(b)If waves travel with a velocity of 129 m/s on this string , what is the frequency associated with this long

Question

A string with a length of 0.5m is fixed at both ends.

Answer 1

You can't tell what the frequency will be. However, you can find the minimum frequency.

Velocity of a wave= Frequency * Wavelength
F=V/Wavelength

Maximum Wavelength with both ends fixed is twice the distance between the points. (The points act as nodes for a standing wave)

Wavelenght= 2*.5m
=1 m

therefore

Minimum frequency= 129 m/sec * 1/1m
=129 Hz

Answer 2

In the fundamental mode of vibration ,both ends of string are nodes with only one anti node in between

Thus length of the string equals half wavelength

Largest wavelength=2L

where L is length of the string

Frequency=velocity / wave length

Frequency=129 /2*0.5 =129 hertz

The smallest frequency associated with this string is 129 hertz

In higher modes of vibration, the wavelengths will be 2L/2=L
and 2L/3 ,2L/4

The next higher frequency will be 129*2=258 Hz