Question

A trumpet uses an open-close tube thats 17cm long. There is another instrument that use a shorter open close tube and it makes 67 beats per second. How long is the other tube ?

- 15 cm

- 16 cm

- 14 cm

- 19 cm

- 18 cm

Please show full solution.

Answer 1

The frequency of sound (fundamental frequency) from an open-closed tube is

f=- 4L

v is the velocity of sound and L denotes the length of the tube.

We see that

I-L

Hence, shorter the tube, higher the frequency.

The shorter trumpet will hence have higher frequency.

Frequency of the longer trumpet is

1-4 × 0.17

Similarly, for the shorter tube

XX% ts =41Hz S 4L

As we inferred,

By the given problem, beat frequency is 67

fsf 67

or, v(1-1-)-67 4 L 0.17 or,- ) = 67

or, 343 (1-017) = 67 '4 L 0.17 ) 67

343 343 or, +67-571.41 4L 4×0.17

343 4 × 571.41 or, L = m = 0,15 m 15 cm

Hence, the other tube is 15 cm long