Sound

Hello, and welcome to today's physics lesson. We are going to explore the fascinating world of sound. In this chapter, we will learn how sound waves reflect to create echoes, discover the different types of vibrations that objects can undergo, and understand what makes sounds loud, high-pitched, or unique in quality. Let us begin our journey into the physics of sound.

Sound is a mechanical wave that requires a medium to travel. When a body vibrates, it causes the particles of the surrounding medium to vibrate, and these vibrations propagate as sound waves. Our ears can detect sounds only within a specific range of frequencies, from 20 hertz to 20,000 hertz, which we call the audible range. Sounds with frequencies above 20,000 hertz are called ultrasonic, while those below 20 hertz are called infrasonic. Both are inaudible to human ears.

Let us recall some fundamental properties of waves. The maximum displacement of a particle from its mean position is called the amplitude. The time taken for one complete vibration is the time period, denoted by capital T. The number of vibrations per second is the frequency, denoted by small f. The distance travelled by a wave in one time period is the wavelength, denoted by lambda. The wave velocity, denoted by capital V, is related to frequency and wavelength by the formula: wave velocity equals frequency multiplied by wavelength.

Or, V = fλ. Also, frequency equals one divided by time period.

Or, f = 1/T.

Sound waves are longitudinal waves, meaning the particles of the medium vibrate along the direction of wave propagation, creating compressions and rarefactions. They can travel through solids, liquids, and gases. The speed of sound in a gas depends on the pressure, density, and a constant called gamma, which is the ratio of specific heats. For air, gamma equals 1.4. The formula is: velocity equals the square root of gamma P over d.

Or, V = √(γP/d). Importantly, the speed of sound increases with temperature and humidity, but it is independent of pressure.

Sound waves, like all waves, obey the laws of reflection. When a sound wave strikes a hard surface, it bounces back into the same medium. The angle of reflection equals the angle of incidence, and the incident ray, reflected ray, and normal all lie in the same plane. Unlike light, sound does not need a smooth or polished surface to reflect. The only requirement is that the reflecting surface must be larger than the wavelength of the sound wave.

This reflection of sound leads to a phenomenon you have surely experienced: the echo. An echo is the sound heard after reflection from a distant obstacle, such as a cliff or a wall, after the original sound has ceased. For an echo to be heard distinctly, the reflected sound must reach your ears at least 0.1 second after the original sound. This is because the sensation of sound persists in our ears for about 0.1 second.

Let us calculate the minimum distance needed to hear an echo. If d is the distance to the obstacle and V is the speed of sound, the total distance travelled by sound is 2d. The time taken is 2d divided by V. Setting this equal to 0.1 second and using 340 metres per second as the speed of sound in air, we find that d equals 17 metres. Thus, to hear a clear echo, the reflecting surface must be at least 17 metres away. In water, where sound travels much faster at about 1400 metres per second, the minimum distance becomes 70 metres.

The echo method provides a practical way to measure the speed of sound. By producing a sound at a known distance from a reflecting surface and measuring the time interval until the echo returns, we can calculate velocity using the formula: velocity equals 2d divided by t.

Or, V = 2d/t.

Echoes have remarkable practical applications. Bats navigate in complete darkness using echolocation. They emit ultrasonic waves and interpret the returning echoes to locate obstacles and prey. Dolphins use similar ultrasonic echolocation to detect enemies and hunt for food. Fishermen use ultrasonic pulses to locate schools of fish in the sea.

One of the most important applications is SONAR, which stands for Sound Navigation and Ranging. Ships use SONAR to detect underwater objects like submarines, icebergs, or sunken ships. Ultrasonic waves are sent in all directions, and by measuring the time interval between transmission and reception of the reflected waves, the distance to the obstacle is calculated as d equals Vt over 2.

Or, d = Vt/2. This same principle, called echo depth sounding, helps measure ocean depths.

In medicine, ultrasonography uses ultrasonic echoes to create images of internal organs like the liver, gall bladder, and uterus. Echocardiography similarly images the heart. These techniques are safe and non-invasive, making them invaluable diagnostic tools.

Now let us explore how objects vibrate. When a body vibrates without any external force acting on it, we call these natural or free vibrations. The frequency of these vibrations depends only on the body's shape and size, and is called its natural frequency. In an ideal vacuum, natural vibrations would continue forever with constant amplitude.

