Question

A string of length 100cm has three resonant frequencies 120Hz, 200Hz and 280Hz .If a node is formed at the end of the string the speed of the transverse wave on this string is
Ans 80m/s

Answer 1

Find the fundamental frequency. It is the greatest common factor of the sequence:

$$f_1=\text{GCF}\{120,200,280\}=40\text{ Hz}.$$

On the other hand, that frequency can be found from the velocity of the transverse wave:

$$f_1=\frac{v}{2L},$$

therefore (keep in mind that 100 cm is 1 m and we perform all calculations in SI):

$$v=2f_1L=2\cdot40\cdot1=80\text{ m/s}.$$