Validate string input from from console

#include <iostream>
#include <string>
using namespace std;

// Receive input from the user. If it starts with a vowel,
// store the word. If not, ask to re-enter the input.

// This function takes a character and returns
// true if it is a vowel. Otherwise, it returns false.
int is_vowel(char letter)
{
    // The character must be one of these.
    string vowels = "AaEeIiOoUu";

    // Go from the beginning to the
    // end of the list of vowels.
    for (size_t i = 0; i < vowels.size(); ++i)
    {
        // If the letter matches that vowel.
        if (letter == vowels[i])
        {
            // The letter is a vowel.
            return true;
        }
    }

    // The letter didn't match any vowel.
    return false;
}

int main()
{
    string input; // User input.

    cout << "Enter a word that starts with a vowel:" << endl;
    getline(cin, input); // Get the user's input.

    char first_letter = input[0]; // Get the first letter.
    bool valid = is_vowel(first_letter); // Test the first letter.

    while (!valid) // While the letter is not a vowel,
    {
        cout << "Your word doesn't start with a vowel.\n";
        cout << "Please enter a word that starts with a vowel:" << endl;
        getline(cin, input); // Get new input.
        first_letter = input[0]; // Get the first letter.
        valid = is_vowel(first_letter); // Test the first letter.
    }

    cout << "Thank you!";

    return 0;
}