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?

When we speak, our voices are not made up of single, pure tones. Instead, the human voice creates complex signals constituted by a combination of several frequencies. The lowest of these frequencies is called the fundamental frequency, which is most often recognized as the 'pitch' of the voice. But, what gives the voice its unique timbre, the distinct quality that allows us to differentiate one person's voice from another, are the harmonics—also known as overtones.

Harmonics are integral multiples of the fundamental frequency. For example, if a person's speaking voice has a fundamental frequency of 100 Hz, the voice also contains harmonics at 200 Hz, 300 Hz, 400 Hz, and so on. These higher frequencies add richness and clarity to the voice. They are essential for phonetic sounds, such as the crispness of consonants and the fullness of vowels, contributing heavily to speech intelligibility.

Even if the lower frequencies are not heard, our brain can use these harmonics to infer the entire speech signal. The resilience and capability of our auditory processing explain why, even with some information missing, we can still understand speech. It's like fitting the pieces of a puzzle together; our brain can fill in the blanks.

When it comes to telecommunication, the standard range of audio frequency that traditional landline telephones transmit—300 Hz to 3400 Hz—was determined by the bandwidth limitations and the need for economic use of the available frequencies on telephone networks. This range, commonly referred to as the voiceband, was established to preserve the most critical elements for speech comprehension while simultaneously keeping the demands on the system reasonable.

The science behind this designated range takes advantage of the human voice's nature. Our voices produce energy across a broad spectrum of frequencies, but the majority of the vocal energies that are essential for understanding speech are within this telephone frequency range. By excluding frequencies outside of this range that contribute less to understanding human speech, telephone systems historically have been able to maximize efficiency.

Modern digital systems have allowed for broader ranges, enabling higher fidelity voice transmission, because digital systems can effectively compress and decompress the audio frequencies without the same physical limitations as the older analog systems.

Speech intelligibility is essentially how easily and clearly speech can be understood. It's a crucial aspect of communication and deals directly with the listener's ability to recognize the words and sentences being spoken. Many factors influence speech intelligibility, including the presence and strength of harmonics in the speaker's voice, the transmission medium, and the listening conditions.

While the presence of low-frequency tones (below 300 Hz), like the fundamental frequency of a deep voice, may enrich the sound, high-frequency harmonics play a more pivotal role in the clarity of speech. Articulation of consonant sounds, which contribute greatly to the intelligibility of speech, primarily relies on these higher frequencies. Telephone systems emphasize this range to capitalize on this principle, ensuring that, even if the deeper tones of a voice aren't transmitted, the message being conveyed remains understandable.

Our brains are adept at piecing together familiar language patterns from partial information. This adaptability is a testament to the complexity and efficiency of human language processing. The optimization of the audio frequency range in telecommunications harnesses our natural linguistic abilities, ensuring clear and comprehensible conversations, even over the constrained medium of early telephone technology.