Modern Physics - AQA GCE Physics B - Revision Notes

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Music and sound

All sounds are formed by a vibration and require a medium to travel through. Sound travel as a longitudinal wave (compression waves) where it forms a series of compression (region of higher pressure than surrounding) and rarefaction (region of lower pressure than surrounding)

Distance between 2 compressions is one wavelength and the frequency is number of waves / compression passing a certain point per second - measured in Hertz (Hz).

Wave speed (c) = frequency (f) x wavelength (λ)

Typical human ear can detect frequency ranging from 15 – 20000 Hearts. The frequency below this range is called infrasound and those above are ultrasound.

When sound is turned into electrical signal (i.e. recorded by a microphone) the frequency can be measured with an oscilloscope, here:

Frequency =    and vice versa,   Time period =

The pitch of a sound is produced form the fundamental frequency (lowest frequency when it’s vibrating freely) plus harmonics (multiples of the fundamental frequency).

When hearing sound waves of certain pitches together it produces consonants or harmonics. These sound waves form the basis of a musical interval. I.e. any 2 musical not of frequency ratio of 2:1 are separated by an octave. Whereas 2 notes with frequency ratio of 5:4 are separated by an interval of a third.

Quality can be called timbre. The same frequency note with same loudness can produce different waves form when played on 2 different musical instruments. Timbre is a factor that can help distinguish between instruments / voice.

Timbre of a wave is made up of the attack, decay and the vibrato:

The attack of a sound is a measured of how quickly it reaches its peak amplitude whereas the decay is the measure of how long the sound takes to die away.

Vibrato is a periodic change in pitch of the waveforms as the sound is produced. Usually, it is accompanied by a change in amplitude – known as tremolo.

Listening to Sounds

The amplitude is the maximum displacement of a particle forms its rest position of the medium that carries the waves. There are graphs that cam show displacement of all particle against distance – showing how the amplitude can be relate to the pressure of the sir molecules

A graph can also show how one particle moves as time changes, this graph would be exactly what is seen on an oscilloscope – sound can be treated as a transverse wave.

Sound is a mechanical wave (requires a medium to travel), whereas light doesn’t need any substance to travel through - most substances easily absorbs light.

Light slows down when travelling through transparent substances (denser than first medium) and it travels as an EM wave. This is a varying electric field and a varying magnetic field at right angle to each other & the direction of travel of the wave.

Light waves is an example of transverse wave which is ne where the energy travels in a right angle to the direction of vibration – speed of light = 3 x 108.

Both sound and light waves reflect, refract, diffract and superpose. Polarisation of transverse waves restricts the direction of oscillation so it only occurs in one plane perpendicular to the direction of travel.

However, longitudinal waves such as sound waves cannot be polarised, due to the fact that they travel in the same direction / parallel to the oscillation of particle.

Speed of sound can be measured by setting two microphones at a certain distance apart. As the nearer microphone picks up the sound pulse, it generates an electrical pulse and trigger and timer to start. Then same happens at the second microphone and this stops the timer.

Another way is to connect a signal generator output to a loudspeaker, so the generator produced a pulse of voltage causing the loudspeaker to make a sound pulse; the voltage also triggers a pulse in the oscilloscope.

The sound pulse is picked up by the microscope a certain distance away leading to traces of pulse on the screen of the oscilloscope when the sound wave is picked up. For both experiments, you can find the:

Speed of sound =

The surround sound of a home theatre arrangement is set up assuming the listener is equidistance form each speaker. Otherwise, sound from each speaker would have a difference time delay before reaching the listening; this can be corrected by balancing the system.

Echoes are sound reflections, this adds to the overall sound that is emitted from a source. In poorly designed concert halls, the echoes can add to or subtract from the initial sound – causing constructive or destructive interference.

Sound production

When two or more waves meet, their total displacement is equal to the sum of their individual displacement, taking their direction into account. Having met, the waves continue on their way as if they have never met – for a consistent pattern, waves must have the same frequency and speed and ideally the same amplitudes.

Violin, piano and guitars all have springs that are made to vibrate – setting up a standing wave on the string, when a travelling wave is restricted; it reflects at each end and forms a standing wave, i.e. on a string with fixed ends.

Although strings on a guitar don’t produce a very loud sound due to their small amplitudes and that they cannot move a large volume of airs. The strings transfers vibrations to the body of the guitar – making it vibrate as a whole.

