8. What is the frequency heard by a person driving at 18 m/s toward a blowing factory whistle (600 Hz) if
the speed of sound is 340.6 m/s?

631.7 Hz

Explanation:

The Doppler effect is a phenomenon that occurs when there is relative motion between an observer and a source of a wave. When this occurs, the is a change in the apparent frequency of the wave, as observed by the observer.

In particular, the new apparent frequency can be calculated as:

where

f is the real frequency

f' is the apparent frequency

v is the speed of the wave

is the velocity of the observer (positive if the observer is moving towards the source, negative if moving away)

is the velocity of the source (negative if the source is moving towards the observer, positive if moving away)

In this problem:

v = 340.6 m/s is the speed of the sound wave

f = 600 Hz is the real frequency of the sound

is the velocity of the person

is the velocity of the source

Substituting, we find:

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.

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