When a sound wave travel from one medium to another its frequency remains unchanged while its wavelength changes. But we know wavelength is indirectly proportional to frequency. So, how could wavelength change but not frequency?

Dear student,

 

As sound waves travel from one medium to another, its speed changes hence the wavelength. The wavelength may become shorter in denser medium like water. The wave's speed v is related to both the frequency f and the wavelength  l : v =  l f.

 

Combining the above expression for velocity with the definition of index of refraction, we find a relationship between the wavelength  l = v/f in a medium and the wavelength l ₀ = c/f in vacuum:

 

In the above equation, the frequencies cancel because frequency does not change as waves moves from one medium to another.

 

Hope this helps.

Team

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