Two musicians are comparing their trombones. The first produces a tone that is known to be 438 hz. When the two trombones play together they produce 6 beats every 2 seconds. Which statement is true about the second trombone?

The second trombones might produce frequency of 435 Hz or 441Hz.

Explanation:  

Beat frequency is defined as number of beats produced per second and numerically equal to the difference between the frequency of super imposing waves.The sound waves interfere constructively.

Beat is the phenomena of interference.

The frequency of the resultant wave is given by

F = f₁ - f₂ eqn 1

where f₁ , f₂ are frequency of waves.

The frequency of first trombones is 438Hz, 6 beats are heard every 2 second,

Beat frequency is F = = 3Hz.

Substituting in eqn 1 , we get two possible solution for frequency of second trombones.

f₂ =f₁ -F = 438 -3 =435Hz

f₂ = f₁ +F = 438+3 =441 Hz.

The second trombones might produce frequency of 435 Hz or 441Hz.

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