A sound wave traveling in air has a frequency f and wavelength λ. A second sound wave traveling in air has wavelength λ/2. What is the frequency of the second sound wave?

Since the speed of a sound wave depends only on the medium, we can say that the second wave travels at same speed v (because it is still travelling in air, as the first wave). The wavelength of the second wave is [tex]\frac{\lambda}{2}[/tex], so if we call its frequency f', the new equation is

[tex]v=\frac{\lambda}{2}f'[/tex] (2)

And if we equate (1) and (2), we find

[tex]\lambda f = \frac{\lambda}{2}f'\\f'=2f[/tex]

johanrusli johanrusli · Answer 2 · 2019-12-13T04:47:49+01:00

The frequency of the second sound wave is 2f

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Further explanation

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

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

f = frequency of wave ( Hz )

v = speed of wave ( m/s )

λ = wavelength ( m )

Let's tackle the problem!

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Given:

frequency of first wave = f

wavelength of first wave = λ

wavelegnth of second wave = λ/2

Asked:

frequency of second wave = f' = ?

Solution:

Because the speed of wave depends on the medium, then:

[tex]\texttt{Speed of First Wave = Speed of Second Wave}[/tex]

[tex]v_1 = v_2[/tex]

[tex]\lambda_1 f_1 = \lambda_2 f_2[/tex]

[tex]\lambda f = \frac{1}{2}\lambda f'[/tex]

[tex]f = \frac{1}{2} f'[/tex]

[tex]f' = 2f[/tex]

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Conclusion:

The frequency of the second sound wave is 2f

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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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Keywords: Sound, Wave , Wavelength , Doppler , Effect , Policeman , Stationary , Frequency , Speed , Beats, Medium, Space