Question

1.) The lowest- pitch sounds humans can generally hear have a frequency of roughly 0.02kHz. What is the approximate wavelength of these sound waves if their wave speed is 340 m/s?

2.) What is the speed of a sound wave that has a wavelength of 2,000 mm and a frequency 170.5 Hz?

3.) What is the frequency of a wave if it has a velocity of 25m/s and a wavelength of 2.5 meters?

Answer 1

1) The frequency of the sound is
$f=0.02 kHz = 20 Hz$
while the speed of sound is 
$v=340 m/s$
So we can use the relationship between wavelength, speed and frequency of a wave to find the wavelength corresponding to this sound:
$\lambda= \frac{v}{f}= \frac{340 m/s}{20 Hz}=17 m$

2) The wavelength in this case is
$\lambda=2000 mm=2.0 m$
while the frequency of the wave is 
$f=170.5 Hz$
So we can use the same relationship we used in part 1) to find the speed of the sound wave:
$v=\lambda f = (2.0 m)(170.5 Hz)=341 m/s$

3) The velocity of the wave is
$v=25 m/s$
while its wavelength is
$\lambda=2.5 m$
therefore we can find its frequency by using the usual relationship:
$f= \frac{v}{\lambda}= \frac{25 m/s}{2.5 m}=10 Hz$