Another Beat Frequency Question

[Alain12345]

I have another beat frequency question. I understand how to get the possible frequencies of a string or tuning fork, but I don't know how to determine which one is the original frequency.

When a guitar string is sounded against a 440 Hz tuning fork, twelve beats are heard in two seconds.
a) What are the possible frequencies of the string?
b) If the person tightens the string, the beat frequency decreases. What then is the original frequency of the string, and why?

 

[cscott]

So, I assume you know $\#beats = |f_1 - f_2|$:

Since the beat frequency decreases [tex]f_1[/itex] and $f_2$ must approach each other. If this is the case, which one would you pick?

 

[kyle8921]

a) The possible frequencies of the string can be determined by using the formula for beat frequency, which is the difference between the two frequencies being sounded. In this case, we know that the beat frequency is 12 beats in 2 seconds, which translates to 6 beats per second. Using this information, we can set up the equation 6 beats/1 second = f1 - 440 Hz, where f1 is the frequency of the string. Solving for f1, we get a possible frequency of 446 Hz. However, this is not the only possible frequency. The string could also be tuned to a frequency of 434 Hz, which would also result in a beat frequency of 6 beats per second.

b) If the person tightens the string, the beat frequency will decrease. This is because tightening the string increases its tension, which in turn increases its frequency. If we use the same formula as before, but with the new beat frequency (let's say 4 beats per second), we can solve for the new frequency of the string. This would give us a frequency of 442 Hz. However, since we know that the original frequency of the string was either 434 Hz or 446 Hz, we can deduce that the original frequency must have been 446 Hz. This is because tightening the string would decrease the beat frequency, which means that the frequency of the string must have been closer to 446 Hz (since the beat frequency was originally 6 beats per second). Therefore, the original frequency of the string is 446 Hz.