Question

Two guitarists attempt to play the same note of wavelength 64.8 cm at the same time, but one of the instruments is slightly out of tune and plays a note of wavelength 65.2 cm instead. What is the frequency of the beats these musicians hear when they play together? Should the out of tune guitarists tighten or loosen his guitar string to correctly tune his guitar?

Answer 1

The musicians will hear a beat frequency of 2.33 Hz. The out-of-tune guitarist should loosen his guitar string to correctly tune it.

Step-by-step explanation:

When two notes with slightly different frequencies are played together, they create what is known as beats. The beat frequency is equal to the difference between the frequencies of the two notes being played. In this case, the two guitarists are playing notes with wavelengths of 64.8 cm and 65.2 cm. To find the beat frequency, we need to convert these wavelengths to frequencies using the formula:

Frequency = Speed / Wavelength

The speed of sound is approximately 343 m/s. Plugging in the wavelength values, we get:

Frequency1 = 343 m/s / (64.8 cm / 100 cm/m) = 529.32 Hz

Frequency2 = 343 m/s / (65.2 cm / 100 cm/m) = 526.99 Hz

Now, we can find the beat frequency:

Beat Frequency = |Frequency1 - Frequency2| = |529.32 Hz - 526.99 Hz| = 2.33 Hz

Therefore, the musicians will hear a beat frequency of 2.33 Hz.

To correctly tune his guitar, the out-of-tune guitarist should loosen his guitar string. When two frequencies create beats, it means they are slightly out of phase with each other. By loosening the string, the frequency will decrease, bringing it closer to the desired note and reducing the beat frequency.