Chapter 2: Q40E (page 540)

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?

Short Answer

Expert verified

The beats have the frequency $3.29 Hz$ .

Step by step solution

Beat frequency formation

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

$f_{b} = | f_{1} - f_{2} |$

Calculate the two frequencies

The values of wavelengths are given and the velocity of sound in air is $344 m / s$ .

role="math" localid="1655810925277" $\begin{matrix} f_{1} = \frac{v}{λ_{1}} \\ = \frac{344 m / s}{0.65 m} \\ = 530.86 Hz \end{matrix}$

$\begin{matrix} f_{2} = \frac{v}{λ_{2}} \\ = \frac{344 m / s}{0.65 m} \\ = 527.60 Hz \end{matrix}$

Calculate the beats frequency

$\begin{matrix} f_{b} = | f_{1} - f_{2} | \\ = | 530.86 Hz - 527.61 Hz | \\ = 3.29 Hz \end{matrix}$

So, the beat frequency is $3.29 Hz$ .

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

Short Answer

Step by step solution

Beat frequency formation

Calculate the two frequencies

Calculate the beats frequency

One App. One Place for Learning.

Most popular questions from this chapter

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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

Step by step solution

Beat frequency formation

Calculate the two frequencies

Calculate the beats frequency

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Magnetism

Wave Optics

Translational Dynamics

Electromagnetism

Nuclear Physics

Thermodynamics

Study anywhere. Anytime. Across all devices.

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?