A flute player hears four beats per second when she compares her note to a 523 Hz tuning fork (the note C). She can match the frequency of the tuning fork by pulling out the 'tuning joint' to lengthen her flute slightly. What was her initial frequency?

Verified step by step guidance

1. Identify the frequency of the tuning fork, which is given as 523 Hz.
2. Understand that the beats per second heard by the flute player is the absolute difference between the frequency of the flute and the frequency of the tuning fork. The number of beats per second is given as 4 beats per second.
3. Set up the equation for the beat frequency: |f_{flute} - 523 Hz| = 4 Hz, where f_{flute} is the frequency of the flute.
4. Solve the equation for f_{flute}. This equation has two possible solutions: f_{flute} = 523 Hz + 4 Hz or f_{flute} = 523 Hz - 4 Hz.
5. Conclude that the initial frequency of the flute could either be 527 Hz or 519 Hz, depending on whether the flute's frequency was initially higher or lower than the tuning fork's frequency.

Key Concepts

Beats Frequency

Beats frequency occurs when two sound waves of slightly different frequencies interfere with each other, resulting in a periodic variation in amplitude. The frequency of the beats is equal to the absolute difference between the two frequencies. In this case, the flute player hears four beats per second, indicating that the frequency of her note differs from the tuning fork's frequency by 4 Hz.

Frequency Matching

Frequency matching is the process of adjusting the frequency of a sound source to match a reference frequency. In this scenario, the flute player adjusts her flute's length to match the 523 Hz frequency of the tuning fork. The initial frequency of her note can be determined by adding or subtracting the beats frequency from the reference frequency.

Tuning Fork

A tuning fork is a metal instrument that produces a specific pitch when struck, commonly used for tuning musical instruments. The frequency of the tuning fork provides a standard reference point for musicians. In this question, the 523 Hz tuning fork represents the note C, which the flute player aims to match by adjusting her instrument.