Answer the following questions.

An Application CLASSROOM EXAMPLE 5 Analyzing Pressures of Upper Harmonics Suppose that the A key above middle C is played on a piano. Its fundamental frequency 1s f, =440 Hz, and its associated pressure is expressed as =0.002sin880t. The string will also vibrate at f, =880, , =1320, f, =1760, f, =2200,... Hz. The corresponding pressures of these upper harmonics are as follows. P, =292 i 1760mr, P, = 222 in 2640, ; : 002 . P, = A sin3520z, and P, = it sin 44007zt The graph of g p ( msww:w:ovnom\ s P=P+P+P+P+P, shown in the figure, is \"saw-toothed.\" . - {}.005 (a) Approximate the minimum value of P. (b) At what values of f = x does this minimum occur over the interval [0, 0.01]