Practice Frequency in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

The number of complete wave cycles passing a fixed point per second, measured in hertz (Hz).

Frequency counts how many complete cycles occur per unit of the horizontal axis — higher frequency means the wave oscillates more rapidly in the same space or time.

Showing a random 20 of 76 problems.

Example 1

medium
Write a cosine model with amplitude 22 and period 66, where tt is the variable.

Example 2

easy
Find the period of y=sin⁡(6x)y = \sin(6x).

Example 3

medium
Find the period of y=sin⁡(3x)+cos⁡(3x)y = \sin(3x) + \cos(3x).

Example 4

easy
A wave completes 55 cycles per second. What is its frequency?

Example 5

medium
Two waves have frequencies 33 Hz and 66 Hz. How do their periods compare?

Example 6

easy
Find the period of y=cos⁡(5x)y = \cos(5x).

Example 7

medium
A pendulum makes 3030 swings in 1515 s. Find its frequency and period.

Example 8

medium
What is the angular frequency ω\omega of a wave with frequency 10 Hz10 \text{ Hz}?

Example 9

medium
A wave has wavelength 2.5 m2.5 \text{ m} and frequency 120 Hz120 \text{ Hz}. Find its speed.

Example 10

medium
Frequency is f=0.25f = 0.25 Hz. Find the period.

Example 11

medium
Angular frequency ω=10π\omega = 10\pi rad/s. The frequency is ___ Hz.

Example 12

easy
A wave has period T=0.1T = 0.1 s. Find its frequency.

Example 13

easy
Which has a shorter period: y=sin⁡(x)y = \sin(x) or y=sin⁡(3x)y = \sin(3x)?

Example 14

medium
Find the period of y=sin⁡(πx)+cos⁡(πx)y = \sin(\pi x) + \cos(\pi x).

Example 15

hard
Two tones sin⁡(2π⋅200t)\sin(2\pi \cdot 200 t) and sin⁡(2π⋅203t)\sin(2\pi \cdot 203 t) are heard together. What is the beat frequency?

Example 16

easy
What is the period of y=sin⁡(πx/2)y = \sin(\pi x / 2)?

Example 17

challenge
Two waves of frequencies 498 Hz498 \text{ Hz} and 502 Hz502 \text{ Hz} are superimposed. How many beats per second are heard, and what is the average tone frequency?

Example 18

easy
Find the frequency (in cycles per unit) of y=sin⁡(2πx)y = \sin(2\pi x).

Example 19

easy
Convert 1 kHz1 \text{ kHz} to hertz.

Example 20

medium
A pendulum swings with period 0.250.25 s. Find its frequency.
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