Shorter period, higher frequency

The idea

Frequency and time period are inversely related, ν = 1/T, so a shorter time period means a higher frequency.

Two clocks of sound

Sound A takes 0.5 s for one complete oscillation at a fixed point. Sound B takes 0.1 s for one complete oscillation.

Which sound do you think has the higher frequency?

• Sound B
• Sound A
• They have the same frequency

Pick the period

Choose a time period T. The graph shows one second. The numbers are only examples.

Inverse partners

As the time for one oscillation gets shorter, more oscillations fit into each second. So frequency goes up when the time period goes down. Frequency and time period are inversely related.

Frequency and time period are inversely related: ν = 1/T. A shorter time period means a higher frequency.

Notes

ν = 1/T: frequency and time period are inversely related, so a shorter time period means a higher frequency.

Check yourself

The time period of a sound wave is 0.01 s. What is its frequency, in Hz?

Answer: 100 Hz

ν = 1/T = 1 ÷ 0.01 s = 100 Hz.

A sound has a frequency of 50 Hz. What is its time period, in s?

Answer: 0.02 s

T = 1/ν = 1 ÷ 50 Hz = 0.02 s.

One sound has a time period of 0.1 s and another 0.5 s. Which has the higher frequency?

Which relation links frequency ν and time period T?

• The one with the time period of 0.5 s. A shorter time period corresponds to a higher frequency, and 0.1 s is shorter than 0.5 s.
• The one with the time period of 0.1 s — correct. Yes!
• Both have the same frequency. Frequency is 1/T. Different time periods give different frequencies.
• ν = T. They are inversely related, not equal. The relation is ν = 1/T.
• ν = 2T. Frequency and time period are inversely related, so ν = 1/T, not a multiple of T.
• ν = 1/T — correct. Yes!