The lecturer with a monotone voice of 440 Hz and you are both 2m away from the long, smooth and tall wall.You will hear sound that comes directly to you from

the lecturer along with sound that comes back from the wall on it’s way to reaching you.You need the path here needs to have the same angle onto the wall as it has after reflection.How far from the lecturer will you pick your seat so you can’t hear the voice at all and find your well deserved rest?

To find the distance from the lecturer where you won't hear their voice at all, you need to consider the phenomenon of sound reflection. Here's how we can go about it:

Step 1: Determine the wavelength of the sound.
The wavelength (λ) of a sound wave can be calculated using the formula: λ = v/f, where v is the speed of sound in air (approximately 343 m/s) and f is the frequency of the sound (440 Hz).

λ = 343/440 = 0.78 m

Step 2: Consider the angle of incidence and the angle of reflection.
According to the law of reflection, the angle of incidence and the angle of reflection are equal. In this case, both angles should be such that the sound does not reach your ears.

Step 3: Calculate the distance from the lecturer.
To find the distance from the lecturer where you won't hear their voice at all, you need to determine the path difference between the direct sound and the sound reflected off the wall. This path difference should be such that the waves interfere destructively when they reach your ears.

The path difference (Δx) can be calculated as:
Δx = λ/2

Δx = 0.78/2 = 0.39 m

Since the path of the reflected sound consists of two parts (from the lecturer to the wall and from the wall to you), the total distance from the lecturer should be equal to the path difference (Δx) divided by 2.

Distance from lecturer = 0.39/2 = 0.195 m

Therefore, you would need to pick your seat approximately 0.195 m (19.5 cm) away from the lecturer to ensure that you can't hear their voice at all and have a well-deserved rest.