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## Homework Statement

*Before I write the question you should know that my maths is all correct in my solution but I must have used the formulas incorrectly (or used the wrong formulas). I can't pinpoint where I've gone wrong or if I have left a formula out (I'm a teacher solving this question for an exam my students will be completing).*

A student carries out an experiment to measure the speed of sound in air and its temperature. He uses the equipment shown at the right. The student measures the length of the air column when resonance is produced in the tube by the tuning fork.

Her results are listed below:

Frequency of Tuning Fork = 625Hz

Length of Air Column = 136mm = 0.136m

Temperature = ?

a) At what length of pipe raised out of the water would the student obtain a second resonant point?

b) From the student’s results, what is the

__speed of sound__in air and the surrounding

__temperature__?

*(Ignore end correction factors)*

## Homework Equations

v = f.λ

λ

_{n}=4L/(2n-1)

*(Closed Pipe)*

Velocity of sound through air at different temperatures

v

_{T}=331√(T/273+1)

f

_{n}=nv/4L

*(Closed Pipe)*

I have only included the closed pipe equations since this is a closed pipe question. If there are any other equations needed to solve this question please tell me.

I have only included the closed pipe equations since this is a closed pipe question. If there are any other equations needed to solve this question please tell me.

## The Attempt at a Solution

a)

second resonant is the middle pipe in this diagram (I think). There forethere the length of pipe out of the water is 3/4 of a wavelength.

λ

_{n}=4L/(2n-1)

λ

_{3}=4x0.136/(2x3-1)

λ

_{3}=0.1088

L=3/4λ

L=3/4 x 0.1088

L=0.0816m

b)

v = f.λ

v = 625 x 0.1088

v = 68 m/s

v

_{T}=331√(T/273+1)

68 = 331√(T/273+1)

...

T = -261.47

^{o}C