Question

In Melde's experiment in the transverse mode, the frequency of the tuning fork and the frequency of the waves in the string are found to be in the ratio as,
$\begin{align}
  & A.2:1 \\
 & B.4:1 \\
 & C.1:1 \\
 & D.1:2 \\
\end{align}$

Answer 1

Hint: Melde's experiment is an experiment done to represent that the mechanical waves undergo phenomenon of interference. In this experiment the variation in frequency is created if the tension is increased in the string. This is similar to the variation in pitch if a guitar string is tuned. This way a resonance in tuning fork and frequency of standing waves developed is needed. This will need the frequencies of the two to be identical to each other.

Complete answer:
A string is in transverse vibration indicating so many properties which are in general to all vibrating acoustic systems, if these are the vibrations of a guitar string or the standing wave nodes in any monitoring room in a studio. In this experiment the variation in frequency created if the tension is enhanced in the string will be the same as the variation in pitch occurs if a guitar string is tuned. This is measured in this experiment. Using this the mass per unit length of the string or the wire can be obtained. This is the basic principle of the Melde's Experiment.
Therefore a resonance in the tuning fork and frequency of standing waves developed is needed. That is the frequencies of the two will be identical. Hence the ratio of the frequencies will be $1:1$.

The answer is mentioned as option C.

Note:
Melde's experiment is the basic experiment in order to learn the nature of standing waves in a string or a metal wire. We can even visually calculate the wavelength, period and amplitude of the waves. A string which is undergoing a transverse vibration represents many characteristics which are very common to all acoustic vibrating systems such as the vibrations of a violin or a guitar string.