Explanation:
It is given that, a wave on a string with constant tension. The frequency of a wave and its speed is related by the following relation as :
............(1)
Where
v is the speed of the wave
l is the length of the string
(a) It is clear from equation (1) that the frequency of a wave is directly proportional to its speed. If the frequency of the wave is doubled, the speed of the wave also becomes double i.e. the speed increases by a factor of 2.
(b) The relationship between the frequency and the wavelength is given by :
![\lambda=\dfrac{v}{\nu}](https://tex.z-dn.net/?f=%5Clambda%3D%5Cdfrac%7Bv%7D%7B%5Cnu%7D)
It is clear from the above formula that the frequency is inversely proportional to the wavelength of the wave. If the frequency of a wave is doubled, the wavelength becomes half.
Hence, this is the required solution.