Sound Waves and Ultrasound for the ESAT

The Production and Nature of Sound

Sound waves are produced by a vibrating source. When an object oscillates, it causes the surrounding medium to vibrate, and this pattern of vibrations travels away from the source as a wave. For example, a loudspeaker cone vibrates back and forth, moving the air in front of it to create a sound wave.

There are three critical relationships between the source and the resulting sound wave:

1. The frequency of the sound wave matches the frequency of the vibrating source.
2. The amplitude of the sound wave depends on the amplitude of the source vibrations.
3. The speed of the sound wave is determined solely by the medium it travels through, not by the source.

Examples of sound sources include vibrating strings (pianos, guitars), vibrating surfaces (drums, speakers), vibrating air columns (saxophones, flutes), and vibrating vocal cords.

The Need for a Medium

Sound waves are mechanical waves. This means they consist of the vibrations of material particles and therefore require a medium (solid, liquid, or gas) to travel. Sound cannot travel through a vacuum because there are no particles to transmit the oscillations. This is famously demonstrated by the bell jar experiment.

In this setup, an electric bell is placed inside a jar. As air is removed by a vacuum pump, the sound fades until it becomes silent, even though the bell hammer is still seen moving. This also proves that while sound cannot travel through a vacuum, light can.

Sound as a Longitudinal Wave

Sound is a longitudinal wave. In a longitudinal wave, the direction of particle vibration is parallel to the direction of wave travel. As the wave passes, particles in the medium are pushed together to form regions of high pressure called compressions (C) and are pulled apart to form regions of low pressure called rarefactions (R).

The distance between two adjacent compressions or two adjacent rarefactions is equal to one wavelength ($\lambda$).

Worked Example: Dust in Sound Waves A tiny particle of dust is suspended in still air. If a sound wave passes horizontally from left to right, how does the dust move? Because sound is longitudinal, the particle will vibrate back and forth about its original position, parallel to the wave direction, rather than moving steadily with the wave.

Loudness, Pitch, and Oscilloscopes

We perceive the physical properties of sound waves qualitatively:

• Loudness is related to the amplitude of the wave. Larger amplitudes represent more energy and result in louder sounds.
• Pitch is related to the frequency of the wave. Higher frequencies result in higher pitched sounds.

An oscilloscope can be used to visualize these properties by converting sound pressure into a voltage signal.

• Greater height of the trace (amplitude) indicates a louder sound.
• Peaks closer together (shorter period $T$, higher frequency $f$) indicate a higher pitch.

Reflection and Echoes

Sound waves obey the law of reflection, where the angle of incidence equals the angle of reflection. An echo is simply the sound heard after it has reflected off a surface and returned to the listener. Because the reflected path is longer than the direct path, the echo is heard after a time delay.

Worked Example: Ranging with Echoes A man stands $170$ m from a cliff and bangs wood together. He wants the echoes to occur exactly halfway between his hits. If the speed of sound is $340$ ms$^{-1}$, at what frequency should he bang the wood?

1. Distance to cliff and back $= 2 \times 170 = 340$ m.
2. Time for echo $= \text{distance} / \text{speed} = 340 / 340 = 1.0$ s.
3. For the echo to be halfway between hits, the period $T$ between hits must be $2.0$ s.
4. Frequency $f = 1 / T = 1 / 2.0 = 0.5$ Hz.

Human Hearing and Ultrasound

The standard range of human hearing is $20$ Hz to $20$ kHz. Sounds below $20$ Hz are infrasound, and sounds above $20$ kHz are ultrasound. While humans cannot hear ultrasound, many animals can (e.g., dogs up to $45$ kHz, bats up to $100$ kHz).

Applications of Ultrasound

Ultrasound is used for ranging and imaging because it has a very short wavelength, allowing for high resolution. The distance $d$ to an object is calculated using $d = \frac{vt}{2}$, where $v$ is the wave speed and $t$ is the total travel time.

1. SONAR: Used by ships to measure sea depth or locate fish shoals.
2. Medical Scanning: Ultrasound pulses reflect off internal tissue boundaries. This is used in prenatal scanning as it is non-ionising and safe for the foetus.
3. Crack Detection: In industrial settings, ultrasound identifies flaws in solids by detecting reflections from internal cracks.

Worked Example: Sea Depth A sonar pulse is detected $0.40$ s after emission. If the speed in water is $1500$ ms$^{-1}$, find the depth. $\text{Depth} = \frac{1500 \times 0.40}{2} = 300$ m.