Answer :
The new frequency of a violin string shortened from 33 cm to 30 cm, initially vibrating at 260 Hz, is calculated to be 286 Hz using the inverse proportionality between frequency and length.
The frequency of a violin string is inversely proportional to its length. A string that is 33 cm long vibrates at a frequency of 260 Hz. If the string is shortened to 30 cm, to find the new frequency of vibration, we use the concept that frequency (f) is inversely proportional to the length (L), i.e., f \\u221d 1/L. This implies that [tex]f_1[/tex] \\u00d7 [tex]L_1[/tex] = [tex]f_2[/tex] \\u00d7 [tex]L_2[/tex], where [tex]f_1[/tex] and [tex]L_1[/tex] are the initial frequency and length, and [tex]f_2[/tex] and [tex]L_2[/tex] are the final frequency and length, respectively.
By substituting the given values into the formula, we get:
260 Hz \\u00d7 33 cm = [tex]f_2[/tex] \\u00d7 30 cm
Therefore, [tex]f_2[/tex] = (260 Hz \\u00d7 33 cm) / 30 cm = 286 Hz
Thus, the new frequency when the string is shortened to 30 cm is 286 Hz.
