We describe a simple terahertz (THz) time domain spectrometer with a bandwidth extending up to 7.5 THz. We show that by keeping the generation and detection crystals close to each other a high signal-to-noise ratio (SNR) can be achieved without using lock-in detection and dry nitrogen flushing. The observed spectra show very good agreement with the spectra calculated based on a simple model which includes phase matching and absorption in the generation and detection crystals. Using this set-up we have measured the absorption lines in D-tartaric acid from 0.5 THz up to 7 THz. We show that the high frequency region > 3 THz is the better choice to measure small changes in the water content of a hygroscopic sample compared to the low frequency region.