Traditionally, the efficiency and effectiveness of search systems have both been of great interest to the information retrieval community. However, an in-depth analysis on the interplay between the response latency of web search systems and users' search experience has been missing so far. In order to fill this gap, we conduct two separate studies aiming to reveal how response latency affects the user behavior in web search. First, we conduct a controlled user study trying to understand how users perceive the response latency of a search system and how sensitive they are to increasing delays in response. This study reveals that, when artificial delays are introduced into the response, the users of a fast search system are more likely to notice these delays than the users of a slow search system. The introduced delays become noticeable by the users once they exceed a certain threshold value. Second, we perform an analysis using a large-scale query log obtained from Yahoo web search to observe the potential impact of increasing response latency on the click behavior of users. This analysis demonstrates that latency has an impact on the click behavior of users to some extent. In particular, given two content-wise identical search result pages, we show that the users are more likely to perform clicks on the result page that is served with lower latency.