What is a logarithmic scale?
Q: What is a logarithmic scale?
A: A logarithmic scale is a scale used when there is a large range of quantities.
Q: What are some examples of things that can be measured on a logarithmic scale?
A: Earthquake strength, sound loudness, light intensity, spreading rates of epidemics, and pH of solutions can all be measured on a logarithmic scale.
Q: How is a logarithmic scale different from a standard linear scale?
A: A logarithmic scale is based on orders of magnitude, rather than a standard linear scale. The value of each mark on the scale is the value at the previous mark multiplied by a constant.
Q: What is the benefit of using a logarithmic scale?
A: The logarithmic scale can reduce a large range of values to a more manageable range, which can be helpful when dealing with data that covers a wide range of values.
Q: What is Stevens' power law and how does it relate to logarithmic scales?
A: Stevens' power law describes how some of our senses operate in a logarithmic fashion, where multiplying the actual input strength adds a constant to the perceived signal strength. This makes logarithmic scales for these input quantities especially appropriate.
Q: Why is a logarithmic scale particularly useful for measuring sound loudness?
A: Our sense of hearing perceives equal multiples of frequencies as equal differences in pitch, so a logarithmic scale can accurately represent this relationship between sound frequency and perceived loudness.
Q: What is the relationship between small multiples of the underlying quantity and the logarithmic measure on most logarithmic scales?
A: On most logarithmic scales, small multiples (or ratios) of the underlying quantity correspond to small (possibly negative) values of the logarithmic measure.
