Longitudinal and transverse waves

[Abhishekdas]

Longitudinal and transverse waves...

Homework Statement

A string is stretched so that its length is increased by 1/n of its original length. The ratio of fundamental frequency of transverse vibration to that of fundamental frequency of longitudinal vibration will be?

Homework Equations

v=(T/(mass per unit length))^1/2
v= f*lambda

v= velocity
f=frequency
lambda= wavelength

The Attempt at a Solution

How to deal with these questions? I don't have much of a clue...Please help...
The textbook has not dealt with situations where two waves are occurring simultaneously...
Ususally its either one of them and i know how to deal with them...using the formula for frequency as mentioned above...

 

[lippyka]

Answer:The ratio of fundamental frequency of transverse vibration to that of fundamental frequency of longitudinal vibration will be n:1, where n is the factor by which the length of the string was increased. This is because when the length of the string is increased, the wavelength for both transverse and longitudinal wave will increase by the same factor (n). But since the velocity of transverse wave is higher than that of longitudinal wave, the frequency for transverse wave will decrease by the same factor (n) as wavelength has increased by n. Therefore, the ratio of fundamental frequency of transverse wave to that of the longitudinal wave will be n:1.