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The sound from a single source can reach point O by two different paths. One path is 20.0 m long and the second path is 21.0 m long. The sound destructively interferes at point O. What is the minimum frequency of the source if the speed of sound is 340 m/s?

Respuesta :

Answer:

minimum frequency = 170 Hz

Explanation:

given data

One path long = 20 m

second path long = 21 m

speed of sound = 340 m/s

solution

we get here destructive phase that is path difference of minimum [tex]\frac{\lambda}{2}[/tex]

here  λ is the wavelength of the wave

so path difference will be

21 - 20 = [tex]\frac{\lambda}{2}[/tex]  

λ = 2 m

and

velocity that is express as

velocity = frequency × wavelength    .............1

frequency  = [tex]\frac{340}{2}[/tex]  

minimum frequency = 170 Hz

The minimum frequency of the source if the speed of sound is 340 m/s is 170 Hz.

Based on the given information,

• The length of the first path is 20 m and the length of the second path is 21 m.  

• The speed of the sound is 340 m/s.  

Now the path difference between the first and the second path is,

[tex]= 21 m - 20 m \\= 1 m[/tex]

The minimum path difference required for a complete destructive interference is,

ΔS = λ/2 = 1 m

The wavelength for the minimum frequency possible is,

λ = 2 × 1 m = 2 m

Now the minimum frequency (f) is,

f = v/λ (v is the speed of sound, that is, 340 m/s)

[tex]f = \frac{340 m/s}{2 m} \\f = 170 Hz[/tex]

Thus, the minimum frequency is 170 Hz.

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