Question

How is the frequency of a stretched string related to its tension?

Answer 1

Hint: To solve this question, we will simply use the formula of frequency and a vibrating object causes a sound wave, just like any other wave. A tuning fork or the sound of a human voice the particles in the medium vibrate back and forth at a specific frequency, regardless of the source of vibration. When a wave passes through a medium, the term frequency refers to how often the particles vibrate. In layman's terms, frequency is the total number of complete vibrations per unit of time.

Complete step by step answer:
The stretched string produces transverse waves. The frequency of these waves is determined by the stretched string's tension as well as its length. The frequency of transverse waves decreases as the length of the string increases. In a stretched string, the frequency of transverse waves is given by,
\[f = \dfrac{n}{{2l}}\sqrt {\dfrac{T}{\mu }} \]
Where, $f$ is the frequency, $l$ is the length of the string, $T$ is the tension of the string and $\mu $ is the mass per unit length

As we can easily say that $f \propto \sqrt T$.Therefore as the tension increases the frequency will increase.

Note: Note that frequency also depends upon density. The density of a string has an effect on frequency, causing denser strings to vibrate at slower speeds, resulting in lower frequencies. The frequency is inversely proportional to the square root of the density of the string, $f \propto \sqrt {\dfrac{1}{d}} $ where $f$ is the frequency and $d$ is the density of the string.