Sound: Concepts & Theories in Physics

Listening to the radio or Television, playing music, shouting at each other – they all depend on the science of sound (and its called acoustics). We cannot see sound waves but we can hear them. They are ripples of high and low pressure in air. The peak (highest point) of the wave is where a region of air is squashed under high pressure. The trough (lowest point) of the wave is a region where air is expanded under low pressure.

How does sound travel in air?

A wave is a disturbance that carries energy without the transfer of matter.

Sound travels through air as a mechanical wave, which means it requires a medium (like air, water, or solids) to propagate.

Sound begins when a source (such as a vibrating object like a speaker, vocal cords, or a guitar string) causes nearby air particles to vibrate. It creates regions of compression (where air molecules are pushed together) and rarefaction (where air molecules are spread apart).

The region of a sound wave in which air particles are crowded together creating a region of high pressure is called compression (density of particles is greater than normal).

The region of a sound wave in which air particles are spread apart, creating a region of low pressure is called rarefaction (density of particles is lower than normal.

The vibration of the molecules causes them to collide with neighboring molecules, transferring the energy of the sound wave. Thus the sound wave propagates through the air as the energy is transferred from one molecule to the next. These alternating regions (compression and rarefaction) move outward from the source in the form of longitudinal waves.

What is a longitudinal wave?

A longitudinal wave is a type of wave where the particles of the medium through which the wave travels move in the same direction as the wave’s motion. In other words, the oscillations or vibrations of the medium’s particles occur parallel to the direction of energy transfer.

Wavelength: The distance travelled by the wave in one time period of vibration of particle of medium is called its wavelength. It is denoted by the letter λ (lambda). Its S.I. unit is metre (m). It depends on the nature of medium through which the wave travels.

In a longitudinal wave, the distance between two consecutive compressions or between two consecutive rarefactions is equal to one wavelength (λ).

A wave is made of crests and troughs. One crest + one trough = 1 Wave (one cycle).

Factors on which loudness of sound depends

The loudness of sound depends on the following three factors:

• Amplitude of the sound wave: A larger amplitude results in a louder sound, while a smaller amplitude results in a softer sound.
• Distance from the sound source: The closer the listener is to the source of the sound, the louder the sound will be. As the distance increases, the sound becomes weaker due to the spreading of the sound wave.
• Medium and its properties: The loudness can also depend on the medium through which the sound travels (such as air, water, or solid materials). For instance, sound travels more efficiently in denser mediums, leading to louder sounds in such media compared to air.

Characteristic of sound affected due to change in amplitude, wave form and frequency

• Amplitude (Affects Loudness): A higher amplitude results in a louder sound, while a lower amplitude results in a softer sound.
• Waveform (Affects Timbre or Quality of Sound): Waveform affects the sound’s timbre, which is what makes one sound distinct from another (e.g., the difference between a piano and a violin playing the same note). Changes in the waveform alter the richness and tonal quality of the sound.

• Frequency (Affects Pitch): A higher frequency results in a higher pitch (a “high” note), while a lower frequency results in a lower pitch (a “low” note).

  Frequency is calculated based on the number of cycles (waves) that occur in a given period. Frequency (f) = Number of cycles / Time in seconds.

Amplitude determines loudness of a sound wave. A loud sound causes air particles to move more, while a soft sound causes them to move less. Loud note produces wave with a larger amplitude, meaning the compressions and rarefactions are more intense (greater pressure changes). Soft note produces wave with a smaller amplitude, meaning the compressions and rarefactions are less intense (smaller pressure changes).

In the displacement-time graph, if number of waves in same time interval increases, it means that the time period of wave has decreased i.e., its frequency or pitch) has increased. In the displacement-distance graph, if number of waves in the same distance increases, it means that the wavelength of wave has decreased so its frequency (or pitch) has increased.

Mathematical Relationship

Relationship between time period and frequency:

The relationship between the time period (T) and frequency (f) is defined mathematically as follows:

Time Period (T): The time taken to complete one full cycle of a wave or oscillation.

Frequency (f): The number of cycles or oscillations that occur in one second, measured in Hertz (Hz).

In time T, the number of waves = 1.

Therefore in 1 second, number of waves (or frequency) f is :-

frequency(f) = 1/time period (T) [f = 1/T] OR Time period (T) = 1/frequency(f) T = 1/f

Thus, time period and frequency are inversely proportional; as one increases, the other decreases.

Amplitude: The loudness of sound is directly proportional to the square of amplitude of wave. It implies that on doubling the amplitude of wave, the loudness becomes (2)2 = 4 times. If amplitude of wave is tripled, the loudness become (3)2 = 9 times and so on.

