# Step 1: Explanation of Table Calculations ### **Table Calculations (Columns Explained):** 1. **Frequency [Hz]**: The frequency of the sound used in the experiment. 2. **n**: The harmonic number (1st, 3rd, 5th...). 3. **L (meters)**: The measured length of the air column where resonance occurs (from the experiment/video). 4. **Calculate (4L/n)**: This calculates four times the length divided by the harmonic number. 5. **Velocity (v = (4L/n) * frequency)**: This formula gives the velocity of sound for each measurement. #### **Explanation for Each Column:** - The formula comes from the resonance condition for a tube closed at one end: \( L = \frac{n\lambda}{4} \) where \( n \) is an odd integer. - Rearranged, \( \lambda = \frac{4L}{n} \). - Velocity, \( v = f\lambda = f \times \frac{4L}{n} \). **You will fill in the table for each frequency and harmonic using your measured values of \( L \) from the video.** --- # Step 2: Explanation of Analysis Questions ### **1. Possible Reasons for Percentage Error** - **Instrumental error** (imprecise measurement of L). - **Parallax error** (reading the ruler at an angle). - **Room temperature variation** (actual temperature might differ from 20°C). - **Humidity and air pressure** (not accounted for). - **Assumption of perfect resonance** (may not be exact). ### **2. Effect of Air Temperature on Speed of Sound** - **Higher temperature** → air molecules move faster → sound travels faster. - **Lower temperature** → molecules move slower → sound travels slower. - **Reason**: Speed of sound depends on the kinetic energy (temperature) of air molecules. ### **3. Fraction of a Wavelength for n = 3 Pattern** - For n = 3, \( L = \frac{3\lambda}{4} \). **So, the length is 3/4 of a wavelength.** ### **4. Why n = 3 at 256 Hz (or n = 5 at 512 Hz) Can't Be Found** - **Tube may be too short** to accommodate higher harmonics at low frequencies (wavelength too long). - **Physical limitation**: The required resonance length exceeds the possible tube length. --- ## **Final Answer** **Step 1:** - The table uses the formula \( v = (4L/n) \times \text{frequency} \) to find experimental sound velocities. - You fill in each row with your measured \( L \), calculate \( 4L/n \), then multiply by frequency for velocity. **Step 2:** 1. Possible errors: measurement, parallax, temperature, humidity, resonance. 2. Higher temperature increases speed; lower decreases it, due to molecular motion. 3. n = 3 pattern is 3/4 of a wavelength. 4. n = 3 at 256 Hz (or n = 5 at 512 Hz) can't be found if the tube can't fit that harmonic's length. --- **If you provide the measured values of L, I can help fill out the table and calculate the average velocity and % error!**