Chapter 6: Problem 35

Normal telephones do not transmit pure tones with frequencies below about \(300 \mathrm{~Hz}\). But a person whose speaking voice has a frequency of \(100 \mathrm{~Hz}\) can be heard and understood over the phone. Why is that?

Short Answer

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Answer: A person with a 100 Hz speaking voice can be heard and understood over a normal telephone because the telephone can transmit the higher harmonics of the voice that fall within the audible frequency range (300 Hz to 3,400 Hz). These higher harmonics contain enough information to reconstruct an understandable approximation of the original voice, even without the fundamental frequency.

Step by step solution

Understanding pure tones and harmonics

A pure tone is a sound wave with a single frequency, and it can be represented as a sine wave. When a person speaks, they produce multiple frequencies simultaneously, which are known as harmonics. Harmonics are multiples of a fundamental frequency. In the case of the person with a 100 Hz speaking voice, the harmonics would be integer multiples of 100 Hz.

Identify the audible range of frequencies for normal telephones

Normal telephones can transmit frequencies ranging from about 300 Hz to 3,400 Hz. This means that while the phone cannot transmit the fundamental frequency of the person's voice (100 Hz), it can transmit the higher harmonics of the voice, which fall within this range.

Relate harmonics to voice recognition

When a person's voice is transmitted over the telephone, the harmonics serve as the building blocks to reconstruct an approximation of the original voice. Since the higher harmonics contain information about the original voice, even if the fundamental frequency is below the transmitting range, the voice can be reconstructed and understood by the listener.

Determine which harmonics are involved in this case

For the person with a 100 Hz speaking voice, the first harmonic (fundamental frequency) cannot be transmitted. However, the third harmonic (3 x 100 Hz = 300 Hz), fourth harmonic (4 x 100 Hz = 400 Hz), and all other higher harmonics within the transmission range would be transmitted. These higher harmonics are sufficient to create an understandable voice for the listener.

Conclusion

In summary, a person with a speaking voice of 100 Hz can be heard and understood over a normal telephone because the telephone can transmit the higher harmonics of the voice, which are within the audible frequency range. These higher harmonics contain enough information to reconstruct an understandable approximation of the original voice, even without the fundamental frequency.

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Normal telephones do not transmit pure tones with frequencies below about \(300 \mathrm{~Hz}\). But a person whose speaking voice has a frequency of \(100 \mathrm{~Hz}\) can be heard and understood over the phone. Why is that?

Short Answer

Step by step solution

Understanding pure tones and harmonics

Identify the audible range of frequencies for normal telephones

Relate harmonics to voice recognition

Determine which harmonics are involved in this case

Conclusion

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