Sound Waves and Ultrasound
Sound is a longitudinal wave, meaning the vibrations of particles are parallel to the direction the wave travels, produced by a vibrating source and transmitted through a medium (solid, liquid or gas) as a series of compressions and rarefactions; sound cannot travel through a vacuum. Like all waves, sound obeys wave speed = frequency x wavelength (v = f x lambda), and the human ear can typically detect frequencies between about 20 Hz and 20000 Hz; ultrasound refers to sound waves with frequencies above 20000 Hz (20 kHz). Calculating wave speed, frequency and wavelength for sound, using an oscilloscope trace to find frequency and amplitude, and applications of ultrasound in medical imaging and industrial flaw detection extend beyond the core GCSE course with quantitative echo-timing (depth) calculations.
Before you start
Make sure you're comfortable with these topics first:
Method
- Recall that sound is a longitudinal wave: the particles of the medium vibrate back and forth parallel to the direction of energy transfer, creating regions of compression (particles close together) and rarefaction (particles spread apart).
- Use v = f x lambda to calculate wave speed, frequency or wavelength, rearranging as needed, keeping speed in m/s, frequency in Hz and wavelength in metres.
- For an oscilloscope trace, read the time taken for one complete wave (the period) from the horizontal (time) axis and the timebase setting, then calculate frequency using frequency = 1 / period.
- Read the amplitude of a sound wave from the oscilloscope trace as the maximum height of the trace from the centre line, and relate a larger amplitude to a louder sound and a higher frequency to a higher pitch.
- For echo or ultrasound distance calculations, use the fact that the pulse travels to the reflecting surface (or boundary) and back, so distance = (wave speed x time) / 2, being careful to halve the total travel time or total distance as needed.
- For ultrasound applications, explain that ultrasound partially reflects at a boundary between two different materials (for example tissue and bone) because of the change in density, and the time delay of each reflected pulse is used to calculate depth and build up an image.
Worked example
An ultrasound pulse is sent from a transducer toward a boundary inside a patient's body and the reflected pulse returns after 0.080 ms. The speed of ultrasound in the tissue is 1500 m/s. Calculate the depth of the boundary below the transducer.
- Convert the time to seconds: 0.080 ms = 0.080 / 1000 = 0.000080 s (8.0 x 10^-5 s).
- Recognise that this time is for the pulse to travel to the boundary and back again, so the time for one-way travel is half of this: 0.000080 / 2 = 0.000040 s (4.0 x 10^-5 s).
- Use distance = speed x time for the one-way journey: distance = 1500 x 0.000040.
- Calculate: 1500 x 0.000040 = 0.060.
- State the final answer with its unit: the boundary is 0.060 m (6.0 cm) below the transducer.
Practice questions
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Q1State whether sound is a longitudinal or a transverse wave.Show answer
Answer: Longitudinal.
Q2State why sound cannot travel through a vacuum.Show answer
Answer: Sound needs particles of a medium to vibrate and pass the wave on; a vacuum has no particles.
Q3A sound wave has a frequency of 400 Hz and a wavelength of 0.85 m. Calculate its speed. Use v = f x lambda.Show answer
Answer: 340 m/s (400 x 0.85).
Q4State the typical range of frequencies audible to a healthy human ear.Show answer
Answer: About 20 Hz to 20000 Hz (20 kHz).
Q5State what is meant by ultrasound.Show answer
Answer: Sound waves with a frequency above 20000 Hz (20 kHz), above the upper limit of human hearing.
Q6An oscilloscope trace shows one complete wave taking 0.0025 s. Calculate the frequency of the sound. Use frequency = 1/period.Show answer
Answer: 400 Hz (1/0.0025).
Q7State one medical use of ultrasound.Show answer
Answer: Prenatal scanning (imaging a fetus in the womb), or breaking up kidney stones, or measuring blood flow.
Exam-style questions
Written in the style of a IGCSE Science exam paper, with a full mark scheme.
An ultrasound pulse travels through soft tissue at a speed of 1540 m/s and reflects from a boundary 0.077 m below the skin. Calculate the total time between the pulse being sent and the reflected pulse being detected.
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Describe how ultrasound is used to produce an image of internal organs during a medical scan, including how depth information is obtained and why ultrasound, rather than X-rays, is generally used to image a fetus during pregnancy.
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Free printable worksheet
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This topic is chapter 27 of IGCSE Science Workbook, the whole course as one free printable PDF.
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