The cosine function goes from -1 to 1. [ "article:topic", "authorname:openstax", "license:ccby", "showtoc:no", "program:openstax" ], https://phys.libretexts.org/@app/auth/2/login?returnto=https%3A%2F%2Fphys.libretexts.org%2FBookshelves%2FUniversity_Physics%2FBook%253A_University_Physics_(OpenStax)%2FMap%253A_University_Physics_I_-_Mechanics_Sound_Oscillations_and_Waves_(OpenStax)%2F16%253A_Waves%2F16.04%253A_Wave_Speed_on_a_Stretched_String, Creative Commons Attribution License (by 4.0), Determine the factors that affect the speed of a wave on a string, Write a mathematical expression for the speed of a wave on a string and generalize these concepts for other media. In solids and liquids the particles are closer together so pass on their vibrations faster. You've learned five ways of describing a wave using your wave parameters. The speed of a wave is related to its wavelength and frequency as v = ν λ Where, v is the velocity of the wave, ν is the frequency of the wave and λ, its wavelength. Speed of Compression Waves in a Fluid The speed of a wave on a string depends on the square root of the tension divided by the mass per length, the linear density. The speed of a wave is related to its frequency and wavelength, according to this equation: \ [v = f~ \times \lambda\] where: v is the wave speed in metres per second, m/s. The tension would need to be increased by a factor of approximately 20. The two clips show the same rope, stretched over the same distance. To obtain the y-components of the force, note that tan \(\theta_{1} = − \frac{F_{1}}{F_{T}}\) and \(\tan \theta_{2} = \frac{F_{2}}{F_{T}}\). The wave equation governs a wide range of phenomena, including gravitational waves, light waves, sound waves, and even the oscillations of strings in string theory.Depending on the medium and type of wave, the velocity v v v can mean many different things, e.g. … Most solid materials are elastic, so this equation describes such phenomena as seismic waves in the Earth and ultrasonic waves used to detect flaws in materials. For example, sound is a mechanical wave that travels through a fluid or a solid. The wave equation relates the frequency, wavelength and speed (HS-PS4-1). Happy teaching Wave speed is related to wavelength, frequency, and period by the equation wave speed = frequency x wavelength. This lesson looks at units, the wave speed equation and the wave period equation. The Wave Equation One of the most fundamental equations to all of Electromagnetics is the wave equation, which shows that all waves travel at a single speed - the speed of light. , follow this equation. We discuss some of the tactics for solving such equations on the site Differential Equations . … The mass element is at rest and in equilibrium and the force of tension of either side of the mass element is equal and opposite. The frequencies depend on the speed of the waves on the string and the wavelength of the waves. The standard notes of the six string (high E, B, G, D, A, low E) are tuned to vibrate at the fundamental frequencies (329.63 Hz, 246.94 Hz, 196.00 Hz, 146.83 Hz, 110.00 Hz, and 82.41 Hz) when plucked. The sheet is included in Word and PDF formats. Wave speed is often calculated using the quantities of wavelength and time period or frequency. A wave has a frequency of 46 Hz and a wavelength of 1.7 meters. The equation for wave speed can be written to solve for wavelength or frequency if the speed and the other value are known. Because the density depends on temperature, the speed of sound in air depends on the temperature of the air. 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