Question

A string is attached to a wall while the other end of the string is in your hand.  You make waves on the string by pumping your hand up and down.  If you double the tension in the string while maintaining the same frequency of motion, will the wavelength of the wave on the string increase, decrease, or remain the same? Explain.

Answer 1

Wavelength of the wave on the string increases.

Velocity of propagation of wave in a string is related to the frequency and the wavelength of the wave as

The velocity of propagation of wave is related to the tension in the string T and linear mass density of the string as

Using these two relations we can determine the relation between the wavelength and the tension in the string

For constant frequency

If we double the tension in the string, the wavelength increases by a factor of