SP Unit 2.5
Practicals
Waves properties
SP Unit 2.5PracticalsWaves propertiesLearners should be able to demonstrate and apply their knowledge and understanding of: |
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| 1. | Determination of wavelength using Young’s Double Slits |
| 2. | Determination of wavelength using Diffraction Grating |
| 3. | Determination of the speed of sound using Stationary Waves |
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1. Determination of Wavelength Using Young’s Double Slit Experiment
- ⇒ Objective:
- Measure the wavelength of a monochromatic light source by analyzing the interference pattern produced by two closely spaced slits.
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⇒ Apparatus:
- – Coherent light source (e.g., laser)
- – Double slit plate with known slit separation (d)
- – White screen or photographic plate
- – Ruler or measuring tape
- – Optical bench
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⇒ Procedure:
- 1. Setup:
- – Mount the light source so that its beam is incident on the double-slit plate.
- – Place the screen at a known distance (L) from the slits.
- – Ensure the setup is stable and aligned so that the interference pattern is clear.
- Figure 1 Young’s Double slit experiment
- 2. Observation:
- – When light passes through the two slits, it produces an interference pattern of bright and dark fringes on the screen.
- – Measure the distance between several adjacent bright fringes (or dark fringes) to determine the fringe spacing ([math]\Delta x[/math]).
- 3. Calculation:
- – For small angles, the fringe separation is related to the wavelength (λ) by:
- [math]\Delta x = \frac{\lambda L}{d}[/math]
- – Rearranging to solve for λ:
- [math]\lambda = \frac{\Delta x \cdot L}{d}[/math]
- Using your measured values of Δx, d, and L, compute the wavelength.
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⇒ Points to Consider:
- Ensure that the distance L is large compared to d for small-angle approximations to be valid.
- Take multiple measurements of fringe spacing to improve accuracy.
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2. Determination of Wavelength Using a Diffraction Grating
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⇒ Objective:
- Determine the wavelength of light using a diffraction grating which produces multiple diffraction orders.
- Figure 2 Wavelength using a diffraction grating
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⇒ Apparatus:
- – Monochromatic light source (e.g., laser or filtered lamp)
- – Diffraction grating with a known number of lines per millimeter (or known grating spacing, d).
- – Rotating stage or goniometer to measure diffraction angles
- – Screen or detector
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⇒ Procedure:
- 1. Setup:
- – Shine the monochromatic light on the diffraction grating
- – The grating diffracts the light into several orders (bright spots) on either side of the central maximum.
- – Place a screen at a distance or use a goniometer to measure the angle θ for a given order m (typically m=1).
- 2. Measurement:
- – Measure the angle θ between the central maximum (zeroth order) and one of the diffracted maxima.
- 3. Calculation:
- – Use the grating equation:
- [math]d sinθ = mλ[/math]
- Where:
- – d is the grating spacing (the reciprocal of the number of lines per unit length)
- – m is the order of the maximum,
- – λ is the wavelength.
- Rearranging, solve for the wavelength:
- [math]\lambda = \frac{d \sin \theta}{m}[/math]
- – Insert the measured angle and known d to calculate λ.
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⇒ Points to Consider:
- Use the first order maximum (m=1) for ease of measurement.
- Ensure the grating is well aligned with the incident beam for accurate angle measurements.
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3. Determination of the Speed of Sound Using Stationary Waves
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⇒ Objective:
- Measure the speed of sound by creating and analyzing standing (stationary) waves in a resonant tube.
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⇒ Apparatus:
- – Resonance tube (open at one end and closed at the other, or both ends open)
- – Tuning forks of known frequency, or a signal generator with a speaker
- – Meter stick or measuring tape
- – Water bath (if using a variable-length tube submerged in water)
- – Microphone and oscilloscope or sound level meter (for precise detection of resonance)
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⇒ Procedure:
- 1. Setup:
- – Arrange the resonance tube vertically or horizontally. For a tube with one closed end and one open end, the resonant condition occurs when a node forms at the closed end and an antinode at the open end.
- – If using a water-filled tube, adjust the water level to change the effective length of the air column.
- 2. Generating Standing Waves:
- – Strike a tuning fork with a known frequency (f) and hold it near the open end of the tube, or drive a speaker with the signal generator at a fixed frequency.
- – Slowly adjust the length of the tube (or water level) until a strong resonance (maximum sound amplitude) is detected. The positions of resonant conditions can be identified by observing peaks in the sound amplitude (using an oscilloscope or sound level meter).
- Figure 3 Speed of sound using stationary wave
- 3. Determining Wavelength:
- – For a tube open at one end, the fundamental mode of resonance occurs when the length LLL of the air column is approximately:
- [math]L = \frac{λ}{4}[/math]
- – For higher modes, the relation is:
- [math]L = \frac{(2n – 1)\lambda}{4}, \quad n = 1, 2, 3, \ldots[/math]
- – Measure the length L corresponding to a resonance and calculate the wavelength:
- [math]L = \frac{4\lambda}{2n – 1}[/math]
- (Use n=1 for the fundamental frequency.)
- 4. Calculating the Speed of Sound:
- – The speed of sound v is related to the wavelength and frequency by:
- [math]v = fλ[/math]
- – Substitute the measured frequency and calculated wavelength to obtain v.
- ⇒ Points to Consider:
- The accuracy of the speed of sound measurement depends on precise determination of the resonant length and the frequency of the tuning fork.
- Temperature, humidity, and air pressure affect the speed of sound, so record environmental conditions if high precision is required.