Thus Loudness α (amplitude)2 i.e. L α a²

A rubber band plucked softly produces a soft sound, while a rubber band plucked with greater force produces a louder sound. A Soft Pluck generates smaller vibrations with lower amplitude, resulting in a softer sound. A Forceful Pluck creates larger vibrations with higher amplitude, producing a louder sound. Thus, more force leads to greater energy transfer, resulting in louder sounds.

Pitch (frequency)

The pitch of a sound is determined primarily by the frequency of the sound wave. In simple terms, the faster an object vibrates, the higher the pitch of the sound it produces.

Whether a sound is high or-low is called its pitch, or frequency. It is measured in Hertz, Hz.

• A singing bird or whining motorcycle has a high pitch.
• A rumble of thunder or a massive truck has a low pitch.
• People can hear frequencies from 25 to 20,000 Hz.

String instruments like guitars and violins have a hollow box. When the strings vibrate, they make the air inside the hollow body of the box vibrate too, which amplifies the sound and makes it louder. It also helps the sound travel further.

• Stringed insturments 1. Violin , 2. Guitar , 3. Cello 4. Sitar 5. Sarangi , 6. Piano
• Wind instruments. 1. Flute , 2. Trumpet , 3. Clarinet , 4. Saxophone , 5. Bugle , 6. Shehnai
• membrane instruments. 1. Drum, 2. Bongos, 3.Tambourine, 4.Tabla, 5. Mridangam, 6. Dhol

A thin wire on a guitar results in a higher pitch due to faster vibrations. A wire under less tension results in a lower pitch due to slower vibrations. The pitch of sound produced by a string instrument also depends on the place where it is plucked. If a string stretched between its ends, is plucked closer to the one fixed end, higher is the pitch of the sound produced.

A monotone voice doesn’t effectively deliver a message because it lacks changes in pitch and volume.

• Pitch Changes (frequency variation): Varying the pitch helps express emotions and emphasize important points. A monotone voice sounds flat and dull.
• Volume Changes (amplitude variation): Changing the volume can highlight key ideas. Without this, the message feels flat and unimportant.

Overall, without these variations, listeners may lose interest and not understand the message.

Loudness in decibels dB

Scientists measure the loudness or intensify of sound in decibels dB. The decibel scale measures the intensity, or energy in sound.

A very quiet sound like a ticking watch is around 10 dB.

• Ordinary speech is around 50—60dB.
• Loud music is 90 dB.
• A jet plane taking off is 120 dB.
• Too much noise damages the ears.

Characteristics of a Musical Sound

Depending upon the amplitude and frequency of the sound wave, two sounds can be distinguished from on another by the following three different characteristics :

1. Loudness,
2. Pitch (or shrillness), and
3. Quality (or timbre or wave form).

The above characteristics of a given sound can be known from the wave pattern of that sound.

Surface area of vibrating air

The loudness of sound heard from a plucked wire is increased when it is mounted on a soundboard due to the following reason: When the wire is plucked, it vibrates and creates sound waves in the air. However, the wire itself is relatively small, so its vibrations alone might not produce much sound. When the wire is mounted on a soundboard (such as the body of a guitar or piano), the vibrations of the wire are transferred to the soundboard, which is much larger in surface area. It can thus move larger volume of air.

Unbelievable and amazing facts about sound, especially for school children.

1. Sounds are like invisible waves in the air. Vibrating object generates sound waves.
2. Loudness of sound is measured in decibels (dB). Whether a sound is high or low is called its pitch, or frequency (measured in Hertz, Hz)
3. Certain animals, including dogs can hear sound at a higher frequency than humans, allowing them to hear noises that we can’t.
4. Sound waves travel in air at speed of about 330 metres per second. This is fast, but is one million times slower than light waves.
5. Sound travel four times faster in water (compared to air). The voice of a whale can travel up to 800 kilometers (479 miles) through the ocean waters!
6. There’s no sound in space because sound cannot travel in vacuum, there are no particles that can carry the vibration.
7. Sound waves also bounce off hard, flat surfaces. This is called reflection. The returning waves are heard as an echo.
8. Loudspeakers change electric signals into sounds.
9. Scientific study of sound waves is known as acoustics.

 

Loudspeakers change electrical Signals into sounds.
The signals in the wire pass through a wire coil inside the speaker. This turns the coil into a magnet, which pushes and pulls against another magnet.
The pushing and pulling make the cone vibrate, which sends sound waves into the air.

Sound waves spread out from a vibrating object that is moving rapidly to and fro.
Stretch an elastic band between your fingers and twang it. As it vibrates, it makes a sound. A similar thing happens when you speak. When you speak, vocal cords in your neck vibrate, which you can feel through your skin. (The vocal cords are tough flaps in your voicebox, in your neck).