By touching a string lightly at its center while bowing, a violinist can produce a note exactly one octave above the note to which the string is tuned—that is, a note with exactly twice the frequency. Why is this possible?

Solution 22DQ Introduction We have to discuss how by touching at the middle of the string, the violinist produce sound that has frequency double to the initial frequency. Step 1 If you touch at the middle of the string, the effective length of the string becomes half of the initial length. Now since the wavelength of the wave is directly proportional to the length of the string ( = 2L), the wavelength will also be half of the initial wavelength. Now the frequency of the wave is f = Since the speed of wave c is constant, the wavelength is inversely proportional to the wavelength of the wave. Hence if the wavelength is halved, the frequency will be doubled.