Let me clarify the concept of wavelength and its relationship to the speed of propagation.
In general, the speed of propagation of a wave is determined by the properties of the medium through which it travels, rather than the wavelength itself. In the case of sound waves, their speed is influenced by various factors, including temperature, pressure, and the composition of the medium.
In the book you mentioned, it is correct that sound waves generally travel slower in colder air compared to warmer air. This is because colder air tends to have a higher density and lower molecular speed, which affects the propagation of sound. However, it is important to note that the wavelength of a sound wave does not change due to the temperature of the medium.
The wavelength of a sound wave is determined by the frequency of the wave and the speed of sound in that particular medium. The wavelength is inversely proportional to the frequency, meaning that as the frequency increases, the wavelength decreases, and vice versa. The speed of sound is directly proportional to the square root of the temperature of the medium, so as the temperature decreases, the speed of sound also decreases.
Therefore, when sound travels through colder air, its speed decreases, but the wavelength remains the same. This means that for the same frequency of sound, the wavelength remains constant regardless of the temperature of the medium.