Final answer:
To increase the frequency of a vibrating string, you should decrease the mass of the string, which reduces its linear density and allows waves to travel faster. Other options would not lead to an increase in frequency.
Step-by-step explanation:
To increase the frequency of a vibrating string, you need to make changes that will affect the wave speed or the wavelength in ways that lead to an increase in how often the waves pass a fixed point per second. So, out of the given options:
- Decreasing the tension in the string and increasing the mass of the string will decrease frequency, not increase it. Tension is directly proportional to wave speed, and increasing mass (linear density) decreases it.
- Decreasing the mass of the string causes an increase in frequency because it means you're reducing the linear density, which allows waves to travel faster.
- Increasing the length of the string does not directly affect the frequency. Frequency is inversely proportional to wavelength, and in a given mode of vibration, the wavelength is determined by the length of the string. Increasing length would typically increase wavelength, thus lowering frequency.
- Decreasing the tension in the string also decreases frequency, because tension is directly proportional to the wave speed.
Therefore, the correct answer is B) Decreasing the mass of the string will increase the frequency of a vibrating string.