The question asks us to identify the correct phonetic symbol for the underlined sound in the words "Thin", "Method", and "Author". The underlined sound in all these words is the 'th' sound.

Understanding the 'th' Sound Phonetic Symbol

In English phonetics, the International Phonetic Alphabet (IPA) is used to represent sounds accurately. The 'th' sound can actually represent two different sounds:

• A voiceless sound, as in "thin", "method", "author".
• A voiced sound, as in "this", "mother", "with".

The words provided - "Thin", "Method", and "Author" - all contain the voiceless 'th' sound. To produce this sound, you place your tongue between your teeth and push air through without vibrating your vocal cords.

Identifying the Correct Phonetic Symbol

The phonetic symbol used in the IPA for the voiceless dental fricative, which is the 'th' sound found in words like "Thin", "Method", and "Author", is the Greek letter theta.

Let's look at the given options:

• Option 1: θ
• Option 2: t∫
• Option 3: F
• Option 4: ^

The symbol θ directly corresponds to the voiceless 'th' sound in phonetics. Therefore, this is the correct phonetic symbol for the underlined sounds in "Thin", "Method", and "Author".

Other options represent different sounds:

• t∫ represents the 'ch' sound (voiceless post-alveolar affricate), as in "church".
• F represents the 'f' sound (voiceless labiodental fricative), as in "fun".
• ^ (caret or wedge) represents the 'uh' sound (near-open central unrounded vowel), as in "cut" or "up".

Conclusion

Based on the analysis of the sounds in "Thin", "Method", and "Author", the underlined 'th' sound is the voiceless dental fricative, which is represented by the phonetic symbol θ.