For a sound wave travelling through a medium, which factor primarily determines the frequency (pitch) of the sound that we hear?

Introduction / Context:
Sound is a mechanical wave that requires a medium to travel and has several important characteristics, including frequency, amplitude and speed. The frequency of a sound wave is closely related to the pitch we perceive: higher frequency means higher pitch. This question asks which factor primarily determines the frequency of a sound wave.

Given Data / Assumptions:

• Frequency is defined as the number of vibrations or cycles per second.
• Amplitude measures the loudness or intensity of sound, not its pitch.
• Speed of sound depends on the medium and its conditions.
• The source of sound is some vibrating object, such as a string, vocal cords or loudspeaker diaphragm.

Concept / Approach:
The frequency of a sound wave is set at the moment it is created by the vibrating source. For example, a guitar string plucked at a certain tension and length vibrates at a specific frequency, which determines the pitch of the note. Once the wave is generated, it travels through the medium with a frequency that remains the same, although its wavelength may adjust according to the speed of sound in that medium. Amplitude affects loudness, not frequency. The medium and speed influence how fast the wave propagates and what wavelength it has, but they do not change the fundamental frequency already set by the source, as long as there is no change in the source itself.

Step-by-Step Solution:
Step 1: Recall that frequency f is the number of complete vibrations per second of the source.Step 2: Recognise that pitch is directly related to frequency: higher frequency means higher pitch.Step 3: Identify that the vibrating object (string, vocal cords, diaphragm) sets the vibration rate when sound is produced.Step 4: Understand that as sound energy travels through a medium, the wave frequency remains the same even if speed and wavelength change.Step 5: Note that amplitude corresponds mainly to loudness, not to the number of vibrations per second.Step 6: Conclude that the source of the sound wave is the factor that determines its frequency.

Verification / Alternative check:
Musical instruments provide clear evidence of the source controlling frequency. Tightening a guitar string (changing its source properties) raises the pitch by increasing the vibration frequency. Similarly, a tuning fork of a specific size and material always vibrates at its characteristic frequency and produces a specific pitch. When the fork is sounded in air or water, the medium changes but the perceived pitch (frequency) remains almost the same, although the speed and wavelength of sound in the medium differ. This shows that the source, not the medium, sets the frequency.

Why Other Options Are Wrong:
Amplitude affects loudness, meaning how strong or intense the sound seems, but does not change pitch, so option A is incorrect. Speed of sound in the medium and the nature of the medium influence how quickly the wave travels and the wavelength, not the frequency produced, so options B and D are not primary determinants of frequency. Only changes in the source vibration rate can change the frequency.

Common Pitfalls:
Students sometimes think that because the formula v = f * λ links speed, frequency and wavelength, changing speed must change frequency. In reality, when sound enters a new medium, speed and wavelength may change, but frequency usually stays constant, because the source continues to vibrate at the same rate. To avoid confusion, always remember that the vibrating source determines frequency, while the medium primarily affects speed and wavelength.

Final Answer:
The frequency of a sound wave is primarily determined by the vibrating source that produces the sound.