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Chapter 2: Q40E (page 540)

Two guitarists attempt to play the same note of wavelength 64.8鈥�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鈥塇锄.

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=|鈥�f1-f2鈥�|

02

Calculate the two frequencies

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

role="math" localid="1655810925277" f1=v位1=344鈥尘/s0.65鈥尘=530.86鈥塇锄

f2=v位2=344鈥尘/s0.65鈥尘=527.60鈥塇锄

03

Calculate the beats frequency

fb=|f1鈭�f2|=|530.86鈥塇锄鈭�527.61鈥塇锄|=3.29鈥塇锄

So, the beat frequency is 3.29鈥塇锄.

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