Wolfgang Mozart was not only an outstanding composer, but also an excellent violinist. His violin teacher was his father, Leopold, and historical records show that Leopold advised his students to tune all four strings of the violin to the same tension. A typical violin string tension is about 45 N, and the four strings of the violin (Fig. P12.73) are all 0.33 m long. Their lowest standing wave frequencies are 196 Hz (the note G), 294 Hz (D), 440 Hz (A), and 659 Hz (E). If the E string has a mass per unit length ?_E, what are the ratios ?_G/?_E, ?_D/?_E, and ?_A/?_E? (Here, ?_G denotes the mass per unit length of the G string and so forth.)

Figure P12.73

?