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A guitar string vibrates with an unknown frequency. If the the guitar string is played along with a 440 Hz tuning fork, a beat frequency of 5 Hz is heard. What are the possible frequencies the guitar string could be vibrating at?

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hamzaahmeds

This question involves the concept of the beat frequency.

The possible frequencies of the guitar string could be "445 Hz" (or) "435 Hz".

Beat Frequency

When two sounds with a very minor difference in their frequency are played, they produce a frequency equal to the absolute value of the difference between their frequencies. This frequency is known as beat frequency.

[tex]f_b=|f_1-f_2|[/tex]

where,

  • [tex]f_b\\[/tex] = beat frequency = 5 Hz
  • f₁ = frequency of first guitar string = 440 Hz
  • f₂ = possible frequencies of other string = ?

Therefore,

5 Hz = |440 Hz - f₂|

f₂ = 440 Hz ± 5 Hz

f₂ = 445 Hz (OR) 435 Hz

Learn more about beat frequency here:

https://brainly.com/question/10306260