Question

You are inside the Great Hall, 15 m from the north wall with the doors to the RMC, and centered between two open doors that are 3 m apart. Someone is blairing a 200 Hz tone outside the Great Hall so that it enters the doors as a plane wave. You hear a maximum intensity in your current position. As you walk along the direction of the wall with the doors (but maintain a distance 15 m from the wall), how far will you walk (in m) to hear a minimum in the sound intensity

Answer 1

To find the distance, use the formula distance = (wavelength/2) * (number of wavelengths between the doors). The distance to hear a minimum in sound intensity is 0.85 m when walking along the direction of the wall with the doors.

Step-by-step explanation:

To find the distance you need to walk to hear a minimum in sound intensity, we can use the concept of constructive and destructive interference. As you walk along the direction of the wall with the doors, the path difference between the waves from the two doors changes. At the point of minimum intensity, the path difference is equal to half a wavelength. The formula to calculate the distance is given by: distance = (wavelength/2) * (number of wavelengths between the doors).

The wavelength can be calculated using the formula: wavelength = speed of sound / frequency. In this case, the frequency is given as 200 Hz. So, wavelength = 340 m/s / 200 Hz = 1.7 m/ cycle.

Substituting the value of wavelength, we have: distance = (1.7 m/ cycle / 2) * (number of wavelengths between the doors).

Since the doors are 3 m apart, there is one wavelength between them. Therefore, the distance to hear a minimum in sound intensity is given by: distance = (1.7 m/ cycle / 2) * 1 wavelength = 0.85 m.

Answer 2

Δr = 0.425 m

Step-by-step explanation:

This is a sound interference exercise, the expression for destructive interference is

Δr = (2n + 1) λ / 2

in this case the movement is in the same direction as the sound, therefore the movement is one-dimensional

let's use the relationship between the speed of sound and its frequency and wavelength

v = λ f

λ = v / f

the first minium occurs for n = 0

Δr = λ / 2

Δr = v / 2f

Δr =
`(340)/(2 \ 400)`

Δr = 0.425 m

this is the distance from the current position that we assume in the center of the room