Speed of Sound
Aim
The aim of this practical is to measure the speed of sound using the resonance method.
Variables
Independent: Frequency
Dependent: Length of Tube
Constants: Temperature
Diameter of Tube
Theory
The general equation used for finding the speed of a wave is v=fλ, as v∝f and v∝λ.
The goal of this experiment will be to find v, the speed of sound. The only given is f, the frequency emitted by the tuning fork, however the wavelength, λ is not given.
This value is derived from the length of the tube at its first harmonic or resonance, in which the length between the water level and end of the tube will be ¼ of the wavelength. Meaning λ=4l
This can be substituted into the equation: v=f×4l
The theory states that the antinodes of the waves are not exactly at the lip of the tube. Therefore an end correction is put in place which holds a value of 0.4d (where d is the diameter), this is added to the length of the tube in the equation: v=4(l+0.4d)×f ∴v=4f(l+0.4d) If we put this equation in terms of l and in the form y=mx+c, the result will be: l=v×1/4f-0.4d, where y=l, x=1/4f, c=-0.4d and m=v. Therefore if we graph l against 1/4f, the slope of the graph will equate to the speed of sound. The graph should also not pass through the origin, but -0.4d, as it is the value of c in the equation y=mx+c. The speed of sound should also increase by 0.63ms-1 per degree Celsius. Therefore we can find the speed of sound at 0˚C with the formula v_0=(v-0.63T) where v is the speed of sound calculated and T is the temperature recorded. This can then be used to determine the speed of sound at any temperature with the formula: v_T=v_0+0.63T Hypothesis It is hypothesised that the length is directly proportional to 1/4f, and the resultant slope will present the value of the speed of sound. It is also hypothesised that the speed of sound will equate to 331.4ms-1 at 0˚C. Materials Measuring cylinder Tube Tuning Forks Rubber Stopper Thermometer & Ruler Procedure Measure the internal diameter of the tube. Measure the room temperature. Fill the measuring cylinder with water to a few cm from the top. Lower the tube into the cylinder. Hold the tuning fork slightly above the tube. Strike the tuning fork with the rubber stopper; do not touch the fork to the tube. Slowly raise the tube and fork until the first resonance position is reached. Clamp the tube in this position. Test for resonance again. Measure the length between the water level and the end of the tube. Repeat steps 5-10 with different tuning forks. Results Constants: Temperature: 22˚C Diameter: 0.038m Frequency ‘f’ (Hz) 1/4f (m) Length of Tube ‘l’ (m) l1 (m) l2 (m) l3 (m) lav (l_1+l_2+l_3)/3 (m) 512 4.88×〖10〗^(-4) 0.160 0.162 0.158 0.160 426.6 5.86×〖10〗^(-4) 0.188 0.192 0.194 0.191 384 6.51×〖10〗^(-4) 0.210 0.214 0.212 0.212 320 7.81×〖10〗^(-4) 0.245 0.245 0.245 0.245 288 8.68×〖10〗^(-4) 0.270 0.275 0.270 0.272 Unknown 1 0.235 0.240 0.236 0.237 …show more content…
The most likely source of systematic error is parallax error. It is highly likely that measuring the length of the tube was affected by the positioning of the ruler against the tube as well as the eye against the ruler. The absence of millimetre measurements on the ruler also required the observer to estimate to the nearest millimetre which also likely resulted in inaccuracies. The mouth of the tube was also rigid which has possibly had an effect on the end correction value of 0.4d, however this error is simply an assumption and it is uncertain whether or not it did have an …show more content…
It was hypothesised that the length would be directly proportional to 1/4f, this was proven correct in the graph, although systematic error has had an effect and created a line that is slightly off of what was hypothesised, in which the slope would be closer to 340ms-1 and pass through -0.4d. The calculated frequencies as well as the speed of sound at zero are likely to be fairly close the correct values, although not exactly, due to the presence of error in finding the speed of sound. This practical has been a success, the aim was achieved and the unknown frequencies found, however the accuracy can be improved in the future via the previously mentioned
Aim
The aim of this practical is to measure the speed of sound using the resonance method.
