Question

akash is currently tuning their guitar with the help of a tuning fork. the fifth string on the guitar is currently out of tune, and they would like to tune it to the correct value of . (you can assume the tuning fork is perfectly in tune.) when akash strikes the tuning fork and plucks the guitar string, they hear a beat with a frequency of . (a) what are the two possible frequencies the guitar string is currently at? lower frequency: hz unanswered upper frequency: hz unanswered (b) when akash slightly loosens the string, they now hear a beat frequency of . what frequency is the string now at? what frequency is the string now at? hz unanswered (c) guitar strings have a fundamental harmonic with a wavelength of . what is the magnitude of the difference in wave speed between the frequency in part b) and a perfectly tuned string?

Answer 1

The guitar string is either slightly higher or lower than the tuning fork's frequency when a beat frequency is heard. The fundamental harmonic and wave speed play crucial roles in tuning the string to achieve the correct frequency. Beats are employed by tuners to adjust string tension until the frequencies match and the beat disappears.

Step-by-step explanation:

When tuning a guitar using a tuning fork, if Akash hears a beat frequency, the frequency of the guitar string is either slightly higher or lower than the frequency of the tuning fork. If the tuning fork has a frequency of 264 Hz, for instance, and a beat frequency is heard every 2 seconds (0.5 Hz), the string could be vibrating at 263.5 Hz or 264.5 Hz. When the guitar string is loosened and the beat frequency changes, the string's frequency shifts further away from the fork's frequency. For example, if the beat frequency becomes 1 Hz, the string's frequency is now at either 263 or 265 Hz, depending on whether it was higher or lower than the fork's frequency to begin with.

Using the fundamental harmonic and the speed of the waves on the string, the slight difference in frequencies between the tuning fork and the string leads to a difference in wave speed. This can be calculated by understanding that the speed of a wave on a string depends on its tension and linear mass density, as well as its frequency and wavelength. By comparing the string's frequency when it is out of tune to the desired frequency, we can determine the magnitude of the difference in wave speed. Piano tuners and guitarists use beats to tune instruments by adjusting the tension of the strings until the beat frequency disappears, indicating the instrument is in tune.