Learning object
- 2. • Wave motion is very different from the motion of objects. Some waves need a medium in which to travel, such as waves in ocean, but some do not, such as light. • Wave Speed: The speed at which a disturbance travels through a medium is called the wave speed, v • Transverse Waves: The constituents of the medium move perpendicular to the direction of propagation of the wave in a transverse wave. • Longitudinal Waves: In a longitudinal wave, the constituents of the medium move parallel to the direction of motion of the wave.
- 3. • Waves carry energy: The pulse carries this energy as it travels along the sting. It takes energy to generate a pulse, and the pulse carries this energy as it propagates through the medium. A wave can be described as the motion of energy through a medium. • The medium does not travel with the wave: The pulse always pass through its equilibrium position and then returns to the equilibrium position. There is no net movement of the string in the direction of motion of the pulse. (eg, a sound wave does not carry air along with it) • Equation of a Pulse Moving in One Dimension: The transverse displacement of an element of the string form its equilibrium position is denoted by D(x, t); where x is displacement of the transverse wave, t is time. A function of the form D(x+/-vt) is called a wave function.
- 4. • Wave Speed on a String: 𝜇=M/L, where M is the total mass of a string; L is the length of the string. • F=ma, a=v2/R, m*( 𝑣2 𝑅 )=Ts( 𝐿 𝑅 ), therefore, v=√ 𝑇𝑠 𝜇
- 5. • Question: A string of linear mass density 10g/m and length 10m is hanging vertically from a high ceiling. A mass of 1kg hangs freely from the lower end of the string. A pulse is generated at the lower end of the string and travels upward. What is the speed of the pulse ate the lower end of the string, at the middle of the string, and at the top of the string? • Solution: use the equation v(x)=√ 𝑀𝑔+𝜇𝑥𝑔 𝜇 because the tension force in this case is the total weigh hanging below the point x, then, evaluating the wave speed at x=0, x=5m,and x=10m • We can get: v(0)=√ 𝑀𝑔 𝜇 = √ 1𝑘𝑔∗9.81𝑚/𝑠 10∗10−3 = 31.30m/s; v(5)=√ 𝑀𝑔+5𝜇𝑔 𝜇 = √ 1∗9.8+5∗10∗10−3∗9.8 10∗10−3 = 32.08m/s v(10)=√ 𝑀𝑔+10𝜇𝑔 𝜇 =√ 1∗9.8+10∗10∗10−3∗9.8 10∗10−3 = 32.83m/s
- 6. Thank you!