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A bugle can be represented by a cylindrical pipe of length L = 1.35 m. Since the ends are...

A bugle can be represented by a cylindrical pipe of length L = 1.35 m. Since the ends are open, the standing waves produced in the bugle have antinodes at the open

ends, where the air molecules move back and forth the most. Calculate the longest three wavelengths of standing waves inside the bugle. Also calculate the three lowest frequencies and the three longest wavelengths of the sound that is produced in the air around the bugle.

Step-by-Step Solution

Solution 1
Step #1 of 4

Express the relation for the speed of sound at the temperature.

Here, is the speed of sound at the temperature, is the speed of the sound, is the temperature of air, and is the temperature at .

Substitute for , for and for to find .

Thus, the speed of sound at the temperature is .

Step #2 of 4

Express the length of the pipe is constructed to produce a fundamental frequency.

Here, is the speed of sound at the temperature, L is the length of the pipe, and is the fundamental frequency.

Rewrite the expression in terms of length.

Substitute for and for to find length of the pipe.

Thus, the length of the pipe is.

Step #3 of 4

Express the relation for the speed of sound at the temperature .

Here, is the speed of sound at the temperature, is the speed of the sound, is the temperature of the overheated building, and is the temperature at .

Substitute for , for and for to find .

Thus the speed of sound at the temperature is .

Step #4 of 4

Express the frequencies of the sound heard.

Here, is the frequency of sound heard, is the speed of sound at the temperature, and L is the length of the pipe.

Substitute for and for L to find .

Therefore, the frequencies of the sound heard is .

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Solutions For Problems in Chapter 16
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