"An airplane traveling at one third the speed of sound (i. e., 114 m/s) emits a sound of frequency 3.65 kHz. At what frequency does a stationary listener hear the sound as the plane approaches? Answer in units of kHz."

Explanation:

velocity of source, Vs = 114 m/s

original frequency, f = 3.65 kHz

velocity of observer , Vo = 0 m/s

velocity of sound, v = 334 m/s

let the frequency is f'.

The formula for the doppler effect is given by

where, v is the velocity of sound.

f' = 5.54 kHz

i think it because equal matrices have equal dimensions, only square matrices can be symmetric. for all indices and . every square diagonal matrix is symmetric, since all off-diagonal elements are zero. in linear algebra, a real symmetric matrix represents a self-adjoint operator over a real inner product space.