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= (v)/(f)= (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= (v)/(\lambda)= (25 m/s)/(2.5 m)=10 Hz`