String `I` and `II` have identical and linear mass densities, but string `I` is under greater tension than string `II`. The accompanying figure shows four different situations, `A` to `D`, in which standing wave patterns exist on the two strings. In which situation it is possible that strings `I` and `II` are oscillating at the same resonant frequency ?

The frequency of vibration of a string depends on, (i) tension in the string (ii) mass per unit length of string, (iii) vibrating length of the string. Establish dimension the relation for frequency.

The tension, length, diameter and density of a string B are double than that of another string A. Which of the following overtones of B is same as the fundamental frequency of A?

The tension, length, diameter and density of a string B are double than that of another string A. Which of the following overtones of B is same as the fundamental frequency of A?

Column I shows different sets of standing waves in a string of length L whose ends are fixed or free according to respective figure and Column - II shows possible equations for them where symbols have usual meaning

A long string is constructed by joining the ends of two shorter strings. The tension in the strings is the same but string I has 4 times the linear mass density of string II. When a sinusoidal wave passes from string I to string II:

Figure shows different standing wave patterns on a string of linear mass density 4.0 xx 10^-2 kg//m under a tension of 100 N. The amplitude of antinodes is indicated in each figure. The length of the string is 2.0m. (i) Obtain the frequencies of the modes shown in figures (a) and (b). (ii)Write down the transverse displacement y as a function of x and t for each mode. (Take the initial configuration of the wire in each mode to be as shown by the dark lines in the figure).