How does the frequency of wave in the string compare to the frequency of the sound wave in the air?
The correct answer and explanation is:
The frequency of the wave in the string is typically the same as the frequency of the sound wave in the air. This is because when a string is vibrating (for instance, in a musical instrument like a guitar or violin), it generates sound waves by disturbing the surrounding air molecules. The vibration of the string causes periodic compressions and rarefactions of air, which propagates as sound waves.
Here’s how it works:
- Vibrating String and Frequency: When a string vibrates, its vibrations move at a certain frequency determined by factors such as the tension of the string, its length, and its mass per unit length. This frequency determines the pitch of the sound that the string itself produces.
- Sound Waves in Air: The vibrating string causes the surrounding air to vibrate as well, transferring the energy from the string into the air. The frequency of these air vibrations corresponds to the frequency of the string’s vibration. If the string vibrates at a frequency of 440 Hz, for example, it will produce sound waves in the air at the same frequency, resulting in a 440 Hz sound that we perceive as the musical note A4.
- Propagation of Sound: The string’s vibrations are transmitted to the surrounding medium (usually air), and those vibrations cause air molecules to oscillate. The sound wave produced in the air has the same frequency as the wave in the string because they are directly related: the string’s vibration generates the sound wave, and both are tied to the same oscillatory motion.
In conclusion, the frequency of the wave on the string and the frequency of the sound wave in the air are the same, though they can have different characteristics in terms of amplitude, wavelength, and energy. The string’s vibrations initiate the sound waves in the air, and their frequencies match.