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The highest frequency humans can hear is about 20,000 hz. what is the wavelength of sound in room temperature air at this frequency? what is the wavelength of the lowest sounds we can hear, about 20 hz?

Respuesta :

skyluke89
(a) Wavelength and frequency of a wave are related by the following equation:
[tex]\lambda= \frac{v}{f} [/tex]
where
[tex]\lambda[/tex] is the wavelength
f is the frequency
v is the speed of the wave.

The speed of sound at room temperature is approximately [tex]v=343 m/s[/tex], so we can find the wavelength corresponding to a frequency of [tex]f=20000 Hz[/tex] by using the previous relationship:
[tex]\lambda= \frac{v}{f}= \frac{343 m/s}{20000 Hz}=0.017 m [/tex]


(b) the lowest sound we can hear has a frequency of f=20 Hz. Using the same relationship we used in the previous part of the exercise, we can find the corresponding wavelength:
[tex]\lambda= \frac{v}{f} = \frac{343 m/s}{20 Hz}=17.15 m [/tex]
johanrusli

The wavelength of these sound waves are :

The minimum wavelength is about 0.0173 m

The maximum wavelength is about 17.3 m

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Further explanation

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

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

where:

c = speed of wave ( m/s )

λ = wavelength ( m )

f = frequency of wave ( Hz )

Let us now tackle the problem!

[tex]\texttt{ }[/tex]

Given:

maximum frequency of sound wave = f_max = 20 000 Hz

minimum frequency of sound wave = f_min = 20 Hz

speed of sound wave in room temperature = v = 346 m/s

Asked:

A) The minimum wavelength = λ_min = ?

B) The maximum wavelength = λ_max = ?

Solution:

Part A:

[tex]\lambda_{min} = v \div f_{max}[/tex]

[tex]\lambda_{min} = 346 \div 20000[/tex]

[tex]\boxed {\lambda_{min} = 0.0173 \texttt{ m}}[/tex]

[tex]\texttt{ }[/tex]

Part B:

[tex]\lambda_{max} = v \div f_{min}[/tex]

[tex]\lambda_{max} = 346 \div 20[/tex]

[tex]\boxed {\lambda_{max} = 17.3 \texttt{ m}}[/tex]

[tex]\texttt{ }[/tex]

Learn more

  • Frequency of Sound Wave : https://brainly.com/question/12441470
  • Frequency of Beats : https://brainly.com/question/12367463
  • Amplitude of Sound Wave : https://brainly.com/question/2675676
  • Kinetic Energy : https://brainly.com/question/692781
  • Acceleration : https://brainly.com/question/2283922
  • The Speed of Car : https://brainly.com/question/568302

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Answer details

Grade: High School

Subject: Physics

Chapter: Sound Wave

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