A string under tension produces a note of frequency 14Hz. Determine the frequency when the tension is quadrupled????
frequency is proportional to the √ of the tension
To determine the frequency when the tension is quadrupled, we need to understand the relationship between tension and frequency in a vibrating string.
The frequency of a vibrating string is determined by several factors, including the tension in the string, the length of the string, and the mass per unit length of the string. However, for this question, we will assume that all these other factors remain constant.
According to physics principles, the frequency (f) of a vibrating string is inversely proportional to the wavelength (λ), which in turn is directly proportional to the tension (T) in the string. Mathematically, this relationship can be expressed as:
f ∝ 1/λ ∝ T
This implies that if the tension is quadrupled (T → 4T), the frequency will also quadruple (f → 4f).
Now, since we know the initial frequency is 14 Hz, we can calculate the new frequency when the tension is quadrupled using the given relationship:
4f = 4 * 14 Hz = 56 Hz
Therefore, when the tension is quadrupled, the new frequency will be 56 Hz.