Understanding Sound Waves: Frequency, Wavelength, Interference, and Ultrasonic Experiment, Lab Reports of Experimental Physics

Download Understanding Sound Waves: Frequency, Wavelength, Interference, and Ultrasonic Experiment and more Lab Reports Experimental Physics in PDF only on Docsity! M2.1 Lab M2. Ultrasound: Interference, Wavelength, and Velocity The purpose of this exercise is to become familiar with the properties of waves: frequency, wavelength, phase, and velocity. We use ultrasonic waves because the wavelength is easily measured with an ordinary meter stick. The frequency of ultrasound is above the range of human hearing, so the experiment does not create an audible sound. The experiment also illustrates the interference of waves Sound is a pressure wave in air. When we hear a sound, we are sensing a small variation in the pressure of the air near our ear. The speed of a sound wave in air is about 340m/s or about 5 seconds to travel one mile, and this speed depends only on the properties of the air (temperature, composition, etc.) and not on the frequency or wavelength of the wave. Consider a sinusoidal sound wave in air with frequency f and wavelength λ. The speed v is related to f and λ by (1) v = f λ. To see where this relation comes from, think: speed = change in distance change in time The time it takes for one wavelength of the sound to go by is the period T, so v = λ/T. But f T= 1 so v = λf . Note that as f increases, λ goes down, but the speed v stays the same. The frequency range of human hearing is about 20 Hz to 20,000 Hz. (The upper end drops as we age; for people over 60, it is about 12 kHz, while dogs can hear up to about 35 kHz.) Consider two sound waves of equal f , equal λ, and nearly equal amplitude, both approaching a detector, such as a human ear. If the two waves arrive at the ear in phase, that is with successive maxima arriving at the same time and successive minima arriving at the same time, then the waves interfere constructively, their amplitudes add, and the ear hears a loud sound. But if the waves arrive at the ear exactly out of phase, that is, with the maxima of one wave arriving at the same time as the minima of the other wave, then the waves interfere destructively; they cancel and the ear hears little or no sound. + = + = in phase out of phase Fall 2004 M2.2 Now, in order to observe the interference of sound waves in the way just described, the two waves must have exactly the same frequency. One way to insure that the two waves have the same frequency is to arrange to have both waves generated by the same source. This is the principle of the so-called Lloyd's Mirror arrangement, shown in the diagram below. A source of sound — a speaker emitting a pure tone with known frequency f — sits a height S above a flat table. A receiver sits a distance R above the table, a distance L along the table away from the source. Sound from the source can travel to the receiver along two different paths: the sound can travel directly from the source to the receiver (path 1 with total length D1) or the sound can reflect from the surface of the table to the receiver (path 2 with total length D2). (Sound, like light, can reflect from a smooth flat surface with the angle of incidence equal to the angle of reflection.) The receiver "sees" a reflection of the speaker in the table top which appears to be at a distance D2 . Whether the two waves arrive at the receiver in phase or out of phase depends on the path difference (D2 − D1). If the path difference is an integral number of wavelengths ( D D n2 1− = λ ) then the waves arrive in phase. If D D n2 1 1 2− = +( ) λ , then the waves arrive out of phase and the detector receives a small amplitude total wave. In this lab, you will measure the heights R and S at which interference maxima and minima occur. From this information, you will compute the wavelength λ of the sound. Finally, from the wavelength and the known frequency f, you will compute the speed of sound . v f= λ R+S table top path 1 path 2 receiver source reflected image of source S L S R-S R Fall 2004 M2.5 where the temperature T is in degrees Celsius (there is a big dial thermometer on the wall in the lab). Compare this known v with your measured v . Find the difference between your measured v from Eq(1) and the known v from Eq(4) and compare this difference to your calculated uncertainty δv. Discuss the results, commenting on the agreement/disagreement of the theory with the experiment, the most significant sources of uncertainty in the measurement and how these might be improved. PreLab Questions: 1. If the speed of sound is v = 345 m/s, what is the range of wavelengths of sound which the human ear can detect? 2. (Counts as two questions.) Show how you will define the wavelength λ in your Mathcad document. [Just write the Mathcad definition like it will appear on the computer screen, except write it on paper with your pen.] Also show how you will make a Mathcad graph of λ vs. n. For instance, if I want to show how to define a function y(x,t) = x t2 ,where x = 3 t 1/2, and how to graph y vs. t in Mathcad, I could write either the commands on the left or the commands on the right: ti (Enter values for t.) xi .3 ti y( ),x t .x t2 y ,xi ti ti ti (Enter values for t.) xi .3 ti yi .xi ti 2 yi ti 3. What conditions must be satisfied in order to have complete destructive interference of two sound waves? 4. Explain with a diagram and a few words why equations (2) are the correct expressions for the two paths D1 and D2. Fall 2004 M2.6 5. Sketch the graph h vs. n. [No numbers on this graph! And no calculations. Just think a minute and make a qualitative sketch, showing what the graph should look like. Ask yourself, should h increase, decrease, or stay constant as n increases.] 6. Sketch the graph λ vs. n. [No numbers! Just a qualitative sketch, showing what the graph should look like.] 7. Ultrasound is used as a tool in obstetric medicine to "see" inside the body objects larger than about a wavelength. The speed of sound in humans is about 1500 m/s, the same as in water. What would be the wavelength of 5 MHz medical ultrasound waves in humans? 8. How do you compute δv, the uncertainty in v, from measurements of f, δf, λ, and δλ? In this experiment, how is δλ determined? 9. What is the value of dv dT , the derivative of the speed of sound with respect to temperature, near room temperature? Sketch a graph of the speed of sound vs. temperature for temperatures near room temperature. [No numbers! Just a qualitative sketch, showing what the graph looks like.] Fall 2004