   Chapter 14, Problem 67P

Chapter
Section
Textbook Problem

A student holds a tuning dork oscillating at 256 Hz. He walks toward a wall at a constant speed of 1.33 m/s. (a) What beat frequency does he observe between the tuning fork and its echo? (b) How fast must he walk away from the wall to observe a beat frequency of 5.00 Hz?

(a)

To determine
The beat frequency of the observer between the tuning fork and its echo.

Explanation

Given Info: The wall is stationary observer that receiving sound from an approaching source of velocity is va.

The frequency received and reflected by the wall is,

fref=fs[vvva] (1)

• fref is the frequency of the reflected sound,
• fs is the frequency of the source,
• v is the speed of the sound,
• va is the speed of the receiving sound,

Consider the wall as a stationary source emitting sound of frequency fref to an observer approaching at velocity is va .

The frequency of the echo heard by the observer is,

fecho=fref(v+vav) (2)

• fecho is the frequency of the echo,

Use equation (1) in equation (2) to find fecho

fecho=fs(vvva)(v+vav)=fs(v+vavva) (3)

Thus, the expression for the frequency of the echo heard by the observer is fs(v+va/vva)

(b)

To determine
the speed of the student moves away from the wall to observe a beat frequency.

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