Question

A string of length $L$ vibrates with a frequency of $7.5\text{Hz}$ to form a standing wave with three antinodes as shown below.


What is the oscillating frequency of this string, if it produces the standing wave pattern shown below?

• A. $10\text{Hz}$
• B. $7.5\text{Hz}$
• C. $2.5\text{Hz}$
• D. $15\text{Hz}$

Answer 1

The correct option is D $15\text{Hz}$

All harmonic frequencies $\left(f_n\right)$ are whole number mulitples $\left(n\right)$ of the fundamental frequency.
$f_n=n{f}_1$
Let's use this relationship to find the fundamental frequency from the first standing wave (third harmonic - 3 loops) and then find the frequency of the new standing wave (sixth harmonic - 6 loops).
We are given the frequency of the third harmonic. So,
$f_3=3f_1$
$\Rightarrow f_1=\frac{f_3}{3}=\frac{7.5\text{Hz}}{3}=2.5\text{Hz}$
Therefore, frequency for sixth harmonic is:
$f_6=6f_1=6\left(2.5\text{Hz}\right)=15\text{Hz}$