4PH1

Sound

Waves

Exam Frequency Analysis

Past paper frequency (2018 to 2024)

This topic accounts for approximately 7% of your exam marks.

stable
Low
Stable7%

Speed of sound calculations, echo timing and ultrasound uses are standard shorter questions.

Longitudinal sound wave from a loudspeaker: air particles bunch into compressions and spread into rarefactions travelling towards an ear, with a sine curve above showing the matching pressure variation and one wavelength spanning the distance between adjacent compressions.
Source: CPT Sound Physical Manifestation by Wikimedia Commons

What an oscilloscope shows

  • An oscilloscope is an instrument that draws a graph of a rapidly changing voltage against time
  • A microphone converts the longitudinal vibration of air into a varying voltage, so connecting a microphone to an oscilloscope lets you "see" a sound wave on the screen
  • The displayed trace looks like a transverse wave, even though the underlying sound is longitudinal, because the screen is plotting voltage (y) against time (x), not the back-and-forth motion of air particles

Reading the trace

  • The time base sets the x-axis: how many milliseconds (or microseconds) correspond to each horizontal division on the screen
  • The y-gain sets the y-axis: how many millivolts correspond to each vertical division
  • Two quantities are read directly off a frozen trace:
    • Amplitude: the vertical height of a peak measured from the centre line; a louder sound gives a taller trace
    • Period (T): the horizontal distance between two corresponding points on the wave (peak to peak is easiest); a higher-pitched sound gives a shorter horizontal gap
  • Once T is known, the of the sound is f = 1 / T
  • A higher-frequency sound fits more wave cycles across the same width of screen
Oscilloscope trace of a single sine wave: a vertical arrow marks the amplitude measured from the centre line to a peak, and a horizontal arrow marks one time period T between corresponding points, with the time base setting the horizontal scale.
Source: Sound & Oscilloscopes by Save My Exams
Worked example

Finding frequency from an oscilloscope trace

A sound wave is displayed on an oscilloscope. One full cycle spans 5 squares horizontally, and the time-base is set to 2 ms per division.

Solution:

  • Period: T = 5 × 2 ms = 10 ms = 0.010 s
  • Frequency: f = 1 / T = 1 / 0.010 = 100 Hz