Bobby Gross

2023-02-22

A person has a hearing range from $20Hz$ to $20kHz$. What are the typical wavelengths of sound waves in air corresponding to these two frequencies? Take the speed of sound in air as $344\frac{m}{s}$.

Michaela Perez

Beginner2023-02-23Added 7 answers

Given data

The person's capacity for hearing$=20Hz-20KHz$

Speed of sound in air $=$$344\frac{m}{s}$

Formula used

Speed $=$ Frequency$\times $Wavelength

Solution

$v=f\times \lambda $

(i). For the frequency $f=20Hz$

$\Rightarrow \lambda =\frac{344}{20}=17.2m$

(ii). For the frequency $f=20kHz$

$\Rightarrow \lambda =\frac{344}{20\times {10}^{3}}=0.0172m$

Hence, the range of wavelength is $0.0172m-17.2m$.

The person's capacity for hearing$=20Hz-20KHz$

Speed of sound in air $=$$344\frac{m}{s}$

Formula used

Speed $=$ Frequency$\times $Wavelength

Solution

$v=f\times \lambda $

(i). For the frequency $f=20Hz$

$\Rightarrow \lambda =\frac{344}{20}=17.2m$

(ii). For the frequency $f=20kHz$

$\Rightarrow \lambda =\frac{344}{20\times {10}^{3}}=0.0172m$

Hence, the range of wavelength is $0.0172m-17.2m$.