If you increase the tension on a stretched string while keeping its length and mass per unit length constant, the frequency and wavelength of the waves traveling on the string will be affected as follows:
Frequency: The frequency of the waves on a stretched string is directly proportional to the square root of the tension in the string. Therefore, increasing the tension will result in an increase in the frequency of the waves. This means that the number of complete oscillations (cycles) of the wave per unit of time will increase.
Wavelength: The wavelength of the waves on a stretched string is inversely proportional to the square root of the tension in the string. When you increase the tension, the wavelength of the waves will decrease. This means that the distance between consecutive peaks or troughs of the wave will become shorter.
The relationship between tension (T), frequency (f), and wavelength (λ) for waves on a string is given by the equation:
v = √(T/μ),
where v is the wave speed (which depends on the properties of the string material), and μ is the linear mass density of the string (mass per unit length).
Since the wave speed remains constant if the string material does not change, an increase in tension will result in an increase in frequency and a decrease in wavelength.