Question

A certain string (fixed at one end and free at the other end) can vibrate at several frequencies, the lowest of which is $200\text{Hz}$. What are next two higher frequencies to which it vibrates?

• A. $600\text{Hz},1000\text{Hz}$
• B. $300\text{Hz},400\text{Hz}$
• C. $200\text{Hz},250\text{Hz}$
• D. $100\text{Hz},150\text{Hz}$

Answer 1

The correct option is A $600\text{Hz},1000\text{Hz}$

Frequency of vibration will be given by,
$f=(n+\frac{1}{2})\frac{V}{2L}$
The lowest frequency is the fundamental frequency of vibration i.e for $n=0$
$\Rightarrow f_{min}=\frac{V}{4L}=f_0$
Given: $f_0=200\text{Hz}$
for next higher frequencies $(n=1,n=2)$
$\Rightarrow f_1=\frac{3V}{4L}=3f_0=600\text{Hz}$
$f_2=\frac{5V}{4L}=5f_0=1000\text{Hz}$