Question

Audible wavelengths. the range of audible frequencies is from about 20.0 hz to 2.00×104 hz . what is range of the wavelengths of audible sound in air?

Answer 1

Given:
f1 = 20 Hz 
f2 = 20000 Hz
speed of sound at 20 degrees celcius = 343 m/s

Solution:

for f1 = 20 Hz,

Using the equation:

lambda = speed of sound / f1 = 343 / 20 = 17.15 m 

For f2: 

lambda = speed of sound / f2 = 343 / 20000 = 0.01775 m

Therefore the wavelength range of audible sound in air would be 17.15 m to 0.01775 m.

Answer 2

The range of the wavelengths of audible sound in air is from about 0.0172 m to 17.2 m

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Further explanation

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

$\large {\boxed {v = \lambda f}}$

f = frequency of wave ( Hz )

v = speed of wave ( m/s )

λ = wavelength ( m )

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$\large {\boxed {I = 2 \pi^2 A^2 f^2 \rho v}}$

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!

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Given:

minimum frequency = f_min = 20.0 Hz

maximum frequency = f_max = 2.00 × 10⁴ Hz

speed of sound in air = 343 m/s ( assumption )

Asked:

minimum wavelength = λ_min = ?

maximum wavelength = λ_max = ?

Solution:

$20.0 \leq f \leq 2.00 \times 10^4$

$20.0 \leq \frac{v}{\lambda} \leq 2.00 \times 10^4$

$20.0 \leq \frac{343}{\lambda} \leq 2.00 \times 10^4$

$\frac{343}{2.00 \times 10^4} \leq \lambda \leq \frac{343}{20.0}$

$\large {\boxed {0.01715 \texttt{ m} \leq \lambda \leq 17.15 \texttt{ m}}}$

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Learn more

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

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Answer details

Grade: College

Subject: Physics

Chapter: Sound Waves