or low-pressure disturbances) from two distinct sound waves collide at the same point, the overall consequence would be that the pressure at that location drops even further. It is also a case of constructive interference in action. Whereas if the interference of two contractions is accompanied by the interference of two rarefactions at a specific place along with the media, the two sound waves would constantly reinforce one another making a very loud sound. The loudness of the sound is caused by the particle in that section of the medium oscillating from extremely high to extremely low pressures.

Destructive interference

When an upward displacement pulse and a downward affected pulse with the same form collide while traveling in opposite directions across a medium, their amplitudes cancel each other out, and also the medium returns to its equilibrium point. Destructive interference is the term for such a type of interference.

Terminologies of sound waves interference

The powerful sound that happens once the sound wave travels on the bottom is understood as a sound wave. The Mach angle is also determined as

$\sin \theta = \frac{v}{v_s} = \frac{1}{M}$

Where 

$M$ is the Mach number, 

$v_s$ is the source speed  

$v$ is the sound speed.

Mach number

Mach number is that the source speed divided by the sound speed written as

$\frac{v_s}{v}=M$

Doppler effect

Typically, the sound wave analysis is completed by utilizing the propagation of a moving source along with the stationary observer, which is Doppler effects, which imply that the determined observed frequency for the source which is moving approaches a stationary observer as

$f_o = f_s\left(\frac{v+v_o}{v-v_s}\right)$

Where 

$f_o$ is observed frequency, 

$f_s$ is the moving source frequency, 

$v$ is the sound velocity in a medium, 

$v_o$  is the velocity of an observer, and 

$v_s$  is source velocity.

Interference of sound with a tuning fork

When someone strikes a tuning fork near one’s ear and spins it, the sound alternates from loud and soft while the user rotates through the angles in which the interference was constructive or destructive. Due to the sheer vast scale mismatch in between tuning fork as well as the wavelengths of a sound generated, visualizing it in a graphic is difficult. A sound wavelength at room temperature for such a tuning fork to generate equivalent tempered Middle-C (C4, 260 Hz) is about 1.5m more than 4 feet.

To use a snapshot of the interferogram in a ripple tank with a double vibrator is an effort to quantitatively visualize the interference from such a binary source. That shot is layered on a tuning fork drawing in the hopes of gaining understanding into the nature of interference in waves from two sources. However, the scale is drastically different: the two ripple tank wave sources are separated by many wavelengths, while the two tines of a C-tuning fork are separated by around 0.624 times of a wavelength. That arrangement would indicate numerous loudness minimum, however when the tuning fork is moved 45 degrees from the axis of the two tines, it produces four local minima.

Dan Russell's site from Penn State has visualizations showing interference patterns for single and many sources. An animation of a lateral quadrupole generator produced the pattern upon that right. Since the tuning fork's twin tines are now out of phases, that's the closest estimate of interference, and Russell points out how a lateral quadrupole output is made up of two opposing phase dipoles. Its sound wavelength again for C tuning fork is 50 times the size of a physical vibrator, and therefore this diagram comes closer to what you perceive by turning the tuning fork via the ear.

Formulae

• Doppler effects formula

$f_0=f_s\left(\frac{v+v_0}{v-v_s}\right)$

• Mach number formula

$\frac{v_s}{v}=M$

• Mach angle

$\sin \theta =\frac{v}{v_s}=\frac{1}{M}$

Context and Applications

This topic is useful for the students who are undergoing the following courses:

• Bachelors in Technology (Electronics)
• Bachelors in Technology (Electronics and Communication)
• Bachelors in Science (Physics)
• Masters in Science (Physics)
• Masters in Technology (Electronics and Communication)

Practice Problems

1. Name the characteristic of the sound which distinguishes a sharp sound from a grave or dull sound?

1. Intensity
2. Echo
3. Pitch
4. Resonance

Answer: Option c

Explanation: Pitch is that characteristic of sound which distinguishes a sharp or shrill sound from a grave or dull sound. It depends upon frequency. The higher the frequency higher will be the pitch and shriller will be the sound and vice versa.

2. Due to which phenomena sound is heard at a longer distance in the night than in the day?

1. Reflection
2. Refraction
3. Interference of sound
4. Diffraction of sound

Answer: Option b

Explanation: Due to refraction sound is heard at a longer distance in the night than in the day.

3. What is the intensity of sound?

1. It is inversely proportional to the square of the distance of a point from the source.
2. It is directly proportional to the square of the amplitude of vibration, square of the frequency, and density of the medium.
3. Both a and b
4. Neither a nor b

Answer: Option c

Explanation: The intensity of any sound at any point in space is the amount of energy passing normally per unit area held around that point per unit time.

4. The angle of the sound wave is equal to

1. $M+1$
2. $M-1$
3. $M$
4. $\frac{1}{M}$

Answer: Option d

Explanation: The sound wave's angle is equal to the inverse of the Mach number or $\frac{1}{M}$, or the inverse of the source speed by the sound speed.

5. What is the Mach number?

1. $v-v_s$
2. $\frac{v}{v_s}$
3. $\frac{v_s}{v}$
4. None of these

Answer: Option c

Explanation: The Mach number is the ratio of the source speed by the sound speed or $\frac{v_s}{v}$ ratio of the speed of a source ($v_s$) and the speed of sound ($v$).

Related Concepts

• Doppler effects concept
• Mach number concept
• Boundary behavior concept
• Reflection, refraction, and diffraction