Question

Two violinists are trying to play in tune. However, whenever they play their A string at the same time they hear a beat frequency of 3.0 Hz. One of the violinists measures with an electronic tuner and finds her A string is at 422 Hz. What are the possible frequencies for the A string of the other violinist?

Answer 1

The other violinist's A string could have a frequency of either 425 Hz (422 Hz + 3 Hz) or 419 Hz (422 Hz - 3 Hz) to produce the observed beat frequency of 3 Hz.

Step-by-step explanation:

When two violinists play their A string simultaneously and hear a beat frequency of 3.0 Hz, this means that the frequencies of their A strings are slightly different. Beat frequency is the result of the interference of two waves of close frequencies. Since one violinist's A string is at 422 Hz, the other violinist's A string could be either 425 Hz or 419 Hz to produce the 3 Hz beat frequency; this results from adding or subtracting the beat frequency from the known frequency.

Answer 2

the possible frequencies for the A string of the other violinist is 419 Hz

Step-by-step explanation:

given information:

`f_(beat)` = 3 Hz

the frequency of the first violinist
`f_(1)` = 422 Hz

to find the possible frequency of the other violinist, we use the following equation':

`f_(beat)` = l
`f_(1)` -
`f_(2)` l

3 = l 422 -
`f_(2)` l

`f_(2)` = 422 - 3

`f_(2)` = 419 HZ