Question

Two organ pipes, open at one end but closed at the other, are each 1.25 m long. One is now lengthened by 1.80 cm .

Find the frequency of the beat they produce when playing together in their fundamental.

Answer 1

Help guys! Please!

Answer 2

Obfiusly, we have to find the fundamentals first. Remember the formula?

Answer 3

for fundamental resonance, L must be equal to 1/4 of lambda. From here, you can find lambda (and then frequency) of each pipe.

Answer 4

So, L is 5m?

Answer 5

No, no, you seem to missed the point. Here:
1/4 lambda =L
lambda=4*L
from this lambda, you can find frequency:
lambda=v/f (v is speed of sound in air)

Answer 6

lambda = 5m
frequency = 5/344 m = .0145
is that good so far?

Answer 7

actually, f=v/lambda :)

Answer 8

whoops. so 344 m/s / 5m = 68.8
what do i do now?

Answer 9

Yep, good. Now find the frequency of second pipe.

Answer 10

344m/s / .072 m = 4777.78

Answer 11

Correct. The result's quite surprising, because huge difference in length. Remember the definition of beat?

Answer 12

unfortunately, i don't

Answer 13

Okay, I'll be patiently teach you :)
Beat is difference frequency. It occurs when two slightly different frequency played simultaneusly. Try pressing two neighboring piano button, you'll recognize it.

Answer 14

ok

Answer 15

Can you find the frequency of the beat now?

Answer 16

is the frequency just the difference of the two frequencies i found? so is it 4708.98?

Answer 17

Yeah, mathematically, you're correct. But practically, beat will only occur (or realized) if the frequencies are slightly different, more like 400 Hz and 402 Hz.

Answer 18

so, my answer is wrong then?

Answer 19

No, you're right. But the problem must be reconsidered. Maybe the unit of second pipe shouldn't be in cm, but in m.

Answer 20

I tried that and got -21.02 but the homework is still saying that i'm not getting the answer right???

Answer 21

21,2 Hz seems more plausible. But you're in the right track if you explain in your homework that beat doesn't really occur.

Answer 22

The homework is masteringphysics though, so I can't exactly say that through an online homework