Humans locate the origin of a sound with several cues. One technique employs the small difference in the time taken for the sound to reach either ear; this is known as the interaural time delay (ITD).

Lord Rayleigh investigated this phenomena, assuming a spherical head with radius a, and sound waves arriving at an azimuth angle .

Sound has to travel a distance  further to reach the left ear than the right ear. Hence, if the speed of the sound is c, then the interaural sound delay is

where c is the speed of sound.

For c = 343 m s^-1, a = 0.11 m and  = 0.5 (that is, a sound hitting a typical-sized head from the side), the sound delay is about 0.8 ms.

This application modifies a single-channel audio file so that the sound appears to originate at an angle from the observer. It does this by introducing an extra channel of sound. The new channel is equivalent to the old channel, but is padded with zeroes.

Despite both channels having the same amplitude, the sound appears to come from an angle simply by delaying one channel.

Speed of sound in m s^-1

Radius of head in m

Angle of sound

Read sound file and calculate statistics

Interaural time delay

Hence we need to delay one channel by this number of samples

× Sign in to Your Maplesoft Account Wrong Email/Password. Please try again. Email Address: Password: Keep me signed in Forgot your password? Create a New Account Cancel Sign in × Register Your Maplesoft Account * First Name Required * Last Name Required * E-Mail Address Required * Invalid E-Mail Address (i.e. user@domain.com) * Company Required * Title Required Select the option that best describes you Academic Commercial Government Student * Segment Required -- Select Country -- * Country Selection Required Country selection required * Region Selection Required * Password Required * Re-entering Password Required * The Passwords entered do not match I agree to the Terms and Conditions of the Maplesoft.com web site. I acknowledge and agree that, in order to process my request, Maplesoft will collect my personal information, including my name, address and email address, share it with third party organizations, and store it at Maplesoft’s headquarters in Canada. For a full list of third parties, please see our detailed privacy policy. Submit