Sound Waves – SS2 Physics Lesson Note (Third Term)

Sound is a form of energy produced by vibrating objects and carried by longitudinal waves through a material medium.

Behavioural objectives

By the end of the lesson, students should be able to:

1. name common sources of sound and explain how sound travels;
2. describe pitch, loudness and quality as characteristics of sound;
3. explain forced vibration and resonance;
4. classify musical instruments as wind, stringed or percussion instruments;
5. use the echo expression 2x = Vt to find the speed of sound;
6. state the harmonics present in strings, closed pipes and open pipes.

How are sound waves produced?

Sound waves are produced by vibrating objects.

• Human voice: talking and shouting make the vocal cords vibrate.
• Struck objects: beating drums and ringing bells.
• Blown instruments: blowing a flute.
• Machines and vehicles: noise from moving cars and aeroplanes.
• Other sources: shooting a rifle, a ringing telephone and musical instruments.

What are the key terms used with sound waves?

These terms describe the parts and measures of a sound wave.

• Medium: the material (solid, liquid or gas) through which sound travels.
• Compression: a region where the air particles are pushed close together.
• Rarefaction: a region where the air particles are spread far apart.
• Wavelength (λ): the distance between two successive compressions or two successive rarefactions.
• Frequency (f): the number of complete vibrations per second, measured in hertz (Hz).
• Amplitude: the maximum displacement of a vibrating particle from its rest position.

How do sound waves travel?

Sound travels as longitudinal waves through a material medium and cannot pass through a vacuum.

• Medium needed: sound must have a substance to travel through.
• No sound in a vacuum: there is nothing in a vacuum to pass on the vibrations.
• Longitudinal wave: the air vibrates backwards and forwards along the direction the wave moves.
• Media: sound can travel through solids, liquids and gases.
• Hearing: the ear changes the vibrations into impulses, which the brain interprets.

What are the characteristics of sound?

There are three characteristics of sound: pitch, loudness and quality.

Pitch

Pitch is how high or low a note sounds, and it depends on frequency.

• High frequency: gives a high pitch.
• Low frequency: gives a low pitch.
• Octave: a note one octave higher has twice the frequency of the original note.

Loudness

Loudness is how strong a sound seems to the ear, and it depends on intensity.

• Intensity: the rate of flow of energy per unit area, perpendicular to the direction of the wave.
• Amplitude link: intensity is proportional to the square of the amplitude.
• Effect: the greater the intensity, the louder the sound.

Quality

Quality (timbre) is the property that lets us tell apart the same note played on different instruments.

• Example: the same note on a piano and on an organ sounds different.
• Cause: quality depends on the harmonics present in the note.
• Fundamental: the lowest frequency heard when a note is produced.
• Harmonics or overtones: all the other frequencies present in the note.

What are the factors that affect the speed of sound?

The speed of sound depends mainly on the medium it travels through.

• Wave equation: for any wave, v = fλ, where v is velocity, f is frequency and λ is wavelength.

What is forced vibration?

Forced vibration is the vibration of a body caused by another vibrating body acting on it.

• Example: a struck tuning fork pressed on a tabletop makes the table vibrate.
• Effect: the sound is louder because a larger mass of air is set vibrating.

What is resonance?

Resonance is the vibration of a system at its natural frequency, caused by forced vibrations of the same frequency from another source.

• Condition: the driving frequency must equal the natural frequency of the system.
• Result: the system vibrates with a large amplitude.

Demonstration with two tuning forks of the same frequency:

1. Place tuning fork B close to tuning fork A.
2. Strike fork A so that it vibrates.
3. Stop fork A with your hand.
4. Fork B is heard sounding, because it was set vibrating by A.

Resonance in strings

A stretched string resonates when the driving frequency matches one of its natural frequencies.

• Method: vary the driving frequency of the string.
• Result: stationary waves form on the stretched string or wire.

What are the types of musical instruments?

There are three types of musical instruments: wind, stringed and percussion.

Wind instruments

Wind instruments make sound from a vibrating column of air.

