Vibration & Sound

Longitudinal waves (series of compressions and rarefactions)

Evidence: Reflection, diffraction, refraction and interference (echoes) (near around corners)

• Further from wall better = take time to hear echo; not mixed with original
• Width of doorway ≈ λ
• On warm day sound refracted upwards (to cold air)
• On cold night sound refracted downwards (to cold air) sound travels faster in warm air and so refracts

To demonstrate interference of sound

• Set up apparatus as shown in the diagram and walk from A to B
• Loudness ↑ ↓ of regular intervals due to constructive and destructive interference. [Signal generator allows for sound of uniform frequency to be emitted which is necessary.]

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If pitch ↑ then ↓ then ↑ [destructive]

If pitch ↑ then ↑ ↑ then ↑ [destructive]

• The frequency of a sound = frequency of vibrating source producing it.
• Molecules vibrate parallel to the direction which compressions and rarefactions are travelling.
• Use destructive interference to reduce the noise of a sound by emitting waves of same and frequency but out of phase.

To show that sound needs a medium to travel through

• Set up the bell jar apparatus as shown.
• The bell is heard ringing
• Remove the air from the bell jar using a vacuum pump.
• The bell can be seen ringing but the loudness is barely audible
• Let air in, sound can be heard [some sound escapes from wires].

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V α T [Boyle discovery]

↑ Temperature ↑ speed of sound

... leads to refraction of sound

V α ρ (density of medium) [general rule] V depends on elasticity also

Time for echo ↓ t₁ ↑ t₂ t₁ = t₂

Overtones are frequencies which are multiples of a certain frequency

f first and lowest frequency.

2f first and lowest frequency.

3f first and lowest frequency.

Characteristics of Notes

Loudness depends on energy entering ear per second

Greater amplitude, more energy came

∴ loudness depends on amplitude and frequency

Pitch depends on frequency of a wave

A high note has a high pitch i.e. high frequency.

Quality depends on # of overtones present and their relative strengths

Same notes on different instruments sound different.

Pure frequency = No overtones

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Emitted by a signal generator

Frequency limits of audibility are the highest and lowest frequencies that can be heard by a normal human ear (infrasonic) [20 Hz – 20,000 Hz] (ultrasonic)

Natural frequency of vibration is the frequency that the object vibrates at when free to do so.

Resonance is the transfer of energy from one body to another that have the same natural frequency

To demonstrate resonance

• Use the identical forks with the same frequency and a sound board.
• Start one fork vibrating and place it on the sound board.
• Place the second tuning fork on the sound board near to but not touching the first and stop the first tuning fork from vibrating.
• The second tuning fork is found vibrating and can be heard.

Examples of Resonance

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Washing machines at particular speed.

Buildings in an earthquake [natural frequency of walls = earthquake f]

Barton's pendulums – all vibrate but those with same length vibrate more

Sound intensity is the rate at which sound energy is passing through unit area at right angles to the direction in which the sound is travelling

Power

Area of sphere unless stated Otherwise 4πr²

Double the radius, I will be 4 times smaller

Threshold of hearing is the smallest sound intensity detectable by the average human ear at frequency of 1 KHz = 1 x 10⁻¹² Wm

Ear is most sensitive to frequency between 200 Hz and 4000 Hz [Above or below that sound doesn't resonate in the ear canal = don't appear as loud]

Sound intensity level: a scale where the large range of intensities can be represented by a smaller range of numbers

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Decibel adopted / frequency weighted scale (dBA scale). Takes into account sensitivity of ear to frequencies between 2 KHz and 4 kHz ┌ *, the sound-level meter responds more to these

Consists of a microphone, an amplifier and an output scale. Measures sound intensity level.

Fundamental Frequency $\frac{\lambda}{2} = l$ is the frequency that a string

vibrates at where there is an antinode at its centre and a node at each end [No other nodes or antinodes]

$\frac{\lambda}{2} = l$

Is the frequency that a string vibrates at where there is an antinode at its centre and a node at each end [No other nodes or antinodes]

$f \alpha \frac{1}{l}$

The mode that the string is vibrated affects how many nodes and antinodes present. Pluck string at its centre for antinode at the centre.

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• Use sonometer to verify f α 1/l and measure frequency of wire
• Adjust length of wire until it sounds same pitch as tuning fork
• Frequency of wire = frequency of tuning fork
• If resonance occur if wire vibrates when fork is on one of bridges
• Harmonics are frequencies which are multiples of a certain frequency

f First harmonic / fundamental frequency 2f Second harmonic 3f Third Harmonic

Stationary waves in a pipe closed at one end

Closed pipe – open at one end and closed at other e.g. clarinet saxophone trombone (no sound if closed at both ends)

Resonance can occur if the length of the pipe is varied

• The longer the pipe, the lower the pitch of the note as the frequency will be lower too l = λ/4
• Only odd numbered harmonics may be present (f, 3f, 5f, 7f)

$f_1 = \frac{c}{\pi} = \frac{c}{4l}$

$f_3 = \frac{c}{\lambda} = c/4l/3 = 3(\frac{c}{4l}) = 3f$

$f_5 = 3f$

$f_7 = 5f$

Stationary waves in a pipe open at both ends

• All harmonics may be present (f, 3f, 5f, 7f)
• E.g. the flute, tin whistle, recorder

Note / frequency varied by blocking and unblocking holes

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(draw 2 harmonics from each to compare)