Therefore making much larger volume of air move, so that surrounding air vibrates at the same frequency as the strings, this is the air resonating.

The pitch of a vibrating string depends on 3 factors:

The mass of the string: more massive string (so greater mass per unit of length_ would vibrate more slowly.

The tension in the string: this can be adjusted with tuning pegs. So the tighter the strings, the higher the pitch.

The length of the string: that is free to vibrate, if you shorten the length, you would be increasing the tension and thus increasing the pitch.

Fundamental frequency of a vibrating string:   f = √

Standing waves on strings are formed from the superposition of 2 identical waves travelling in opposite direction. In string instrument, travelling waves travels to the ends of the string where they reflect and undergo a complete phase change of 180o. They then travel in opposite directions again and are constantly out of phase - they will also be permanently destructive

Nodes: total displacement of 0

Antinodes: varies between the max and min values.

A string has a number of frequency at which it will naturally vibrate, these are known as the harmonics of a strings and it depends on the 3 factors mentions previously. As both and are fixed, there will be node at both ends.

The fundamental frequency (known as the first harmonics) is the lowest frequency for which standing waves will be set up and consists of single loops. Doubling the frequency of vibration will half the wavelength and so 2 loops will be formed – This is called the second harmonics or the first overtone.

In pipes, the wave medium is usually air and the waves themselves are longitudinal. Displacements rather than pressure are used to represent the standing waves in pipes. At the open end, the air molecule can be displaced by a largest amount, so the displacement antinodes will form there. However, at the closed end, there is 0 molecule displacement, so a displacement node is formed.

If the 2 musical notes are sounded together, when they meet they will superpose and form an overall wave similar to how a standing wave is set up. However, if their frequency was not identical, a regular rising and falling of amplitude of the resultant wave will be heard – these are beats.

If the two strings are tuned again, the beats would cease t be heard, if not, the beat frequency (fb) is equal to difference between frequency of the 2 strings  =  f2 – f1.

Loud or soft

The loudness of a sound wave depends on the amount of energy that is transferred to the surrounding by the vibration. The energy is proportional to the square of the amplitude (E ∝A2). Therefore, doubling A would increase amount of energy by a factor of four. Loudness is the listeners’ perception of intensity of a sound.

If a sound wave is being emitted by a point source, they will spread out in all directions. Therefore the total energy that’s emitted will spread increasingly thin the further away from the source.

The intensity has an inverse square relationship with distance from the point source, so as distance doubles, intensity falls to 1 / 9:

Intensity (Wm-2) =

The quietest sound that the typical human ear can detect has an intensity of around 1x10-12 Wm-2 it does this by detecting the change in the atmospheric pressure made by the sound. The faintest sound the human ear can hear is the threshold of hearing.

Loudness can be measured in decibel (dB) scale; the threshold of frequency is assigned a sound level of 0 dB. A 3 decibel decrease would half its amplitude.

Intensity is an objective quantity that can be measured but loudness depends upon the ear of the listener and is therefore subjective. Human ear is more sensitive to frequency range of around 1-4 kHz, as the ears tend to amplify frequency within this range much more than at other frequencies.

Noise is a variation of sound or electrical signal that obscures or reduces the clarity of a signal. -  It is often random and persistent.

White noise has an equal opportunity of being any frequency and so has a uniform frequency spectrum. It also has uniform amplitude across the frequency range.

Some things can be done to reduce the effect of noise:

Reducing it at the source

Masking or absorbing the noise.

Recording and Playback

Analogue signals are those which vary continuously with time, whereas digital signal only has 2 values, information is coded in binary in pulses of voltage / light.

In analogue sound recording, sound waves cause a membrane in a microphone to vibrate. These mechanical vibrations are converted into weak electrical signals whose voltage mimics the displacement of air molecules by the sound.

The signal is amplified; using current from the amplifier’s power supply, the output of the microphone is increased. This amplified signal is fed into the record head, which is an electromagnet – producing a magnetic field.

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The intensity of the magnetic field varied in the same way as the current (and so the original sound) recording tapes have a thin plastic tape coated with a thin layer of ferric oxide powder – which can be permanently magnetised by the magnetic field.

If several microphones are to be recorded together – an electronic box called a mixer is used to balance the relative strength of the signal.

During playbacks the reverse process of the above happens, the tape passes through the playback head where the tape’s magnetic field induces current in this head.


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