However, in real conditions, the surrounding medium offers resistance. The amplitude gradually decreases due to energy loss, and these are called damped vibrations. A swinging tree branch, a tuning fork in air, or a simple pendulum all exhibit damped vibrations. The energy lost transforms into heat, and eventually the motion stops.

When an external periodic force acts on a vibrating body, we get forced vibrations. The body vibrates at the frequency of the applied force, not its natural frequency. The amplitude depends on how close the driving frequency is to the natural frequency. When you press a vibrating tuning fork against a table, the table undergoes forced vibrations, producing a louder sound due to its larger vibrating area.

Resonance is a special and dramatic case of forced vibrations. When the frequency of the external periodic force exactly equals the natural frequency of the body, the body vibrates with a very large amplitude. This phenomenon is called resonance.

Imagine two identical tuning forks on sound boxes, placed facing each other. When one is struck, the other begins to vibrate loudly without being touched. This happens because the sound waves from the first fork force vibrations in the air column of the second fork's sound box at exactly its natural frequency, causing resonance.

Resonance explains many everyday phenomena. When a vehicle is driven at a particular speed, some parts may rattle due to resonance between the engine's vibration frequency and the natural frequency of those parts. Changing speed stops the rattling. Soldiers break step when crossing bridges to avoid resonance that could cause dangerous vibrations. Musical instruments use resonance in their sound boxes to amplify the sound of vibrating strings.

Finally, let us understand how we perceive sound through its three main characteristics: loudness, pitch, and quality.

Loudness is what allows us to distinguish a loud sound from a faint one. It depends primarily on the amplitude of the wave. Greater amplitude means more energy carried by the wave, resulting in louder sound. Loudness also depends on distance from the source, the surface area of the vibrating body, and the density of the medium.

Intensity is the measurable physical quantity related to loudness. It is defined as the sound energy passing per second through unit area, measured in watts per square metre. However, loudness itself is subjective, it depends on the listener's ear sensitivity. The relationship between loudness and intensity is logarithmic. The sound level in decibels is given by: L equals 10 log base 10 of I1 over I0.

Or, L = 10 log₁₀(I₁/I₀). Here, I0 is the minimum audible intensity of 10 to the power minus 12 watts per square metre. Normal conversation is about 50 decibels, while sounds above 120 decibels can cause permanent hearing damage.

Pitch allows us to distinguish shrill sounds from flat ones. It depends entirely on frequency. Higher frequency means higher pitch. A whistle has high pitch, while a drum has low pitch. While frequency is an objective measurable quantity, pitch is subjective and can vary slightly between listeners.

Quality, also called timbre, is what lets us distinguish two sounds of the same loudness and pitch produced by different instruments. It depends on the waveform of the sound. A tuning fork produces a pure sine wave with a single frequency. But musical instruments produce complex waves containing a principal frequency plus subsidiary frequencies that are integer multiples of it. The unique mixture of these frequencies gives each instrument its characteristic quality. This is why you can recognize a person's voice on the telephone, or distinguish a piano from a flute playing the same note.

Let us briefly distinguish between music and noise. Music consists of pleasant, regular, periodic vibrations with a well-defined waveform. Noise consists of irregular, harsh, and unpleasant sounds with no definite pattern. However, the distinction is somewhat subjective, what one person considers music, another might find noisy.

Let us recap the key takeaways from this chapter. First, sound waves reflect from surfaces to produce echoes, which require a minimum distance of 17 metres in air to be heard distinctly. Second, echoes have practical applications in SONAR, medical imaging, and animal navigation. Third, vibrations can be natural, damped, or forced, with resonance occurring when driving frequency matches natural frequency. Fourth, loudness depends on amplitude, pitch depends on frequency, and quality depends on waveform. Fifth, sound level is measured in decibels, with prolonged exposure above 80 decibels potentially harmful to hearing.

That concludes our exploration of sound. I hope you now have a deeper appreciation for how sound travels, how it reflects, how objects vibrate, and how your ears perceive different characteristics of sound. Keep listening to the world around you with curious ears, and remember that physics explains the music of everyday life. Until next time, stay curious and keep learning.