A whistle is often used in dog-­‐‑training exercises and is an integral part of field-­‐‑marking competitions, where signals and commands are relayed to the dog via whistle. Suppose the whistle produces a sound wave with a frequency of 25,100 Hz (outside the range of human hearing) and the propagation speed of sound in air is 343 m/s. 1) What is the wavelength and wave number of this sound from the whistle?
2) Write the wave function for the longitudinal sound wave described above, assuming the amplitude of the sound wave is Smax = 1.57 x 10-­‐‑6 m and it is moving to the right (in the positive x direction).

The wavelength is  

The wave number is  

The wave function is  

Explanation:

From the question we are told that

    The frequency of the sound wave is  

    The speed of the wave is  

The wavelength of the wave is mathematically evaluated as

substituting values

The wave number is  mathematically represented as

substituting values

The general form of  wave function is

given that the amplitude is  

  While which is the angular velocity is  represented as  

  and  k which is the angular wave number is mathematically represented as    

   The wave function becomes  

substituting values

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