• Musical note: it comes from a source vibrating uniformly with one or more constant frequencies.
• Music: a combination of musical notes.
• Examples: clarinets, flutes, saxophones and trumpets.

All wind instruments use resonating air columns. The sound may come from:

• Air vibrating over an opening: as in the organ and flute.
• Vibrating lips of the player: as on a brass instrument such as the trumpet.
• A vibrating reed: as in the clarinet and saxophone.

The pitch is changed in two ways:

• Fixed-length column: opening or closing holes changes the resonant frequencies, as in the clarinet and recorder.
• Changing the column length: the player alters the length of the air column, as in the trumpet.

Stringed instruments

Stringed instruments make sound from vibrating strings.

• Examples: the guitar, the sonometer and the piano.
• Bowed: the violin is set vibrating with a bow.
• Plucked: the guitar is set vibrating with a finger.
• Frequency of a string: it depends on the length, the mass per unit length and the force keeping the string taut.
• Vibration pattern: the string vibrates as a whole and in loops at the same time, giving the fundamental and overtones.

Percussion instruments

Percussion instruments produce musical notes when they are struck or hit.

• Examples: drums, bells and the talking drum.
• Vibrating parts: rods, plates or membranes vibrate when struck.
• Rods: found in bells.
• Plates (bars): found in xylophones.
• Membranes: found in drums.

What are echoes and how are they used?

An echo is the repetition of a sound caused by the reflection of sound waves from a hard surface.

• Good reflectors: buildings, walls and cliffs.

Uses of echoes

• Sonar: echoes are used to find the depth of water or the position of objects under water.
• Speed traps: echoes are used to measure the speed of moving vehicles.
• Prospecting for oil: echoes help to study rock layers underground.
• Speed of sound: echoes are used to determine the speed of sound.

How is the speed of sound found by echo?

The speed of sound by echo is found with the expression 2x = Vt.

• V: velocity of sound.
• x: distance between the source of sound and the reflecting surface.
• t: total time taken for the sound to go and return.
• Why 2x: the sound travels to the surface and back, so the total distance is twice x.

Steps to find the speed of sound:

1. Stand at a measured distance x from a wall or cliff.
2. Make a sharp sound, such as a clap.
3. Measure the time t between the clap and the echo.
4. Calculate V = 2x/t.

How do strings, closed pipes and open pipes vibrate?

Strings, closed pipes and open pipes vibrate in stationary wave patterns that produce a fundamental note and harmonics.

Vibration in strings

A string fixed at both ends vibrates with a node at each end.

• Fundamental mode: the string vibrates in one loop and gives the lowest possible note.
• Fundamental frequency: the frequency of this lowest note.
• Nodes: the distance between two consecutive nodes is λ/2, which equals the string length l.
• Wavelength: l = λ/2, so λ = 2l.
• Fundamental frequency formula: f_o = v/2l, from v = fλ.
• Harmonics present: f_o, 2f_o, 3f_o, 4f_o and so on (all harmonics).

Vibrations produced in closed pipes

A closed pipe has one end closed and gives only odd harmonics.

• Harmonics present: f_o, 3f_o, 5f_o, 7f_o and so on, where f_o is the fundamental frequency.
• Fundamental frequency: f_o = v/4l.

Vibrations produced in open pipes

An open pipe has both ends open and gives both odd and even harmonics.

• Harmonics present: f_o, 2f_o, 3f_o, 4f_o, 5f_o and so on.
• Overtones: 2f_o, 3f_o, 4f_o and so on, both odd and even.
• Fundamental frequency: f_o = v/2l.

Comparison of vibrating systems

Evaluation

1. State four sources of sound.
2. Why can sound not travel through a vacuum?
3. What does the pitch of a sound depend on, and what does the loudness depend on?
4. Write the expression used to find the speed of sound by echo and state what each letter stands for.
5. Which harmonics are present in a closed pipe?

Assignment

1. A pupil stands 85 m from a tall wall and claps. The echo is heard 0.5 s later. Use 2x = Vt to calculate the speed of sound, and say which harmonics a closed pipe produces.