Introduction
When sound waves travel from one medium to another, their speed changes, and this affects their wavelength. This phenomenon can be explained by the relationship between the speed, frequency, and wavelength of a wave.

Explanation
When sound waves travel through a medium, they propagate by compressing and rarefying the particles of the medium. The speed of sound is determined by the properties of the medium, such as its density and elasticity. In the first medium, the sound waves have a speed of v m/s and a wavelength of λ.

Change in Speed
When the sound waves enter the second medium, they encounter a different set of properties that result in a change in speed. In this case, the speed of sound in the second medium is 2v m/s, which is twice the speed in the first medium.

Relationship between Speed and Wavelength
The speed of a wave is directly proportional to its wavelength. This means that as the speed of the wave increases, its wavelength also increases. Similarly, if the speed decreases, the wavelength decreases.

Calculating the Wavelength in the Second Medium
To determine the new wavelength in the second medium, we can use the equation:

λ2 = v2 / f

Where λ2 is the wavelength in the second medium, v2 is the speed of sound in the second medium, and f is the frequency of the sound wave.

Since the frequency of the sound wave remains constant when it travels from one medium to another, we can rearrange the equation as follows:

λ2 = (2v) / f

Therefore, the wavelength of the sound waves in the second medium is equal to 2 times the wavelength in the first medium.

Conclusion
When sound waves travel from a medium with a speed of v m/s to another medium with a speed of 2v m/s, the wavelength of the sound waves in the second medium is twice the wavelength in the first medium. This change in wavelength is a result of the change in speed, as determined by the properties of the mediums through which the sound waves propagate.