   Chapter 14, Problem 78AP

Chapter
Section
Textbook Problem

A flute is designed so that it plays a frequency of 261.6 Hz, middle C, when all the holes are covered and the temperature is 20.0°C. (a) Consider the flute to be a pipe open at both ends and find its length, assuming the middle-C frequency is the fundamental frequency. (b) A second player, nearby in a colder room, also attempts to play middle C on an identical flute. A beat frequency of 3.00 beats/s is heard. What is the temperature of the room?

(a)

To determine
The length of the flute plays under the fundamental frequency.

Explanation

Given Info: The temperature is 20.0°C .

Formula to calculate the speed of the sound is,

v=(331m/s)T273K

• T is the temperature.

Substitute 20.0°C for T.

v=(331m/s)(20+273K)273K=343m/s

The relation between the frequency and wavelength is,

λ=vf

• λ is the fundamental wavelength

(b)

To determine
The temperature of the room.

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