SAN FRANCISCO  Like an impatient audience at intermission, Google’s investors are waiting for its second act.

Google continues to dominate in its core business, search advertising, which accounts for more than 90 percent of its revenue. But as Google grows and search becomes increasingly competitive, analysts and investors are beginning to wonder what is next for the company.

In a sign of their impatience, Google’s stock price has sunk 17 percent over the last three months. It fell about 4 percent, to $474, in after-hours trading on Thursday after its announcement that both revenue and net income rose 24 percent in the second quarter, which ended June 30.

The company said its net income rose to $1.84 billion, or $5.71 a share, from $1.48 billion, or $4.66 a share. Excluding the cost of stock options and the related tax benefits, Google’s second-quarter profit was $6.45 a share.