When the tension on a stretched string is increased, both the frequency and wavelength of the waves traveling along the string are affected.
Frequency: The frequency of a wave is the number of complete oscillations or cycles that occur per unit of time. In the case of a stretched string, increasing the tension causes an increase in the wave speed. This, in turn, results in an increase in the frequency of the waves.
Mathematically, the relationship between tension (T), wave speed (v), and frequency (f) is described by the equation:
v = √(T/μ),
where μ is the linear mass density of the string (mass per unit length). When the tension (T) increases, the wave speed (v) increases, and since the frequency (f) is related to the wave speed, the frequency also increases.
Wavelength: The wavelength of a wave is the distance between two consecutive points that are in phase with each other. When the tension on a stretched string is increased, the wavelength of the waves changes.
The relationship between tension (T), wave speed (v), and wavelength (λ) is given by the equation:
v = λf,
where λ represents the wavelength and f represents the frequency. When the tension is increased, and the frequency increases (as discussed above), the wave speed also increases. In order to maintain a constant wave speed, the wavelength must decrease. This means that as tension increases, the wavelength of the waves on the string becomes shorter.
In summary, increasing the tension on a stretched string leads to an increase in both the frequency and wave speed, while causing a decrease in the wavelength of the waves.