In Figure 5.12, the solid line indicates the just noticeable distortion (JND) curve and the dott

In Figure 5.12, the solid line indicates the just noticeable...

Key Concepts

Thresholds in Auditory Perception

Analyzing thresholds like the absolute threshold and the JND provides insight into how the auditory system processes sounds. By comparing sounds against these thresholds, it becomes possible to predict whether a sound will be audible or masked in a given acoustic scenario.

Auditory Masking

Auditory masking occurs when the presence of one sound makes it difficult or impossible to hear another sound that is nearby in frequency or intensity. This concept is critical in understanding how some sounds, while individually above the absolute threshold, may be masked by stronger simultaneous sounds, preventing their detection.

Absolute Threshold

The absolute threshold represents the minimum intensity level at which a sound can be detected by the auditory system in a quiet environment. It serves as the baseline for measuring audibility, indicating that any sound above this level is potentially perceptible under ideal listening conditions.

Just Noticeable Difference (JND)

The just noticeable difference (or in this context, the just noticeable distortion) is the smallest change in a sound's intensity or quality that can be detected by the listener. The JND curve helps determine at what level a change in sound becomes perceptible, marking the boundary where distortions or additional sounds are noticeable.

Transcript

00:01 Okay, so we've got a question here, and that's taking two loudspeakers, loudspeakers a and b, and they are vibrating in phase and playing the same tone, which has a frequency of 250 hertz.

00:18 Let's just make a note of that.

00:22 Okay, so they're set up as in figure 17 .7, and point c is located as shown there, and figure 17 .7 points point c directly below speaker b like that.

00:33 Question goes on to say, however, the distance between the speakers and the distance between speaker b and point c have the same value.

00:41 That's a value of d.

00:42 So the distance between these two is d and the distance between b and c also d.

00:49 It's just note that there.

00:53 Okay, so it also gives us the speed of sound.

00:55 V for velocity is equal to 343 meters per second.

01:04 And the question asks, what is the smallest value of d such that constructive interference happens at point c.

01:10 So for constructive interference, we basically need to consider that case.

01:15 Take a sine wave, we just model our sound as a sine wave.

01:21 And essentially, we should consider constructive interference being any situation where these two sine waves are adding together constructively.

01:31 So that is, they should be separated by some integer multiple of wavelength.

01:36 We'll note a wavelength on there as lambda.

01:39 If it's the smallest value of d, well, we can consider either the case that it's no wavelength, or one wavelength, but no wavelength is a little silly, as it implies that c is directly on top of b, and a is directly on top of b as well.

01:52 So there's no difference there.

01:54 So there's no question.

01:56 Instead, let's consider that there is just one wavelength of different, path difference, between the path of a to c and a to b.

02:05 So let's work out that path difference.

02:08 We've got some note coming from speaker a to speaker c, sorry, to present c.

02:16 And we've got some note coming from speaker b to person c or point c, whatever we want to call that.

02:23 So what are those lengths? path ac, a simple matter of using pythagoras...

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