PCS 125 Sound Waves & Beats Lab Ryerson University PCS 125

Department of Physics Course Number PCS 125 Course Title Physics: Waves and Fields Semester/Year Winter 2014 Instructor Yuan Xu TA Name Bisma Rizvi Lab/Tutorial Report No. #2 Report Title Sound Waves and Beats Section No. 32 Group No. Submission Date February 12, 2014 Due Date February 12, 2014 Student Name Student ID Signature* Arth Chaudhari Seanan Chabra (Note: remove the first 4 digits from your student ID) *By signing above you attest that you have contributed to this submission and confirm that all work you have contributed to this submission is your own work. Any suspicion of copying or plagiarism in this work will result in an investigation of Academic Misconduct and may result in a “0” on the work, an “F” in the course, or possibly more severe penalties, as well as a Disciplinary Notice on your academic record under the Student Code of Academic Conduct, which can be found online at: Objective The purpose of this experiment was to observe the beats and waves produced when two sounds are overlapped and to measure the frequency, the period, and the amplitude of various sound waves. Background A beat occurs when two sound waves with nearly the same frequencies interfere with one another creating different sound amplitudes. Also, a the pattern of the beat is a wave that has an amplitude that changes at a regular rate (Physics Classroom). There are a series of pressure variations that sound waves consist of. These variations are recorded by a Microphone diaphragm, which is then converted to an electrical signal. There are three properties of common sounds that can be explored through the through the use of a Microphone and a computer interface (Ryerson University Department of Physics). The first property that is measured is the period (T), which is the time it takes for one complete cycle to occur. The frequency (f) is then calculated using the reciprocal of the period (1/T). The frequency is defined as the number of cycles that occur in a second, and it is measured in Hz (hertz). Therefore, 1Hz = 1 s-1. Another property is the amplitude, which is the difference between the highest and the lowest peak of a sound wave. In addition, the amplitude of a sound wave is very closely related to the loudness of that particular sound. Theory: Frequency f is a measure of the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency. The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency. The period is usually denoted as T, and is the reciprocal of the frequency. A wave consists of frequency, time and amplitude. T = 1/ f (1) Where T is period and f is frequency, which is measured in Hz. Wave interference is the phenomenon that occurs when two waves meet while along the same medium. If two upward displaced pulses having the same shape meet up with one another while traveling in opposite directions along a medium, the medium will take on the shape of an upward displaced pulse with twice the amplitude of the two interfering pulses. This type of interference is known as constructive interference. If an upward displaced pulse and a downward displaced pulse having the same shape meet up with one another while traveling in opposite directions along a medium, the two pulses will cancel each other's effect. When two or more sound waves meet at a given point, they collide according to the laws of linear superposition: The waves can add together either constructively or destructively. In constructive interference, the amplitude of the resultant wave is greater than that of the individual waves. In destructive interference, the amplitude of the resultant wave is less than that of the individual waves. Each tone gives can be shown by a y=Asin(2πft) (2) Sound is a longitudinal wave; y is the change in air pressure, which is the wave essentially. A is the amplitude of the wave which is also a measure of loudness, and f is the frequency. The representation of time is t and the sine function needs a factor of 2π when evaluated in radians. A Beat can be shown with the function or trig identity sin(x) + sin(y) = 2sin[(x +y)/2] cos [(x-y)/2] (3) sin(x) represents the first wave and sin(y) represents the second wave, the waves have to contain the sinusoidal functions, but the trig identity cuts the work in half. The waves is described as sin(2π f1 t) and sin(2π f2 t), and subbed in the equations above to calculate for the beat