There are complex interactions between tape speed, track width, frequency response, and dynamic range. This article is an attempt to summarize the major influences.
Track Width
Track width primarily influences dynamic range. Since the noise generated by tape is totally random, each time the track width doubles, the noise only goes up by 3 decibels. That same doubling causes the signal to go up by 6 decibels, so each doubling of the track width provides a 3 decibel improvement in dynamic range.
Another factor with track width is that the wider tracks have fewer “micro dropouts” or “grain noise” from the roughness of the tape particles.
Also, wider tracks provide greater protection against dropouts caused by physical damage.
Finally, track width may negatively impact frequency response at lower speeds. As the track width increases, holding high-frequency losses due to azimuth wander to a minimum becomes more difficult. For a discussion of azimuth, please see this article “Azimuth: Hows and Whys” (click here) in this blog. This writer has found that many 7.5 in/s full track 1/4-inch tapes reproduce better with a narrower reproduce head than the track width. Using a full-track head on these tapes results in a periodic high-frequency loss that is very noticeable and cannot be easily corrected.
Speed
Higher speed will provide better high-frequency response within reason. There are two factors relating to this: tape thickness loss and gap loss. Both are important at lower frequencies and gap loss becomes less of an issue at professional speeds (15 and 30 in/s). Dale Manquen has treated this extensively in “Handbook for Sound Engineers”. I will not try to summarize this here.
Higher speed also produces a corollary loss called “head bumps” in the low frequency. This too is related to the ratio of the wavelength to the length of the tape pole pieces and the tape contact with the pole pieces. Generally, 30 in/s low frequency reproduction is inferior to 15 in/s low frequency reproduction.
Higher speeds also average out the irregularities in the tape better than lower speeds.
Higher speeds also tend to have better dynamic ranges, but this is very dependent on the equalization selected. Jay McKnight has discussed this in various papers. I would suggest starting with ” Tape Recording Equalization Fundamentals and 15 in/s Equalizations“.