A string has length \(0.90\,\mathrm{m}\). Find the wavelength of its fundamental mode.

If the fundamental frequency of a string is \(110\,\mathrm{Hz}\), what is the second-harmonic frequency?

A string supports waves at \(150\,\mathrm{m\,s^{-1}}\) and has length \(0.75\,\mathrm{m}\). Find the third-harmonic frequency.

How many interior nodes does the \(n=5\) mode of a string fixed at both ends have?

A string has \(f_1=80\,\mathrm{Hz}\). A standing wave is observed at \(320\,\mathrm{Hz}\). What mode number is this?

Two strings carry waves at the same speed. String B is twice as long as string A. Compare their fundamental frequencies.

String A has length \(L\) and string B has length \(2L\). The wave speed is the same in both strings. Find a pair of nonzero mode numbers \((n_A,n_B)\) for which the two strings can share the same normal-mode frequency.

Two strings have lengths \(L_A\) and \(L_B\) and wave speeds \(v_A\) and \(v_B\). Derive the condition relating mode numbers \(n_A\) and \(n_B\) for the two strings to have equal normal-mode frequencies.