Question

What is the wavelength of a $1Hz$ sound wave traveling through the air?

Answer 1

Sound like all waves, travels at a certain speed and has the property of frequency and wavelength. Given the frequency of the sound is $1Hz$. We know the speed of the sound in the air is $342m/s$.
If we substitute these values in the formula that is given below we will be able to find out the wavelength of the sound waves.
Formula:
${\text{velocity }}$ =${\text{wavelength}} \times {\text{frequency}}$---- (1)

Complete answer:
The speed of the wave is dependent on the medium. The denser the medium is the faster the wave travels. But that’s not always the case. Here the medium is air. We know the speed of the sound waves in the air is $342m/s$
We know that the frequency = $1Hz$
The unit of frequency is cycles per second.
The unit of wavelength is meters per cycle.
If we rearrange the formula given above we will get
${\text{wavelength = }}\dfrac{{{\text{velocity}}}}{{{\text{Frequency}}}}$
Wavelength= $\dfrac{{343}}{1}$
Wavelength= $343m$
Therefore, the wavelength of the sound wave is $343m$.

Note:
For the sound waves traveling in the air, the vibrations of the particles are best described as longitudinal. Sound waves in air (and any liquid medium) are longitudinal waves since particles of the medium through which the sound is shipped vibrate corresponding to the course that the sound wave moves. No matter what the source of the sound wave is, regardless of whether it is a vibrating string or the vibrating prongs of a tuning fork - sound waves going through the air are longitudinal waves
The wavelength of sound frequencies audible to the human ear is $20Hz$ and $20KHz$. A thing to note is that below $20Hz$ you have infrasound. You wouldn't be able to hear it unless sound pressure was high enough.