What Was the Initial Frequency of the Trumpet Player?

[sugz]

Homework Statement

A trumpet player hears 3 beats per second when she plays a note and simultaneously sounds a
440 Hz tuning fork. After pulling her tuning valve out to slightly increase the length of her
trumpet, she hears 5 beats per second against the tuning fork. What was her initial frequency?
a) 437 Hz
b) 443 Hz
c) Either a) or b).
d) 435 Hz
e) 445 Hz

Homework Equations

fbeat = |f2-f1|

The Attempt at a Solution

I understand how the beat frequency is the difference of the 2 frequencies. So |f1-440| = 3 and |f2-440| = 5. So the first frequency can be 437 or 443 Hz but the answer in only 437 Hz, why?

 

[NascentOxygen]

The tiny increase in length that caused an extra 2 Hz in the beat frequency might provide [what is intended to be] the clue.

 

[Quantum Defect]

Homework Statement

A trumpet player hears 3 beats per second when she plays a note and simultaneously sounds a
440 Hz tuning fork. After pulling her tuning valve out to slightly increase the length of her
trumpet, she hears 5 beats per second against the tuning fork. What was her initial frequency?
a) 437 Hz
b) 443 Hz
c) Either a) or b).
d) 435 Hz
e) 445 Hz

Homework Equations

fbeat = |f2-f1|

The Attempt at a Solution

I understand how the beat frequency is the difference of the 2 frequencies. So |f1-440| = 3 and |f2-440| = 5. So the first frequency can be 437 or 443 Hz but the answer in only 437 Hz, why?

Pulling out the tuning slide lowers all of the pitches. I think you are right.

She could have been flat (437) and pulled out, thinking she was sharp, going even flatter (435). She could also have been a little sharp (443) and pulled out too much, taking her down too far (435).