Properties of Sound Waves
Simple Explanation
A sound wave is described by its amplitude (loudness), frequency (pitch, in Hz), and wavelength (the physical length of one complete wave cycle) β connected by the wave equation v=fΞ».
Why Do We Need It?
These three properties β amplitude, frequency, and wavelength β are the basic vocabulary for describing and analyzing any sound wave, and the wave equation is the tool that connects them to the wave's speed.
See It
A sine curve showing one full wave cycle, with the wavelength marked as the horizontal distance between two consecutive crests, and the amplitude marked as the height from the centerline to a crest
Formula
The Wave Equation
v = fΞ»
A wave's speed equals its frequency times its wavelength β how many complete waves pass a point each second, multiplied by the length of each one.
- v
- β wave speed, in metres per second (m/s)
- f
- β frequency, in hertz (Hz)
- Ξ»
- β wavelength, in metres (m)
When to use it: Whenever relating a sound wave's speed, frequency, and wavelength β given any two, the third can be found.
Worked Example
Find the wavelength of a sound wave
A sound wave travels at 340 m/s with a frequency of 170 Hz. Find its wavelength.
Why Does This Work?
In one second, f complete waves pass a fixed point, and each wave is Ξ» metres long β so the total distance the disturbance covers in that one second (its speed) is exactly f times Ξ», which is the wave equation.
Real-Life Example
Why bass notes need larger speakers
Low-pitched (bass) sounds are produced by larger speaker woofers, while high-pitched sounds come from small tweeters.
Low frequency means a long wavelength (since v=fΞ», with v roughly fixed, small f means large Ξ») β larger speaker cones move more air to effectively generate these longer sound waves.
Practice
A sound wave travels at 340 m/s with a frequency of 680 Hz. Find its wavelength.
MediumCommon mistake
Confusing amplitude with wavelength β amplitude determines LOUDNESS (how much energy the wave carries), while wavelength (together with frequency) determines PITCH; the two are entirely independent properties.
Quick Review
- v = fΞ» β the wave equation.
- Amplitude: loudness. Frequency: pitch. Wavelength: physical length of one cycle.
- Amplitude and wavelength/frequency are independent properties.