Question

The string of a violin vibrating in a certain mode emits a note of $205\text{Hz}$ at its correct tension. The string is tightened slightly and produces six beats in two seconds with a tuning fork of frequency $205\text{Hz}$. The new frequency of the note emitted after the string is tightened is

• A. $210\text{Hz}$
• B. $205\text{Hz}$
• C. $208\text{Hz}$
• D. $202\text{Hz}$

Answer 1

The correct option is C $208\text{Hz}$

Initial frequency of violin, $f_o=205\text{Hz}$
Number of beats per two seconds $=6$
So, number of beats per second, $f_B=3$
Frequency of tuning fork, $f_1=205\text{Hz}$
When the string is tightened, tension increases and the frequency also increases. Therefore the final frequency will be more than initial.
From formula, beat frequency,
$f_B=f_2-f_1$
$\Rightarrow 3=f_2-205$
$\Rightarrow f_2=208\text{Hz}$
$$\begin{array}{c}\text{Tips: When string is tightened its tension increases.}\end{array}$$