What happens to the fundamental frequency of a stretched string when its linear density becomes 1/4 of its intial value?

To decrease the fundamental frequency of a stretched string fixed at both ends one might

How is the frequency of a stretched string related to: Its tension?

How is the frequency of a stretched string related to: Its length?

If v_(1) , v_(2) and v_(3) are the fundamental frequencies of three segments of stretched string , then the fundamental frequency of the overall string is

The fundamental frequency of a sonometre wire is n . If its radius is doubled and its tension becomes half, the material of the wire remains same, the new fundamental frequency will be

A certain organ pipe resonates in its fundamental mode at a frequency of 500 Hz in air. What will be the fundamental frequency if the air is replaced by hydrogen at the same temperature? The density of air is 1.20kgm^-3 and that of hydrogen is 0.089 kgm^-3 .

A wire is stretched between two rigid supports vibrates in its fundamental mode with a frequency of 50 Hz. The mass of the wire is 30 g and its linear density is 4 xx 10^(-2) kg m s^(-1) . The speed of the transverse wave at the string is

Two identical violin strings, when in true and stretched with same tension , have a fundamental frequency of 440.0 H_(Z) . One of the string is retuned by adjusting its tension . When this is done, 1.5 beats per second are heard when both strings are plucked simultaneously. (a) What are the possible fundamental frequencies of the retuned string? (b) by what fractional amount was the string tension changed if it was (i) increased (ii) decreased?

If f_(1) and f_(2) be the fundamental frequencies of the two segments into which a stretched string is divided by means of a bridge , then find the original fundamental frequency f of the complete string.

If f_(1) and f_(2) be the fundamental frequencies of the two segments into which a stretched string is divided by means of a bridge , then find the original fundamental frequency f of the complete string.