Beat frequency

[Testosterone]

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A piano tuner plays an out of tune A note on his piano and then strikes his 440 Hz tuning fork. He notices a beat of 2 Hz. When he loosens the piano string and plays the note again, the beat goes to 4 Hz. What was the frequency of the note before he loosened his string?

a) 438 Hz
b) 440 Hz
c) 442 Hz
d) 444 Hz

Answer A

I understand the reasoning behind the answer. But why isn't C also a correct answer?

BTW this was EK Physics 691

 

[ebasappa]

As the player loosens the string, the Tension is decreased, so the frequency decreases. Had he started at 442 Hz, when he loosened it, it would have created NO beat frequency because the frequency would have decreased to 440 Hz. The only way he could have added 2 MORE to the beat frequency would have been if he had started at 438 Hz..... if that made sense haha

 

[shouldvestudied]

A piano tuner plays an out of tune A note on his piano and then strikes his 440 Hz tuning fork. He notices a beat of 2 Hz. When he loosens the piano string and plays the note again, the beat goes to 4 Hz. What was the frequency of the note before he loosened his string?

a) 438 Hz
b) 440 Hz
c) 442 Hz
d) 444 Hz

Answer A

I understand the reasoning behind the answer. But why isn't C also a correct answer?

BTW this was EK Physics 691

I see exactly what you're saying here. Without knowing that loosening the string results in a frequency decrease of less than 6 Hz, both answers are technically correct.

The piano tuner could have just as easily tested once at 442 Hz (2 Hz beat) and then loosened the string to 436 Hz (4 Hz beat).

EK is wrong here.

 

[ebasappa]

Nevermind, he's right ^^

 

[Testosterone]

Thanks for clarifying that one.