Properties of waves: T = ¹

The idea

The statement 'T = ¹' is a typographical error in the specification extraction for the period–frequency relationship, T = 1 / f. Period (T) is the time for one complete wave cycle, measured in seconds (s); frequency (f) is the number of cycles per second, measured in hertz (Hz). The two quantities are reciprocals, so f = 1 / T as well. For example, a wave of frequency 2 Hz completes two cycles each second, giving T = 1 ÷ 2 = 0.5 s. A wave with period 0.01 s has f = 1 ÷ 0.01 = 100 Hz. When using this equation, always convert milliseconds to seconds, and check that a high frequency gives a short period.

What earns the marks

• Identify that the statement T = ¹ is a typographical error for the equation T = 1 / f, relating period and frequency.
• State that period is measured in seconds (s) and frequency in hertz (Hz).
• Rearrange between T = 1 / f and f = 1 / T as required by the question.
• Substitute numerical values with consistent units, converting ms to s, and state the answer with its unit.
• Check the result for physical sense, for example a frequency of 100 Hz giving a period of 0.01 s.

Common mistakes and how to put them right

• Treating the typographical error T = ¹ literally.

  Put it right by recalling the actual equation is T = 1 / f.

• Using T = f or T = 1 × f.

  Put it right by recalling that period and frequency are reciprocals.

• Mixing units, such as substituting 50 ms as 50 s.

  Put it right by converting to seconds first, so 50 ms = 0.050 s.

Exam tips

• Write the correct relationship in full as T = 1 / f before doing any calculation, ignoring the typographical error in the specification.
• Include the unit with every substituted value and with the final answer to secure accuracy.
• Use an inverse check: multiply your calculated period by the frequency; the product should be 1.