Describe the production of sound by vibrating sources

3.4 Sound – Production of Sound by \cdot ibrating Sources

1. What is a vibration?

A vibration is a rapid back‑and‑forth motion of an object about its equilibrium position. The motion repeats at regular intervals and can be described by:

\$x(t)=A\sin(2\pi ft)\$

where x is the displacement, A the amplitude, and f the frequency (Hz).

2. How a vibrating source creates sound

• The vibrating object pushes against the surrounding medium (air, water, solid).
• This disturbance compresses and rarefies the particles of the medium, creating a longitudinal wave.
• The wave travels away from the source at the speed of sound in that medium.
• When the wave reaches a detector (e.g., a human ear), the pressure variations are interpreted as sound.

3. Key terms

• Amplitude – maximum displacement of the vibrating source; related to loudness.
• Frequency – number of vibrations per second; determines pitch.
• Period (T) – time for one complete vibration, \$T=\frac{1}{f}\$.
• Wavelength (\$\lambda\$) – distance between successive compressions or rarefactions, \$\lambda = \frac{v}{f}\$ where \$v\$ is the speed of sound.

4. Types of vibrating sources

Different objects produce vibrations in characteristic ways:

5. Example: Calculating the frequency of a stretched string

For a string of length \$L\$, tension \$T\$, and linear mass density \$\mu\$, the fundamental frequency is:

\$f_1 = \frac{1}{2L}\sqrt{\frac{T}{\mu}}\$

1. Identify the given values (e.g., \$L = 0.65\,\$m, \$T = 80\,\$N, \$\mu = 0.002\,\$kg m⁻¹).
2. Substitute into the formula:

   \$f_1 = \frac{1}{2(0.65)}\sqrt{\frac{80}{0.002}} \approx 138\ \text{Hz}\$

3. Interpretation: The string will produce a pitch of about 138 Hz, which lies in the lower range of the musical scale.

6. Factors that affect the sound produced

• Tension – increasing tension raises frequency (higher pitch).
• Length – shortening the vibrating length raises frequency.
• Mass per unit length – a heavier string lowers frequency.
• Amplitude of vibration – larger amplitude results in louder sound.
• Medium – speed of sound differs in air, water, and solids, affecting wavelength.

7. Summary

Sound is generated when a source vibrates, causing periodic compressions and rarefactions in a surrounding medium. The characteristics of the source—its tension, length, mass, and the way it is set into motion—determine the frequency (pitch) and amplitude (loudness) of the sound produced.