Experiment Speed of Sound PDF

Prepared by:Dr.Kawther Ali Experiment (3): Speed of sound Purpose of experiment: The aim of this experiment is to use the resonance tube of an air column in a tube to find the speed of sound in air. Apparatus: resonance tube A set of tuning forks rubbe...

Prepared by:Dr.Kawther Ali Experiment (3): Speed of sound Purpose of experiment: The aim of this experiment is to use the resonance tube of an air column in a tube to find the speed of sound in air. Apparatus: resonance tube A set of tuning forks rubber mallet measuring tape thermometer 1  Prepared by:Dr.Kawther Ali THEORY: A sound wave is a longitudinal wave in which the wave oscillates along the direction of propagation. For a traveling wave of speed v, frequency f, and wavelength λ, the following relationship holds. v = f. λ……….(1) v is the velocity in m/s, λ is wavelength in meters ,f is frequency in Hz, or s -1 In this lab, we are going to use a simple characteristic of the traveling wave the resonance to determine the wavelength (and therefore the speed) of a sound wave. Consider a sound wave traveling through a resonance tube as illustrated in fig. 1. Figure 1: Resonance tube A tuning fork is held by hand just above the open end of the tube. When the tuning fork is struck by a rubber hammer, it vibrates and sound waves are 2  Prepared by:Dr.Kawther Ali generated. These sound waves travel down the tube and are reflected upon reaching the surface of the water. The incoming and reflected waves interfere and form standing waves. The sound waves reflected from the water surface change their phase by 180° and therefore are completely out of phase with the incident sound waves. In other words, the amplitude of the standing waves must be zero at the water's surface. This point in space is usually referred to as a node. If a resonance condition is met, the open end of the tube has maximum amplitude of standing sound waves and is called an anti-node. At constant temperature the speed of sound is fixed; in addition, for a given tuning fork the frequency is also fixed, then according to eqn. 1, the wavelength of the sound wave should also be fixed. As a result the resonance conditions can only be satisfied when the length of the tube( L) is such that 1 𝐿𝑛 = (2𝑛 + 1)𝜆 … … … …. (2) 4 where n = 0, 1, 2, 3, 4,..., and the length Ln is defined to be the distance measured from the open end of the tube to the water surface. For the specific 1 example given in fig. 1 (n = 0), the length of the tube is L = λwhich follows 4 from eqn. 2. Fig. 2 shows resonance conditions in which n = 1, 2, and 3. It is 1 easy to notice that L2 − L1 = λ In other words: 2 1 𝐿𝑛+1 − 𝐿𝑛 = 𝜆 … … … ….. (3) 2 1 ∆𝐿 = 𝜆 … … … … …. (4) 2 3  Prepared by:Dr.Kawther Ali This relationship between the two consecutive resonances will be used to find the wavelength of the standing sound wave. The objective of this lab is to measure the speed of a sound wave in the air and compare it to its theoretical value. Figure 2: Examples of resonance for n = 1, 2, and 3. According to the theory, the speed of sound in air depends upon the temperature of the air through the following relationship. 𝑚 𝑉𝑇 = (331.5 + 0.606𝑇) … … … … … (5) 𝑠 Here, T is the temperature in centigrade (degrees Celsius). Method PROCEDURE 1. You will be provided with two tuning forks of known frequencies f. Note that the frequencies of tuning forks are marked on them. Write them down in the Worksheet. 2. Fill the tube with water to about 10 cm to the open end of the tube. The level of the water in the tube (the length of the tube L) can be 4  Prepared by:Dr.Kawther Ali adjusted by moving the side bucket up and down in the vertical direction. 3. Strike the tuning fork with the rubber head of the mallet for forks with frequencies below 512 Hz and place it just above the open end of the tube. Neither the hammer nor the vibrating fork should touch the tube. 4. Find as many resonances as you can for tuning fork one. Repeat your measurements by increasing the water level in the tube. Measure the length of the air column for each resonance from the top edge of the tube. Find the difference in length (ΔL) between the two consecutive resonances to calculate the wavelength of the sound wave. Once the wavelength is determined, the speed of sound follows from eqn. 1 (Note the error in the measurement of the length is 1 mm). 5. Repeat step 4 for the other tuning fork with a different frequency. 6. Record the room temperature. Record your data in the table: Frequency(Hz) 1 length of the tube (𝐻𝑧)−1 𝐹 L(resonance)(m) Part(1):experimental value(VE) ∆𝑳 Slope = 𝟏 = 𝑳𝑭(cm/sec) ∆( ) 𝑭 VE= 4 x Slope (cm/sec)= 4 x Slope x 10-2 (m/sec) 5  Prepared by:Dr.Kawther Ali Part(2):theoretical part(VT) V0=331(m/sec)(speed of sound at standard conditions) 𝟐𝟕𝟑+𝑻 VT=𝐕𝟎 √ 𝟐𝟕𝟑 Where T is room temp.in centigrade. Or 𝑚 𝑉𝑇 = (331.5 + 0.606𝑇) 𝑠 6  Prepared by:Dr.Kawther Ali Medical Applications to Speed of sound Experiment The use of sound in medicine started since long time ago. Doctors have used stethoscopes to listen to human body’s internal sounds since the early 19th century, and the ultrasound imaging has develop to a powerful device in obstetrics and other medical aspects that expectant mothers need to know the gender of their offspring by 20 weeks of development. Also it is used to examine some organs(‫ )فحص بعض األعضاء‬and blood flow and sound reflects at boundary of tissues with different densities. Acoustic energy can be concentrated and used for imaging and curing a variety of ailments which includes cancer, stroke, and Parkinson's disease. Neurosurgeons use a device called a cavitron ultrasonic surgical aspirator (CUSA) to take away brain tumors that were once thought to be very difficult to operate. a cavitron ultrasonic 7  Prepared by:Dr.Kawther Ali The Doppler flow meter plays an important part in the medical application of the Doppler effect. The middle ear contains air and it is important for the air in both sides of the thin eardrum to be the same. Eustachian tube serves to equalize the pressure. DISCUSSION QUESTIONS 1.What was the purpose of the experiment? 2. What is the theoretical concept that explains the expected experimental results? 8