Variables
Independent: Frequency
Dependent: Length of Tube
Constants: Temperature
Diameter of Tube
Theory
The general equation used for finding the speed of a wave is v=fλ, as v∝f and v∝λ.
The goal of this experiment will be to find v, the speed of sound. The only given is f, the frequency emitted by the tuning fork, however the wavelength, λ is not given.
This value is derived from the length of the tube at its first harmonic or resonance, in which the length between the water level and end of the tube will be ¼ of the wavelength. Meaning λ=4l
This can be substituted into the equation: v=f×4l
The theory states that the antinodes of the waves are not exactly at the lip of the tube. Therefore an end correction is put in place which holds a value of 0.4d (where d is the diameter), this is added to the length of the tube in the equation: v=4(l+0.4d)×f ∴v=4f(l+0.4d) If we put this equation in terms of l and in the form y=mx+c, the result will be: l=v×1/4f-0.4d, where y=l, x=1/4f, c=-0.4d and m=v. Therefore if we graph l against 1/4f, the slope of the graph will equate to the speed of sound. The graph should also not pass through the origin, but -0.4d, as it is the value of c in the equation y=mx+c. The speed of sound should also increase by 0.63ms-1 per degree Celsius. Therefore we can find the speed of sound at 0˚C with the formula v_0=(v-0.63T) where v is the speed of sound calculated and T is the temperature recorded. This can then be used to determine the speed of sound at any temperature with the formula: v_T=v_0+0.63T Hypothesis It is hypothesised that the length is directly proportional to 1/4f, and the resultant slope will present the value of the speed of sound. It is also hypothesised that the speed of sound will equate to 331.4ms-1 at 0˚C. Materials Measuring cylinder Tube Tuning Forks Rubber Stopper Thermometer & Ruler Procedure Measure the internal diameter of the tube. Measure the room temperature. Fill the measuring cylinder with water to a few cm from the top. Lower the tube into the cylinder. Hold the tuning fork slightly above the tube. Strike the tuning fork with the rubber stopper; do not touch the fork to the tube. Slowly raise the tube and fork until the first resonance position is reached. Clamp the tube in this position. Test for resonance again. Measure the length between the water level and the end of the tube. Repeat steps 5-10 with different tuning forks. Results Constants: Temperature: 22˚C Diameter: 0.038m Frequency ‘f’ (Hz) 1/4f (m) Length of Tube ‘l’ (m) l1 (m) l2 (m) l3 (m) lav (l_1+l_2+l_3)/3 (m) 512 4.88×〖10〗^(-4) 0.160 0.162 0.158 0.160 426.6 5.86×〖10〗^(-4) 0.188 0.192 0.194 0.191 384 6.51×〖10〗^(-4) 0.210 0.214 0.212 0.212 320 7.81×〖10〗^(-4) 0.245 0.245 0.245 0.245 288 8.68×〖10〗^(-4) 0.270 0.275 0.270 0.272 Unknown 1 0.235 0.240 0.236 0.237 …show more content…
The most likely source of systematic error is parallax error. It is highly likely that measuring the length of the tube was affected by the positioning of the ruler against the tube as well as the eye against the ruler. The absence of millimetre measurements on the ruler also required the observer to estimate to the nearest millimetre which also likely resulted in inaccuracies. The mouth of the tube was also rigid which has possibly had an effect on the end correction value of 0.4d, however this error is simply an assumption and it is uncertain whether or not it did have an …show more content…
It was hypothesised that the length would be directly proportional to 1/4f, this was proven correct in the graph, although systematic error has had an effect and created a line that is slightly off of what was hypothesised, in which the slope would be closer to 340ms-1 and pass through -0.4d. The calculated frequencies as well as the speed of sound at zero are likely to be fairly close the correct values, although not exactly, due to the presence of error in finding the speed of sound. This practical has been a success, the aim was achieved and the unknown frequencies found, however the accuracy can be improved in the future via the previously mentioned