Understanding Frequency and Sound

Frequency is an important part of sound waves. It affects the musical notes we hear every day. Musical notes are linked to specific frequencies, which we measure in Hertz (Hz).

Frequency also decides how high or low a sound is. Higher frequencies make higher notes, while lower frequencies make lower notes.

Frequency and Pitch

• Frequency shows how many times a sound wave goes up and down in one second.
• For instance, the note A4, which is often used to tune instruments, has a frequency of 440 Hz.
• When you double the frequency, the note sounds one octave higher.
  • So, A4 (440 Hz) has an octave called A5 at 880 Hz, and its lower octave is A3 at 220 Hz.

What We Can Hear

• People typically hear sounds in the range of 20 Hz to 20,000 Hz (20 kHz).
• Here’s how different ranges of frequency relate to musical notes:
  • Low Frequencies (20 Hz - 250 Hz): These are bass notes like E1 (41.2 Hz) and C2 (65.4 Hz).
  • Mid Frequencies (250 Hz - 4,000 Hz): Important notes in the tenor and alto ranges are here, like A3 (220 Hz) to C6 (1046.5 Hz).
  • High Frequencies (4,000 Hz - 20,000 Hz): These include high notes like C7 (4186 Hz) and E7 (2637 Hz).

Speed of Sound

• The speed of sound in air at a normal room temperature (about 20°C) is around 343 meters per second (m/s).
• The speed of sound is connected to frequency and wavelength using this simple formula:

$$v = f \cdot \lambda$$

• If we take a sound wave with a frequency of 440 Hz, we can find the wavelength like this:

$$\lambda = \frac{v}{f} = \frac{343 \, \text{m/s}}{440 \, \text{Hz}} \approx 0.78 \, \text{m}$$

Loudness and Frequency

• The loudness of sound relates to its intensity (I), which is about how big the sound waves are.
• While intensity doesn’t depend directly on frequency, how we hear different volumes can change based on frequency.
• This is shown in something called equal-loudness contours (or Fletcher-Munson curves). They show that different frequencies need different levels of sound pressure to sound equally loud to our ears.

Wrapping Up

In short, frequency is key to understanding the musical notes we hear. It affects pitch, wavelength, and our overall experience with sound. Knowing how these factors work together helps us enjoy music even more and provides a foundation for studying sound in science. The way sound works is important for many areas, including music, acoustics, and sound engineering.