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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 65.2cm instead. What is the frequency of the beats these musicians hear when they play together?

Short Answer

Expert verified

The beats have the frequency 3.29 H³ú.

Step by step solution

01

Beat frequency formation

The beat frequency is the frequency that is equal to the difference in the frequency of the waves, forming the beat.

fb=| f1-f2 |

02

Calculate the two frequencies

The values of wavelengths are given and the velocity of sound in air is344″¾/s.

role="math" localid="1655810925277" f1=vλ1=344″¾/s0.65″¾=530.86 H³ú

f2=vλ2=344″¾/s0.65″¾=527.60 H³ú

03

Calculate the beats frequency

fb=|f1−f2|=|530.86 H³ú−527.61 H³ú|=3.29 H³ú

So, the beat frequency is 3.29 H³ú.

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