Pitch and Loudness (HSC SSCE Physics): Revision Notes

Pitch and Loudness

What are pitch and loudness?

When you listen to any sound, you immediately notice two important characteristics: the pitch of the sound and its loudness. Pitch describes how high or low a note sounds on the musical scale, while loudness describes how quiet or loud the sound appears to your ears.

To understand these characteristics scientifically, we need to be able to visualize the sound waves that produce the sounds we hear. This allows us to analyze and measure the properties of sound waves.

Visualising sound waves with an oscilloscope

An oscilloscope is a device that displays how electrical signals change over time on a screen. When we want to study sound waves, we use a microphone to convert the energy of sound waves into electrical signals. These electrical signals can then be sent to an oscilloscope for display and analysis.

On an oscilloscope display:

• The vertical axis represents the amplitude (pressure variations) in the sound waves
• The horizontal axis represents time

The oscilloscope appears to show a transverse wave pattern, even though sound waves are actually longitudinal. This is because the vertical axis represents how much particles move at a specific point, whilst the horizontal axis represents time.

Setting up to investigate sound waves

We can use three pieces of equipment together to investigate sound wave properties:

1. An audio frequency generator - produces sounds of known frequency
2. A loudspeaker - makes the sound audible
3. An oscilloscope - displays the waveform

The audio generator vibrates the loudspeaker to produce sound. Some of this sound vibrates your eardrums (so you hear it), whilst some vibrates a microphone. The microphone converts these vibrations into an electrical signal that feeds into the oscilloscope for display.

The relationship between pitch and frequency

The pitch you hear is directly related to the frequency of the sound wave.

• Higher frequency → Higher pitch
• Lower frequency → Lower pitch

The relationship between loudness and amplitude

The loudness you perceive is related to the amplitude of the sound wave.

• Greater amplitude → Louder sound
• Smaller amplitude → Quieter sound

Calculating period and frequency from oscilloscope displays

Understanding the time-base scale

The time-base scale is the calibration of the horizontal axis on the oscilloscope. It tells you how much real time each centimetre on the screen represents. For example, if the time-base scale is set to $0.5 \text{ ms cm}^{-1}$, then each centimetre on the horizontal axis represents $0.5$ milliseconds.

Measuring the period

The period ($T$) is the time taken for one complete wave cycle. To find the period from an oscilloscope display:

1. Measure the horizontal distance (in cm) between two successive crests (or troughs)
2. Multiply this distance by the time-base scale setting

$T = \text{distance (cm)} \times \text{time-base scale (ms cm}^{-1}\text{)}$

Calculating frequency from period

Once you know the period, you can calculate the frequency ($f$) using:

$f = \frac{1}{T}$

where:

• $f$ = frequency in hertz (Hz)
• $T$ = period in seconds (s)

Alternative frequency formula

You can also calculate frequency as the number of wave cycles passing in a given time:

$f = \frac{n}{t}$

where:

• $n$ = number of wave cycles
• $t$ = time taken

Worked example

Investigation 9.1: Pitch, frequency, loudness and amplitude of sound waves

Aim

To investigate the relationship between pitch and frequency as well as loudness and amplitude of sound waves.

Before beginning, you should write a hypothesis as an "If... then..." statement. For example: "If the frequency increases, then the pitch will increase."

Materials

• Audio signal generator
• Oscilloscope (or equivalent tablet/phone app)
• Loudspeaker (such as computer speakers)

Risk assessment

Method

1. Connect the apparatus as shown in the diagram below.

1. Practice using the features of your oscilloscope, as different models vary considerably in their controls.
2. Set the audio generator to produce a $500$ Hz sound wave. Measure the horizontal distance of one complete wavelength on the oscilloscope display. Calculate the period, $T$, using the method shown previously. You will need to know the time-base scale setting on your oscilloscope.
3. Gradually increase the frequency on the audio generator while observing:
   • The change to the waveform displayed on the oscilloscope
   • The change in pitch of the sound being heard
4. Next, vary the output level (amplitude) from the audio generator, again while observing:
   • The change to the shape of the waveform displayed
   • The change to the perceived loudness of the sound being heard

Results

Record your observations in writing:

1. Describe the change in the waveform shape and the change in the perceived sound as the frequency was increased.
2. Describe the change in the waveform shape and the change in the perceived sound as the output level was varied.

Analysis of results

From your observations, deduce the relationships:

• Between pitch and frequency
• Between loudness and amplitude

Summarize your findings clearly.

Discussion

Consider how these relationships might extend to other types of waves, such as light waves or earthquake waves. Think about whether similar principles apply.

Conclusion

Write a conclusion that refers back to your original hypothesis. State whether your hypothesis was supported by the data you collected.

Investigation 9.2: Measuring the frequency of a sound wave

Aim

To measure the frequency of a sound wave using an oscilloscope.

Materials

• Oscilloscope
• Three tuning forks of different frequencies with sounding boards
• Microphone

Risk assessment

Method

1. Set up the oscilloscope and adjust the display controls so that when a tuning fork is sounded near the microphone, a steady waveform appears on the screen. Adjust the time-base (horizontal axis) input scale to achieve this.
2. Measure the distance on the screen from one crest to the next crest. Convert this distance to the period using the time-base scale.
3. Record your results in a data table with the following columns:

Tuning fork	Time-base setting (ms cm⁻¹)	Crest to crest distance (cm)	Period (ms)	Frequency (Hz)

1. Repeat this procedure for the other tuning forks.
2. Calculate the frequency of each tuning fork using $f = \frac{1}{T}$.
3. Compare your calculated frequencies with the frequencies stamped on the tuning forks themselves.

Analysis of results

After completing your measurements, consider these questions:

1. What relationship did you observe between the frequencies of the tuning forks and the pitch you heard?
2. Describe how the amplitude of the displayed wave changed as the loudness of the sound from the sounding boards changed (as the sound died away).
3. Was there any relationship observed between frequency and amplitude?