It depends on the context. If you are talking about tones, 一声 is the short for 第一声. For other context, it is not the short form but "a/one sound". For example, 雨天一声雷, a clash of thunder on a rainy day. 传来一声, a sound came

In Chinese, sequence numbers can appear in these ways: (1) 第一声 (2) 一声 (3) 习题7 Difference between （1）and (2) : 第一声is more offical. When the breviation is not to cause confusion, 第一（二...）* is often cut into 一（二...）*. 第一号文件---> 一号文件. By contrast, when 第一* and 一* have different meanings, the abbreviation is not allowed. 我吃了第三个苹果 VS 我吃了三个苹果. ( When the abbreviation is possible? I'd rather not discuss here.) Why the abbreviation: the rhythm. Chinese language requires a lot in thythm and symmetry, the basic foot is two syllables. 一 /衣带水 ==> 一衣 /带水. Less frequent foots are monosyllable and trisyllable. Succesive two one-one syllables are often combined into a so-called 'phonological word' bisyllable. An odd monosyllable is often treated in two ways: 1. if it has an accent, lenthen its sound so that it's as long as a bisyllble，and correspondingly shorten the sound of each of the immediate two syllables. 长（-）头发 东方朔（-） . 2. if it does not has any accent, shorten its sound so that the trisyllable sounds like a bisyllable in the length. 不（得）不 ， 小（不）点， 红（-）苹果，红（苹果） So which syllables have accents? (1) those you are puttin emphasis on (2) the core elements in the words ------- And so forth, and so forth

In Chinese, sequence numbers can appear in these ways: 第一声，一声 Difference: 第一声is more offical. Why the abbreviation: the rhythm. Chinese language requires a lot in thythm and symmetry, the basic foot is two syllables. 一 /衣带水 ==> 一衣 /带水. Less frequent foots are monosyllable and trisyllable. Succesive two one-one syllables are often combined into a so-called 'phonological word' bisyllable. An odd monosyllable is often treated in two ways: 1. if it has an accent, lenthen its sound so that it's as long as a bisyllble，and correspondingly shorten the sound of each of the immediate syllables. 长（-）头发 东方朔（-） . 2. if it does not has any accent, shorten its sound so that the trisyllable sounds like a bisyllable in the length. 不（得）不 ， 小（不）点，

In this case, I think it is simply an abbreviation, but the word 第 typically indicates the place in an order; by which I mean 1st, 2nd, 3rd as opposed to one, two, three. Without the 第, a number plus a counter will indicate a quantity of that object.

Is it slang, or...? Why is it shortened like that?