The frequency of the middle a note on a piano is 440.00 hz. What is the wavelength of this note in centimeters? The speed of sound in air is 343.06 m/s.

Respuesta :

Answer:

78 cm

Explanation:

The wavelength of a wave is given by:

[tex]\lambda=\frac{v}{f}[/tex]

where

v is the speed of the wave

f is the frequency

In this problem, we have

v = 343.06 m/s is the speed of the sound wave in air

f = 440.0 Hz is the frequency of the note

So, the wavelength of the note is

[tex]\lambda=\frac{343.06 m/s}{440 Hz}=0.78 m=78 cm[/tex]

The wavelength of this note is about 78 cm

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Further explanation

Let's recall the speed of wave and intensity of wave formula as follows:

[tex]\boxed {v = \lambda f}[/tex]

f = frequency of wave ( Hz )

v = speed of wave ( m/s )

λ = wavelength ( m )

[tex]\texttt{ }[/tex]

[tex]\boxed {I = 2 \pi^2 A^2 f^2 \rho v}[/tex]

I = intensity of wave ( W/m² )

A = amplitude of wave ( m )

f = frequeny of wave ( Hz )

ρ = density of medium ( kg/m³ )

v = speed of wave ( m/s )

Let's tackle the problem!

[tex]\texttt{ }[/tex]

Given:

frequency of  the note = f = 440.00 Hz

speed of sound in air = v = 343.06 m/s

Asked:

wavelength = λ = ?

Solution:

[tex]v = \lambda f[/tex]

[tex]\lambda = v \div f[/tex]

[tex]\lambda = 343.06 \div 440.00[/tex]

[tex]\lambda \approx 0.78 \texttt{ m}[/tex]

[tex]\lambda \approx 78 \texttt{ cm}[/tex]

[tex]\texttt{ }[/tex]

Learn more

  • Doppler Effect : https://brainly.com/question/3841958
  • Example of Doppler Effect : https://brainly.com/question/810552
  • Sound Waves Cannot Travel In Space. : https://brainly.com/question/546436
  • Frequency of The Beats - Doppler Effect : https://brainly.com/question/12367463

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Answer details

Grade: College

Subject: Physics

Chapter: Sound Waves

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