Question: A string in a musical instrument is 50cm long and its fundamental frequency is 800 Hz. if a frequency of 1000 Hz is to be produced then the required length of the string is………………
When the string vibrates in single loop, its frequency corresponds to its fundamental frequency.
In this case two nodes are produced at the two ends and it corresponds to half the wavelength.
i.e. wavelength = 50 x 2 = 100 cm = 1 m
And this corresponds to a frequency of 800 Hz
wavelength x frequency = speed of sound
The speed is constant in the same medium
Therefore a fundamental frequency of 1000 Hz, the length should be
L = 50*800/1000 = 40 cm
If you are familiar with the above ideas you could simply take
f1L1 = f2 L2
and solve the problem