A string emits an unknown sound. You strike a tuning fork which emits a sound at EXACTLY 300 Hz, and you hear a beat frequency of 20 Hz. You then tighten the string, increasing the tension in string. After you pluck the string and strike the tuning fork, you hear a new beat frequency of 30 Hz. What is the unknown frequency of the string, originally?

• A. 270 Hz
• B. 280 Hz
• C. 320 Hz
• D. 330 Hz

Answer: (C)

Verified step by step guidance

1. Understand the concept of beat frequency: When two sound waves of slightly different frequencies interfere, they produce a phenomenon called beats. The beat frequency is the absolute difference between the two frequencies.
2. Initially, the beat frequency is given as 20 Hz. This means the unknown frequency of the string could be either 20 Hz higher or 20 Hz lower than the tuning fork frequency of 300 Hz. Therefore, the possible frequencies of the string are 280 Hz or 320 Hz.
3. When the string is tightened, the tension increases, which typically increases the frequency of the sound it emits. After tightening, the beat frequency increases to 30 Hz.
4. With the new beat frequency of 30 Hz, the possible frequencies of the string are either 270 Hz or 330 Hz. However, since tightening the string increases the frequency, the string's frequency must have increased from its original value.
5. Given the initial possibilities (280 Hz or 320 Hz) and the effect of tightening, the original frequency of the string must have been 320 Hz, as this would increase to 330 Hz, matching the new beat frequency condition.