Lab2_VanLe

Van Thin Le Professor Xiang Song Phys-2426-51700 26 August 2023 LAB 2: WAVE ON STRING Part A Theory Please study concepts of wave on string and answer the following questions. 1. What is standing wave and its characteristics? A standing wave, also known as a stationary wave, is formed by the superposition of two waves propagating in opposite directions. These waves share identical amplitude and frequency. The key characteristics of a standing wave are as follows:  Lack of Propagation: A standing wave remains motionless within a medium and does not exhibit forward or backward movement. It remains stationary at its specific location.  b. Node and Anti-node Distribution: Within the region where the standing wave is present, certain points exhibit maximum amplitude and are referred to as anti-nodes. Conversely, there are points where the amplitude is minimal or even zero, known as nodes.  c. Wavelength Relationship: The distance between consecutive nodes or anti-nodes in a standing wave is equal to half of the wavelength (λ/2).  d. Node-to-Anti-node Distance: The separation between a node and its adjacent anti-node measures a quarter of the wavelength (λ/4).  e. Energy Transfer: The transmission of energy along a standing wave is effectively zero, resulting in minimal or no net energy movement within the wave pattern. 2. For standing wave on string with fixed two ends (a) write down the speed equation, (b) list equations for fundamental frequency, nth harmonics frequency and wavelength, ( c ) draw 1 st , 2 nd , and 3 rd standing waves patterns. a. Speed of wave: v = √ T μ Where: ▪ v is the speed of the wave. ▪ T is the tension in the string. ▪ μ is the linear mass density of the string. b. Fundamental frequency: f 1 = v 2 L = 1 2 L √ T μ

Nth harmonics: f n = n f 1 = n 2 L √ T μ Wavelength: λ n = 2 L n c. 3. Figure shows one moment standing wave on string (fixed ends). The frequency of the wave is 2.85 Hz. Based on the information from the figure, find fundamental frequency and wavelength λ 1 , speed of this standing wave. L = 7.5cm = 0.075m n = 7 f n = 2.85Hz  f 1 = f n n = 2.85 7 = 0.407 Hz  λ n = 2 L n  λ 1 = 2 L 1 = 2 ∗ 0.075 1 = 0.15 m  f n = n f 1 = n 2 L v  v = f n 2 L n = 2.85 2 ∗ 0.075 7 = 0.061 m / s

Notes: If the standing wave pattern is larger than your computer screen, you can set some Damping and toggle the on /off button ►till observe better pattern. Question: • Does the speed of wave depend on frequency f? Explain what quantities decide the speed. Altering the frequency of waves has no impact on the wave speed. In a singular medium, the velocity of a wave remains steady. When frequency increases, wavelength decreases, as wave velocity is the outcome of frequency and wavelength multiplication, as is evident in water waves. The wave velocity hinges on the tension within the string and its linear mass density. Amplified tension leads to heightened wave velocity. However, augmented linear mass density leads to decreased speed. This is due to the inverse relationship between wave speed on a string and the square root of linear mass density, coupled with the direct proportionality to tension. • Predict 6 th harmonic frequency f 6 , λ 6 , and ʋ = f 6 • λ 6 .  f n = n f 1 ⇒ f 6 = 6 f 1 = 6 ∗ 0.41 = 2.46 Hz  λ n = 2 L n ⇒ λ 6 = 2 L 6 = 2 ∗ 7.5 6 = 2.5 cm  v = f 6 λ 6 = 2.46 ∗ 2.5 = 6.15 cm / s Data Table 2: Measure Standing Wave Frequency f n , Wavelength λ n , and Speed ʋ. Basic Operation for Wave on String : Place check marks on Oscillate, Fixed End, Rulers, and Timer. Set Amplitude to 0.50 cm , Damping None , Tension Low . Whenever you change a new Frequency, it is best to Stop ►, Restart, then Play ►, then watch the wave pattern for few seconds before next move. Adjusting Frequency till finding the fundamental frequency f 1 . Freeze screen by click ►, Measure the length of string L with ruler, calculate wavelength λ 1 and speed of wave v. First data f 1 is shown in Figure and recorded in Table 2 as a sample.

Question: • The speed is different between Data Table 1 and 2, explain physics. The reason for this lies in the fact that the string under stimulation for table 1 experiences greater tension compared to the string employed for table 2. The velocity of the wave relies heavily on the tension within the string. Elevated tension results in a swifter wave speed. However, when linear mass density is increased, the wave speed diminishes. This occurs because