SImple question about sound waves but need a good reason

[anarchy.spirit]

Sound waves and frequency

Question:
Compare between the speed of high frequency (short wavelength) sounds to low frequency (long wavelength) sounds.

In my opinion, the answer is that frequency affects directly to the velocity of the sound.
Therefore, high frequency sound have high velocity.
Can someone post if this is right or not? If not, can anyone provide the correct answer? Thanks in advance.

 

[Tide]

It is non sequitur to say "the frequency directly affects the speed of sound therefore high frequency waves travel faster."

You will need to come up with a physical reason why the wavelength would affect the speed of sound. Also, does it make a difference whether you're talking about phase velocity as opposed to group velocity?

 

[quicknote]

You are correct in stating that frequency affects the velocity of sound waves. In fact, the speed of sound in a given medium is directly proportional to its frequency. This is because sound waves are longitudinal waves, meaning they propagate through a medium by causing the particles of the medium to vibrate in the same direction as the wave's motion. Higher frequency sound waves have more vibrations per unit time, which results in a higher velocity. This can also be seen in the formula for calculating the speed of sound: v = fλ, where v is the speed of sound, f is the frequency, and λ is the wavelength. As the frequency increases, the wavelength decreases and the speed increases. Therefore, high frequency sounds with short wavelengths will travel faster than low frequency sounds with longer wavelengths. I hope this clarifies your understanding of sound waves and their relationship with frequency.